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The CFA Program Exam Guides

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Level I Introduction: The four Cs

The simplest way to organize our study planning for the CFA Level I (known from now on as L1), is with a general guideline for the multiple-choice format which dominates the L1, and which we call the "four Cs" for: Concepts, Connections, Categories and Calculations.


L1 has an extensive focus on concepts and definitions, which is one reason the Investopedia dictionary is so valuable for CFA exam preparation.  AIMR calls these concepts and calculations "tools and inputs". (Inputs to what? Read on. Hint: valuation and portfolio models encountered in II and III).

Over of the L1 questions are concept-oriented, and a passing grade literally depends on having a deep rather than a good understanding of those concepts. The exam is especially designed to trap you with good, but not deep enough understanding, as youll see in following pages.

How can you determine a companys cash flow from operations?

Although the answer will likely be a group of calculations and numbers on the L1 exam, the key will be two concepts:

1. Understanding that cash flows are the net of cash in, minus (-) cash out, and...
2. "Accounting" entries and payments over time, via debt, with stock, long term, for depreciation etc. are excluded.

That means every group of answers, statements, accounting entries found in this type of question will often have the word "cash" specified either in the question or the supporting financial statement entriessaving precious time by allowing you to just key in a list on your 12C:

100 (Enter)

(Cash receipts from customers)

20 (-)

(Cash paid to vendors)

20 (-)

(Cash paid for expense reports)




(Remaining cash flow on 12C x-register/display)

This may seem obvious, but understanding how to quickly sift through statements and ignore non-cash items is a huge key to many questions on the L1 exam.  More on this below in the accounting alligators section...


Again, the Investopedia dictionary is outstanding for this category. Connections are like the old "fill in the blanks" questions from school, except that the fill-ins are choices given as A, B, C, or D or in item sets.

A majority of these take one of these four formats:





Partial definition

Rest of definition


Concept defined



Concept example

Application of example


Concept nuance

Competing refinements

Lets take a simple accounting principle encountered a lot on the Level I exam: inventory valuation.

A type one question would be:

Inventory valuation is based upon the flow of:
A. Cash
B. Prices
C. Goods
D. Costs

"A" is tempting because the term "cash" goes well with "flow," but is wrong. "B" and "D," like A, are about money, so if one were right or wrong, they all should be. By exclusion, C is correct and "finishes" the definition given in the question. (Note that item sets, some on the L1, very heavy in 2002 on the L2 and L3, get around this deficiency with multiple questions about the set-up and/or choices like "I and II but not III" where I is "A and B" etc). See the sister Series 7 study guide for numerous examples of item sets. An item set about the above might include "C and D" which together are the flow of COGS, more tempting than D alone...

A type two question would be:
Inventory valuation should take into account all BUT: (exclusion)

A. Goods flows
B. Order of receipt
C. Order of sale
D. Cash

A type three question would be:
Here is a list of goods and their values, what is the inventory valuation today via the FIFO method?

A type four question would be:
Inventory valuation focuses on the flow of goods, in particular, their:

A. Size
B. Type
C. Order
D. Value

Wow, is this a gimmee or what? D says "value" in a question about valuation! Who IS buried in Grants tomb? Actually, refining-connection definitions of concepts are often ALLIGATORS, filled with tempting alternatives; the exam is looking for "C" here. Of all four types, the refining-definition can get you into trouble the fastest!


Category questions on the Level I exam are again about definitions and concepts, and the application of these tools as inputs to valuation and later, portfolio analysis. Categories move deeper into the concepts to explore groups and movements within the definitions to test the depth of your understanding with even more tempting traps and trick alternatives.

Many of the economic questions are concept or category chains telling you that prices went up and asking you what then happens to wages or share prices. In between are chains of up/down/up/up/down motions of other factors like goods, money supply, unemployment, etc.


On the L1, a large number of calculations can be done by simply entering the question correctly into our 12C or BAII.  Numerous worked out examples directly from the CFA exams are available in the three books on and further examples follow below.

But, an important time saver is the fact that many of the quantitative questions on the L1 do NOT require full calculation, but a careful examination of the answers and partial calculations to quickly separate the two closest alternatives.

The trick is to read the question carefully then look at the RANGE of answers WELL BEFORE thinking of picking up the calculator. Try to see if you can answer the question with NO calculation first. Remember, the L1 is about concepts, and if you really understand the underlying principle, many answers that seem to require polynomial calculus will instead "jump off the page."

Time burner: if a question looks like it will take a LOT of calculation, like a yield interpolation with a call feature on a bond, or entries requiring base e and large chains of exponents, theres a 99% chance youre missing something in the question or answer grouping. Look again, there is usually an intuitive concept being tested, not your ability to raise a quadratic to various powers.

The effective annual yield for two investments with a 7% rate compounded 1,000 times a year vs. 10,000 times a year will be:

A. Infinitely different
B. Both about 7 1/4 %
C. Exponentially different
D. Both be 7% but differ greatly to the right of the (.07x) "x" decimal place

Do we really need to take our BAII or HP12C and add 1 to .07/1000 vs. .07/10,000, then raise each to the 1,000 and 10,000th power?

Not if we recognize the underlying concept (UC) behind the question, then look at the answers carefully!

The UC is: as compounding approaches infinite intervals, the yield approaches a single number with differences being in decimals farther and farther to the right as the interval approaches infinity, and thus less and less of a significant difference.

Thats why compounding can be considered infinite (only we call it "continuous") at the number that is being approached as nX to the n.  If you tried the calculation, you see that the number is about 7.25082 with differences being "way right" at the fourth or fifth decimal. Knowing the concept makes "B" obvious with no calculation at all, however, by the process of eliminating the other choices.

The reason UCs are so important on the L1 CFA exam is that the stated purpose of the tricks and traps in the exam is to lead you astray with "close, but no cigar" choices.

AIMR calls these "promising alternatives" and even (somewhat snidely) says: "Candidates will have no advantage in having the correct answer at their disposal..." (as the alternatives are so sneaky!). Heaven forbid we should know the right answer right away!  This does sound a little like the forces of good preparing dangerous traps for those evil enough to try to trick the tricksters, but what theyre getting at is they want to check to see if we get the UC, not just the technique, and TIME BURNERS are a great way to trap us if we dont.

Knowing these techniques is like pulling the curtain away from the wizard, and after a little practice we can easily recognize the "promising alternatives" for what they are: traps.

Look at the other choices above. "Infinite" is "promising" to those of us who remember that continuous compounding raises to a high power, "Exponential" is "promising" to those of us who think of interest in terms of exponents, and "differ to the right" traps those of us who dont understand how miniscule yield differences really get at higher compounding intervals (the UC). This is important to many questions on the L1, both the trapping strategy, and the example, as many yield questions have answers with large enough spreads to spot the right answer quickly.

A crusty, seasoned, old loan officer would look at this question and say, "Yep, about the same..."

Another version of these alligators is the "Would you rather have?" (WYRH) setup/question format, as in: WYRH 7% compounded monthly or 6.9% compounded daily? The UC is still "a horse apiece" but a bunch of exponents later shows 7% a bit better (by.09 if you want to try it). But the moral is: LOOK AT THE ANSWERS first to see if a WYRH is a gimmee or actually requires calculation. If all the other answers are far and one choice is quite close, go for it and save a bunch of time.

Bonds As Example Calculation Alligators

Sometimes UCs take the form of shortcuts:

If a bond pays 12% with a 10% par redemption at 10 years, whats the purchase price for a required yield of 10% compounded semiannually?

By pure luck: If the answers are
A. 1100
B. 1200
C. 1300
D. 1400

A good ballpark is 10% of $1,000 or A, but the exam isnt THAT friendly...

By complex math (with a little help from our 12C):

PV the payments and add that to the $1,000 discounted by 1.05 raised to the -20 power, or the -n, where n=coupons or 2*10=20 (remember semi)

Then, HP12C keystrokes: Clear finance registers, 20=n, 5=I (ALLIGATOR, huge one for Level 1: "i" is NOT 6 or 10 or 12! BUT you can be sure those will be some of the "promising" wrong answers!); pmt=60 (6% of 1,000 semiannually, THIS is where the 6% comes in, for the PMT key, not the I key), calculate (by hitting the PV key)= 747.73 (this will be an answer choice too, guaranteed, but its incomplete, because we have to ADD it to:

(HP strokes): 1.05, enter, x to y, 20, chs, y to the x gives about .38 (or times a thousand) 380 added to 747 or about 1127. Did you do the PV on the 12C and the addition on the BAII for speed? Cool IF you only use one for simple math AND never forget to clear the registers before a calculation that doesnt use an old answer!

By rule of thumb:

  • Add 1,000 plus (60-50) or 10
  • Use the 10 as PMT, then I=5, N=20, PV (calc)= 124.62
  • Simpler, the answer is pretty direct at 1,124.62.


  • 1,000 = FV, 20=N, 5=I, 60=PMT, calc PV=1,124.62 INSTANTLY
  • (We could go on with 10 more methods, but...

MORAL: There are often 5 or more ways to reach an answer for every calculation on the Level I, some really easy and some really involved. The 12C or BAII can save a lot of complex math and formulas/exponents you dont want to memorize anyway, but we still need to understand whats going on under the keys. Rules of thumb, the UC (underlying concepts) and CAREFUL reading of the answers (always remember the word "exam" comes from EXAMINATION: OF THE QUESTIONS AND THE ANSWERS, VERY CAREFULLY AND CLOSELY, AFTER TAKING A DEEP BREATH AND NOT RU.S.HING).

"But you said there are at least 10 ways and only showed 4..."

OK.  A $1,000 semi bond at 12 matures June 1 2012. On 2/3/02 the bond is quoted at 94-7/8, what is the YTM?

A. We could interpolate between 12% and 13% (more examples follow later), computing the market prices with a timeline diagram, creating an interpolation table, calculating 3 DCFs, 6 fractional follow ons, and arrive at the usual proportional equality that always follows an interpolation of x/1%=51/56 and get means/extremes of 12.9%, OR

B. Check the answers FIRST and notice that they are 12, 12.8, 13 and 13.3 (so?) So: many ARE this far apart on the actual exam! An ideal candidate for the method of averages: 21 coupons at $60 plus capital gains of 1,000-948.75 or 51.25, then use income/investment (the definition of a YIELD) such that (21(60)+51.25)/21 (parentheses needed for the BAII, not the 12C) gives 62.44 over 974.38 (948+1000)/2 for an "average guesstimate" of 6.41 (DONT forget to double it) or 12.82%: answer B.

6.41 will probably be one of the choices.

This shortcut takes about 4 minutes compared to 10 for a full interpolation. Is there an even faster method? (Hint: yes).

Why make a partial answer one of the choices? Think about it: how do exam writers come up with tempting "wrong" answers, anyway? For calculation alligators, the writers identify the most common:

  • Misunderstandings
  • Key errors
  • Partial answers
  • Selection criteria
  • Enticing similarities

In other words, they dont just pick the right answer and "hide" it between 3 random errors, but put it among very common and plausible "close" answers.  If they did the former, and we made a mistake, wed immediately see our answer wasnt one of the choices, and with nothing incorrect to "bite" on, would try again.

Every time you use a study guide and practice problems, LOOK AS CAREFULLY at your wrong answers and mistakes as your right ones! You are THEN looking at the multiple choice answer alternatives and learning to recognize BAIT as well as the right answers as you practice. In fact, a GREAT way to prepare for the Level I is to make up your own questions from the texts and study guides to see what "plausible" wrong answers look like, and sharpen your EYE for a great score on the actual exam because those phonies JUMP out at you, leaving the RIGHT ANSWER OBVIOU.S. in numerous cases.

We need to discount an investment for a period with a required return as part of an inflection point problem (for example, at what dollar return would you be indifferent between two investment choices?).

For the first step we need n, I, pmt and PV to get FV, for the second we need only PV, N and I. A very common error is to forget to clear the unnecessary value from the financial register. Checking the underlying logic of the question will help form an immediate "ballpark" for the answer range, and remembering to clear our registers to be sure just the needed problem parameters are there is crucial.

In these days of PCs, were not being taught to "visualize" whats in registers we cannot see, so it is more important than ever to remember to clear values not needed as their incorrect conclusion is very likely to be one of the choices - the 2001 and 2002 revamp of the CFA formats focused on this kind of thoroughness due to the switch away from essay toward item sets and students in the 2001 exams reported a surprising number of questions that came down to "two very close choices difficult to decide between". Forewarned is forearmed!

In many of our prep class seminars (schedule is on we will see a student have the correct answer written on a piece of paper right in front of them from a calculation step, then pick an enticing wrong answer because they were "tempted" to use the right answer incorrectly. This is what AIMR means when they say "even the right answer wont help you."

This is, in essence, getting $234 in a yield requirement question, then forgetting to add it back to the $1,000 bond par, or getting 6.2% on a semi and forgetting to double it. The "close" and partial answers are likely there in both the multiple choice and their more deadly cousins, the item sets.

Both the "i" key and the "n" key on both calculators (I/Y on the BAII is I on the 12C) wreak havoc on all three levels of the exams.  The creators delightfully exploit these common confusions by putting our mistakes in as one or more of the choices:

  • I=12% when it should be monthly (I/12 or 1%).
  • I=only half or of the required answer (return or discount factor, interest, yield, etc.) because the problem had quarterly or semi or monthly compounding/factoring etc. (and remember that coupon interest is used in the PMT calculation, NOT I for required return bond questions!).
  • N=120, not 10 for 10 year securities when I-monthly BUT N=10 when I=annual (in other words, dont forget to match your time period with your discount or interest, the MISMATCHES are guaranteed to be one or more of the false answers

Traps like this also are laid using phrases, definitions and concept, especially in the item sets, which is why using the Investopedia dictionary frequently during study is so important. "What is the gain?" and "What is the payout?" vs. "What is the value?" or "How much would you pay?" are subtle ways to confuse PV and FV in many questions. The exam writers spend beaucoup de time laying definitional subtleties in their enticing trap alternatives and knowing the meaning beneath the common English meaning of a term is often the difference between squeaking by and a top gun score with less stress and much more confidence.

Remember the UC: PV is the value today, and we will need MORE tomorrow to be equivalent or indecisive about what we get today. However, for bonds, do not assume the indecision point (PV) of a call or purchase price is always less than $1,000 (many students fall into this trap) using the logic that "today's value always has to be lower than tomorrows $1,000, because value and price are not the same and you cannot reverse DCV logic mathematically.  Just because you eventually redeem the bond for $1,000, INTEREST makes the TOTAL value of the bond in PRESENT (not nominal) dollars cross over 1,000 as the DCF of the required return in your "required price" decision analysis crosses the coupon. The easy way to remember this is to go in "clean" and not assume the answer range until you look at both the range in the exam answer choices and the question itself. 

The exam writers give you a subtle hint every time they increase the range of an answer set to include likely mistakes: by loosening the range, they also make the right answer stand out more if you DONT BITE on the bait, which saves precious time and a lot of calculation. In other words, knowing the subtleties of concept definitions is a KEY to a less stressful exam experience at all three levels.

Many answer choices on the Level I will include an answer like $747.73 from #2 in the previous example as bait in case you forget to include 1.05 to the -n power (and -n is -20 on a semi, not -10). This serves to trap the unwary but at the same time it is a choice easily ignored when you see that the answer is going to have to be over $1,000 by the question set-up itself, in which case the trappers have given you a CLUE as much as a TRAP.

There are numerous answers like 982.37 when the answer is 1137.16. With practice each of these becomes a time saver and something we just dont have to deal with. We dont have to get confused when our brain sees a bond quoted at 98 as part of the question and then is attracted to the 980 answer, keep that horse on the path!

In later questions and levels, the WACC and CAPM models clarify what a required return or yield is in terms of a risk-free vs. risky investment, or a whole portfolio of varied risks and returns.

For the Level I, we need to remember the concept of opportunity cost, as it is asked about directly as well as subtly in many questions and calculations: Delaying a payment we could get in todays dollars until tomorrow costs us a number of things:

  • We cant spend it today
  • Tomorrows dollar fluctuates but is always worth less adjusted for inflation
  • If we invested that dollar today, it would be worth itself PLU.S. what we made on the investment, minus what we lost to inflations, minus what we lost to taxes, (etc.). So statements like "todays dollar is worth more tomorrow" and "todays dollar is worth more today" are both true! This subtlety confuses a lot of us and is fertile ground for the test creators to lay traps.

There is a concept used in business practically every day called "coming back from where weve never been." This is used to discount simulated cost savings for costs we never would have incurred anyway, and is a reminder of the mistaken tendency of the mind to take simulations, dreams, visions, models as real.

The dollar you "could" have invested (the opportunity cost) and gotten returns/interest payments on isnt REALLY worth more in the future unless you actually completed the action. This also is an important concept in statistics and probability, which well encounter in later levels. The "i" and "n" of the level I used as a mathematical exercise becomes the valuation subtlety of some I questions and most II questions, and the "real world" portfolio is the heart of the III.

In that real world portfolio, todays dollars could have been invested in a portfolio that went down, not up. Getting and keeping a PV dollar vs. getting and investing a PV dollar is more complex than the PV number, and, as the saying goes: no one in the history of mankind has ever spent a FV dollar!

One question simply asks after an item set set-up if the nominal value of your bond at $1,000 is a loss in initial periods while at 95, from a portfolio rather than an accounting standpoint. This question is often mistaken to be about what we paid for the bond vs. where it's being quoted (a mistake many brilliant traders also make) when it is really getting at the 950 bucks ad a great gain compared to the equivalent stock in your portfolio that dropped to 300 - portfolios are always about CONTEXT, even in the L1 questions.

A small part of L1 and much of L2 bridges the gaps between NPV and context with a focus on statement analysis and valuation applications of the tools and valuation inputs seen in the L1 calculations.

L3 then expands the number and variety of contexts to global, market, economic, secular, firm, sector, etc.

Analysts cover securities, companies and sectors.  Technical, fundamental, networking and specialized skills are needed to be successful on both the buy and sell sides, whether your customer is the institutional investor or your own portfolio.

The technical skills covered on the LI exam are about security trending, market shapes, supply and demand and other basics and do not involve the more sophisticated statistical models and pattern recognition shapes of the L2 and especially the L3.  Fundamental skills are about accounting, ratios and statement analysis on the L1, so lets get to that!

Accounting Alligators on the Level I Exam

Although the L1 has a number of basic accounting "input" questions, the majority of both multiple choice and calculation/item set questions fall into the discipline termed financial accounting. This is because the concepts and calculations of Level I are the primary tools and inputs of statement analysis as well as valuation.

An excellent study aid tool for preparing for these types of questions is called a "Key Terms Chart" which lists terms and their common associations/sister terms. Here is a brief example for L1 exam questions. A good exercise is to create your own with your other printed study aids while checking definitions on Investopedia:

Key Terms Chart Example:



Accumulated earnings

Retained earnings

Assets held < a year

Current assets

Who makes Fin acctg. rules?


Revenue > expense

Profit OR "Net Income" on the exam

Cash in: increases--

Assets AND Capital

Assets = Liabilities PLU.S.--

Equity or Capital

Resources used to make goods

Expenses (NOT raw materials here!)

Professional fees

Capital NOT Asset

Heres a favorite accounting alligator in at least half a dozen questions in different forms:

When you sell goods on account, your assets are:
A. Increased
B. Decreased
C. Stay the same
D. Cant determine

As stated, the answer is D with a "tilt" towards A (this is one of those infamous questions ubiquitous on the exams that have two very close alternatives).  AR goes up, inventory goes down, with a net increase in Assets (and capital) (A) AS LONG AS you sold above your cost! (This assumes you know your costs? Amazon didnt for quite some time!). With no reference to revenue (Q x P) compared to cost of goods, the answer cannot be determined.  Numerous variations include adding a price reference as well as asking about capital vs. assets (both go up here, see following paragraph, a common alligator/mistake is to bite on one or the other staying the same).

In general, when we invest cash, pay expenses, receive cash, or suffer losses, assets and capital move together (up and down). They move differently, however, when we buy on credit or account because the liability and asset accounts are increased while the capital account stays the same. Remember the A = L + C equation and do a few T-accounts when the exam has a complex statement or a large list of entries (some students remember A=L PLUC to avoid A + L =C error).

Remember that the exam writers know that many students confuse assets and capital and this will be a no-brainer.

Another favorite alligator/trap is to list a bunch of transactions or show a statement and ask for a net income/profit calculation while throwing in a capital item or three that look like revenue or expenses like:

A. Salaries
B. Owners cash withdrawal
C. Bought equipment
D. Rent

In which case only A, B and the depreciation portion of C count as expenses, while the equipment and owners withdrawal do not affect the analysis. Other names for Capital include owners equity, shareholders equity, capital stock, stockholders equity, Common plus preferred, etc.dont let these entries confuse you on the revenue, asset or expense side when encountered.

A "recording" alligator relates to sales contracts and legal agreements.  Almost all financial events ARE recordable, but the Level I CFA exam will often toss in a ringer and hope you bite on an "All of the above" like:

Which are recordable events?
A. A legally executed agreement for a future loan
B. Revenue received
C. A binding supply contract
D. All of the above

It is tough for many of us to pick B and leave A behind, but thats what the exam is looking for here. Many MANY close encounters like this one are on the 2002 exam. A is marginal (come on, wed record it, wouldnt we?) BUT C makes B the only possible answer (we cant choose two and C makes both C and D wrong, and the exam expressly states it wants the BEST (not the correct) answer.  In the CONTEXT, B has to be right. Please THINK ABOUT THIS SITUATION CAREFULLY as it appears throughout the exam!

Cash vs. accrual is a favorite field for numerous tricks and traps, both in multiple choice and statement questions, as well as some ratio traps.

In practice, the thing that moves a small service company or a professional corporation from cash to accrual accounting is inventory.  Very few companies are on a cash basis beyond the mom and pop or lawyers and doctors (and a few web sites) once inventory becomes involved.

Terms key to accrual accounting all revolve around period-matching of entries: using GAAP to book revenue when earned and expenses when incurred and services when rendered. (Remember these important distinctions and youll defuse a lot of exam mines). These distinctions separate P and L (Income Statement) transaction recognition from actual cash flows.

Wages are also accrued between months when a pay period is after the month in which the days were worked, to properly book that months actual wage expense even though the cash doesnt leave your checkbook until the next month. Its only a little sin if you skip this in a small business without inventory, however, but dont miss the fact that it is done.

AR also is a fertile field for exam traps about accruals as well as AP (not to mention the success of your real-life career). Some companies book huge accruals at the end of the year for "expected invoices" coming from foreign subsidiaries, then reverse them out the next year. Why? To avoid taxes (or rather move the tax burden between years - legal if you have good documentation of the expenses) AND to move performance between quarters.

Say what? Yes, if you have a great quarter and want to "spread the wealth" over the next quarter to better meet analysts expectations, accruals are one somewhat shady way to do it (shady if the next quarter is weaker than it looks and analysts miss a signal).

Another trick used by companies (which good analysts know about), to spread performance between quarters, is manipulating reserves. If they fluctuate a lot when bad debt is about the same, suspect a little hanky-panky going on.

The practice of spreading around earnings is commonly known as "Cookie Jar Accounting".

More sophisticated tricks include M and A, combining books in a pooling, changing accounting periods, restating a past period (which changes year to year comparisons) and lots more. A golden rule is to look at those footnotes very carefully, on the LIII exam, as well as in real life! (OK, ok, so the test writers arent all bad for being so devious, real life is devious sometimes too).

Dates have been called "the bane of the Level I exam" by some students

Dates come in as alligators for numerous problems, and the HP12C and BAII complicate matters by using straight line counters without inter-period flexibility (yes, you have to count the days in the months on these problems without Excel to help you).  Everything from bonds to depreciation to revenue recognition have date alligators thrown in.

A special caution is in order about using either calculator to solve for "n" - N is only valid for integers, when you get "parts" of a period the "decimals" are meaningless (not quite, they are actually "actuarial estimate partial derivative proxy indexes", but think of them as meaningless). This also goes for the YTM key (basis is actual-days as is the price). In other words, dont solve for an N using your 12C and then think that 2.33 means February the 9th, IT DOESNT! (Dont even ask what it really means, like making sausage or creating a business plan, its something you dont want to watch until its done).

So, if you read the programming appendices, does that mean you can avoid the N problems in YTM exam questions by simply programming in a few unconventional-period YTMs like early calls?  Theoretically, no. When you walk into the exam, the proctor/manager is supposed to watch you clear all pre-existing registers and see zero on the displays. In practice, only half or less do this (until AIMR reads this) and even then a lot dont understand that on the 12C, hitting clear-all does NOT clear programs until you switch to (f P/R) program mode THEN hit clear. (This is even true if you actually hit f/CLEAR/PRGM in run mode, try it! Its a safety feature of the 12C so you dont blow away a lot of work unintentionally).

We obviously dont advise cheating in any way, but if you are quick on the program trigger there are some tricks you can quickly re-enter even after clearing legitimately. It also is legitimate to "dump" a few near term memory items onto paper quickly as soon as youre seated (but be sure the proctor sees you, you are not allowed to bring your own scratch paper anyway, but it helps if you let them know what youre doing). Why would anyone do this? Some formulas are just too complex to worry about getting exactly right through many hours of sitting!  And in real life its sadly doubtful that youll ever raise anything to a power again anyway with the tools available today, including your 12C or BAII!

From a depreciation date standpoint, a very helpful memory key is to think of any date intervals as their corresponding fractions (of a year).

If a problem asks, for example, for a depreciation entry on a $12,000 truck purchased 2/1/xx and booked 12/31/xx 5 year straight line, think of the period as 11/12 of a year.

Then, the $2,400 (12K/5) is multiplied by 11/12 to get the $2,200 entry answer for the year end. This will help you stop stressing every time you see a date and think of it as a time-burner.

In general, the exam writers know they need to stick with integers and solvable IRRs rather than "actuarial Ns" and undefined polynomial IRRs but you need to understand WHY for the higher exam levels.

In theory, it is impossible to determine a "correct" IRR which is why finance folks call them "undefined" for some problems. Mathematically, it is not that an IRR doesnt exist, its that no "Quadratic formula" exists for the higher level polynomials so calculators and computers iterate around a guess. In fact, in a polynomial equation, more than one power means a number of roots are all correct (we know that 4 = N squared has two equally right answers, 2 and -2) so the problem has a number of potential "impossible" IRRs that are simultaneously correct mathematically!  Good calculators take close iterative guesses and ignore results that look like 1430% but many people scratch their heads with a result like this if it is displayed on a spreadsheet and dont realize that its "correct" for one of the roots! Or, maybe youre having a REALLY good year... :)

This "polynomial problem" doesnt apply only to IRRs for investments or asset decisions/valuation decisions but any yield that takes the form of a power/root equation. Solving for a callable bond yield X with semi coupons at 10% and a quote of Z can be done by interpolation, but the initial set up is an algebraic polynomial such that 10Z = callable par + (N-Callable par I) pvd to an exponent of 2C where C=callable years end. These equations lie beneath the usual set up of a ratio between (say) 10 and 11% so the differences between the bond prices and the Xs are a proportion like X/1% = 50/70 (the 1% being the difference between 10 and 11), and then solve for X. BUT, how did you get the 10 and 11 and their corresponding values?

Trial and Error!  Thats right, you run TVMs at various % levels with an educated guess near the coupon rate to get started.  Even then, the interpolated answer (actually a quantity indexed to fall between 10 and 11) is an approximation, but close enough to one of the exam answers to separate the choices by at least the 10s decimal place (no deeper separation is required due to time constraints on the exam). So once you have a guess to the right of A.B with a good proxy for B, stop and choose (or better, youll already suspect answer "C" and just CONFIRM your suspicion quickly without a lot of sweat or stress. Knowing the method of averages demonstrated earlier is a POWERFUL TOOL for nailing many YTM problems, as is practicing the YTM function on your 12 C (the BA II has no YTM key, you have to press (2nd) (9) (which is BOND) then go through the menu from SDT to RDT and RV plus ACT and then PRI. Under PRI, the DOWN ARROW KEY will bring up YLD for yield (you have to ender PRI, enter, up arrow, YLD, CPT (compute) for the exact BAII keystrokes).

The BAII isnt as complicated as it sounds, it just has a bond menu instead of the bond keys below n on the 12C. The 12C does have options for straight line vs. other periods but was manufactured (and not updated) before ACRS was invented, visit the programming section in to handle anything but 100 par value, semi, and actual vanilla bonds with the YTM and PRICE keys. These tricks include fooling the calculator into accepting unconventional bonds while still taking advantage of its functions (as in using 100/Par * coupon quote as the actual coupon).

One trick on the "multiple IRR" problem (uneven cash flow in and out events) with the 12C also explained in the manual above in more detail:

If you know the risk and risk free rates, you can use the 12Cs "modified IRR (or MIRR) function to get close enough to an exam answer to be right.

More accounting: These are potential legitimate write-off processes:
I. AR aging wall
II. % of sales allowance
III. % of credit sales
IV. Point actually worthless

Which are NOT legitimate under GAAP as entries?
A. I and II
B. III and IV
C. I only
D. III only

These item sets are familiar to Series 7 candidates but new to CFA candidates. The whole point of these and other types of item sets (master description, question banks follow) are to lay even more subtle traps for the test-taker with VERY close but slightly flawed alternatives.

I II and IV are all legitimate bad debt write off strategies. III is not, as credit sales are real until they become worthless, so the exam is looking for D. Note that III is also redundant: a credit sale could be written off with ANY of the I, II or III processessubtle, but demonstrating the need for care whenever we encounter any version of the item set format, whether essay, written descriptions, or complex multiple choices that inter-relate.

Also, with any type of "scenario" (story) question set-up, a number of questions usually follow the situational description, which (for example) on the Level I can be an ethics situation, II a companys financial situation, III a portfolio scenario, etc.


Ratios are the "bridge" between statement analysis in financial accounting inputs and statement analysis for valuation, so are very important for both levels I and II.

On the L1, statements are given and ratios asked for to test our knowledge of the underlying entry inputs (to the ratios themselves) more than for valuation or interpretation (say, of a business weakness indicator ratio as will be found on the L2).

For the L1, it is an excellent study strategy to create and memorize a chart of what statement entries go upstairs and downstairs in each ratio.  Here is the Investopedia start at your own chart:

The Quick Reference Ratio Guide:


Upstairs (Numerator)

Downstairs (Denom)

Operating leverage

Sales - variable expses

Sales - Fixed expenses

Asset turns


Total assets

Cash turns



Capital sales

Shareholder equity


Fixed asset to sales


Fixed assets (GATOR!)


Current assets

Current liabilities



Current liabilities


Cash + Mktable Secur.

Current liabilities

AR turns

Total credit sales

AR balance


Net inc-pref dividends

Issued + outstdg shares


Mkt price/share


Cap Rate


Mkt price/share

Book value

Shareholders Equity

Common iss & outstdg


Ops income

Interest expense

Debt coverage

Pretax earnings

Int+debt repay/1-T

Net income to equity






Sales per FTE


Total FTEs

Working capital




Net Income


Capital employed (CE)



ROR on capital




Fixed expenses

1-(var exp/sales)

Sales needed for "x" OI

Fixed exp + OI

Complement of 1-(var exp/sales)*


*Computing the Complement of a Normalized Spanning Interval

Given a normalized spanning intervals , its complement is a set of normalized spanning intervals whose extension is the complement of the extension of . One can compute as follows:

This is the method to compute the complement of an interval for a normalized span.

A complement is also the set non-A for every set A in set theory. (Important in mathematical economics because the complement of a complement is the original set).

For the purposes of the Level I exam, when the question asks you to compute the sales necessary to reach a certain level of Operating Income, they want you to take the breakeven denominator in the Investopedia chart entry and subtract it from 1. (The tax rate 1-T is a complement).

In portfolio theory, the complement of a mathematically programmed selection engine is an m x n matrix such that Y:YA=0 and the program steps then select the complement.

For mathematical programming in portfolio theory and in econometrics, a complement refers to dual prices in a linear program (a subset of mathematical programming) in which "dual price" means any dual variables with a primal constraint.

As you can see, mathematically, complement is a key concept throughout both basic and upper levels of analysis. Of course most dictionaries will only give "complement" as the old A + B = 90 degrees for complementary angles, but the original Latin meaning of "complement" was to "complete" so all the 1-Xs found in accounting and finance fall under this rubric. Do NOT confuse the concept with reciprocals!

This chart is just a start, there are obviously infinite ratios possible. At Level I, we need to be able to look at a financial statement and decide which entries to use and which to leave behind in coming up with the ratio. 

Many alligators and traps relate to:

  • Are "Sales" before or after returns and allowances? (usually after, but not always!)
  • Is "Income" before or after interest/taxes etc. (see our Series 7 guide for a thorough discussion of EBIT vs. EBITDA etc.). For CFAs, some ratios have two versions, one more conservative than the other, in evaluating how a company CFO reports numbers.
  • When the numerator of a ratio is bigger than the denominator, the result becomes a "multiple" rather than a percent.  Since all ratios really index one measure to another, for a P/E of 10/1 or 10 to 1 (PPS of $10, EPS of a buck) we say the "price is 10 times earnings" or just "ABCD is at 10 times." Is a high P/E good? (Several questions on all three exams). It can mean investors expect a lot of the denominator in the future, or it can mean the price has gotten way ahead of earnings. Analysts say a company with zero earnings has "an infinite P/E", mathematicians call division by zero "undefined."

Caution:  Several questions asking us to judge a ratio as good or bad have the answer "cannot be determined" if the ratio is RELATIVE rather than ABSOLUTE.  Relative ratios are very industry and even company type specific, absolute ratios (like will our cash cover this months fixed expenses?) cross all industries.

How can ratios be very relative even with similar company sectors? A pharmacy selling low margin oral pharmaceuticals might have a Days Sales Outstanding (DSO) of 2 days and be "terrible" because the rest of the industry processes ARs electronically in seconds.  Another pharmacy down the block selling expensive, high-margin biotech injectables to the home care market might have a DSO of 60 days and be "wonderful" because the rest of the industry with those product types collects in 90 plus via a snail-like claim-by-claim process with HMO case managers.

AIMR covers all nations and all regulatory bodies, so do not assume the exams think you do or do not know a particular industrys standards in this kind of detail. The data will be given (or buried) in the question set-up. You will, however, especially on the II and III, be expected to understand sector differences of "good and bad" where heavy-asset businesses like utilities are supposed to be more leveraged than a comparable-size services business. Especially, for many questions you need to understand the differences between a company with a heavy debt load thats common for the sector vs. a company thats in trouble.

In the Level II material (even Level I candidates should take a peek) ratios are looked at in more detail from the analytical viewpoint as valuation inputs: WHAT do they mean and WHY do we care about them?

At more advanced levels, analysts (and you on the Level III) create and adjust their own ratios and set trends.  We might look at an individual product overhead expense in a company compared to total overhead, then analyze how well company A can amortize new product R and D expenses across their installed base which is 20% the size of competitor-company Bs installed base.

In a Level III essay, we might even invent a ratio never heard of before, by researching a technology companys patent portfolio and pipeline and comparing the firms "expiration to new filings" ratio to the industry and closest competitors.


Like many of the multiple choice and item set questions on the CFA exams, Economics breaks down into a few clear subdivisions such as:

  • Basics
  • Concepts and definitions
  • Underlying concepts
  • Calculations
  • International
  • Frequent/typical alligators

These are still in the general level I context of the four Cs (Concepts, Connections, Categories and Calculations) and is a powerful friend at each of these stages.

There is an obvious link between economics, finance and statistics in the discipline known as econometrics. More on this follows in the statistics section, but in general, economics calculations involve things like interpreting demand curves, pattern recognition in consumer and other indicator indexes, profit maximization curves, etc.  Econometrics then focuses on regressions, mathematical programming statistics, and deep pattern recognition hypotheses.

- a secret economic weapon

The above links give one of the least known "secret weapons" in understanding economics mathematics at a truly intuitive level, and "A-plus" scoring all three levels of the CFA in economics. The secret weapon is a software program known as Mathcad, which is published by Mathsoft, Inc. (  Mathcad converts mathematical formulas (including very complex ones) into "cad" (computer-assisted design) pictures so a student or teacher is able to visualize what the formula "looks" like in 3 dimensions. (Actually the formula symbolizes something in a real or imagined world, so its also the other way around).

A number of sites, publishers and courses offer Mathcad economic resources for hundreds or thousands of dollars to help you study and understand the underlying math you need to do well on the CFA in economics. Professor Andreas Thiemer has kindly created and offered free downloads on his site above of the same idea: visualizing economic models and mathematics in 3D. This is well worth exploring if you have any hesitation in this important area:

If you are a total math-wonk and want to blow your mind with visualizations of every type of financial mathematics, calculus, etc., go to the "World Mathcad" resource site at:

But BEWARE, this stuff is addictive if youre into math (and who on a CFA trackisnt?).


Like many mathematical disciplines, economics has a rich set of formulas, concepts, jargon and favorite buzz-words.  These are, in turn, supported by underlying principles and connections.  The deeper the understanding of this foundation, the faster we can move through the Level I economic questions, such as:

In Economics, "Ceteris Paribus" means:
A. Where Y=Ax1+Bx2+CX3+Nxn + e, B and C (etc.) are held constant
B. Every economic force has an opposite parity effect
C. "Other things must be equal," : If a demand function B has a price domain C, a domain f(c) must also exist.
D. Efficient markets assume certain and equal information flows

The answer choices here each have "bait" if you are not entirely certain of the Ceteris Paribus concept, but remember pieces of it or try to "puzzle it out" (there are definitely strategies for puzzling out item sets as well, but they are not intuitive).

A. Looks "technical" but could be a ruse.
B. Is tempting because parity reminds the brain of paribus
C. Kind of sounds like it might be what the Latin means
D. Ceteris looks like "certain" and I think paribus is "equal?"

See how the exam seeds the questions with close alternatives? They even get closer in item sets and with formula set ups. C is pretty nasty, as the Latin underpinning is very close to the "other equal" statement, except that idiomatically its "all things being equal" or precisely "other things being (held) equal."  The exam is looking for A even though other alternatives could be close (or even true) such as D, but not relevant to the question. An item set might give I. A and B  and II. B only as alternatives, greatly increasing the risk of biting on D.

Ceteris Paribus, mathematically and theory-wise relates to holding independent variables constant in an economic model such as the regression in A, but the point is that close understanding is not the same as deep understanding and AIMR exploits that difference to the extreme on all three levels of examination. Candidates get in trouble very quickly by moving too fast with an answer based even on a pretty good understanding as the exam writers use more subtlety, especially since the changes in 2001, than many other formats we may have become familiar with in our formal educations.

An economy is able to expand the output of good A in a full-employment economy without decreasing the output of good B. This situation is typical of:

A. Elasticity of supply
B. An inefficient production frontier
C. Economic growth
D. Inward shift of the Production Possibility Frontier (PPF)

This question is typical of a lot of the Level I exams "this goes up, what then goes down?" items in Economics, but again is strongly dependent upon a deep understanding of a concept and its elements.

As usual for all the CFA exams the choices each have a very tempting element:
A: Ability to move seems "elastic" and goods output sounds a lot like supply?
B:  Seems like there IS room in this economy?
C:  Definitely sounds like "room to grow?"
D:  Does seem like some curve has, or is about to have, room somewhere and this answer has one of those darn abbreviations which can make an answer enticing but wrong or just be a give away they want you to miss by over-thinking?

D is closest, with the "trivial" exception of the word "inward," the PPF is moving outward in this set-up; C is what the exam is looking for here.

The paradox of thrift in Keynesian economics states that:
A. Increases in consumers desire to save does not affect the economys savings level
B. Greater efficiencies in the economy produce less economic growth
C. The government spending wisely does not decrease taxation
D. Less consumption actually harms the economy

Here, the exam writers assume were not totally clear on this concept of equilibrium output and give us three outstanding pieces of tempting bait - all three completely unproven like many economic theories, yet very logically related to the concepts of paradox and thrift in case we try to determine an answer through logic instead of "specialized understanding."

In fact, the amazing thing about this sequence of answers is that they seem less and less true as you go D-C-B-A, when, in fact, they become less and less true as you go A-B-C-D, with A being what the exam is looking for.

Moral: Even a slight correct association with an economic principle (here: thrift/savings) is better than trying to use logic because of all the special meanings within economic theory. If we can only remember that tiny association within the paradox (thrift/savings), wed get it right quickly and not even be tempted to over-think or bite on the other bait.

Which causal chain is typical of capital deepening?

A. Capital needed - greater labor supply - capital/labor ratio increases
B. Capital/labor ratio decreases - labor productivity increases - per capita output increases - higher standard of living
C. Capital increases - capacity increases - labor demand increases - employment increases - consumer spending increases - economy grows
D. Capital/labor ratio increases - labor productivity increases - per capita output increases - higher standard of living

The whole set-up of these choices is tempting - almost immediately we suspect that it will be a competition between D and B because they are so close, but is it really?

There is a subtle distinction in economics between deepening and widening in the economy and this is typical of the exams "chain" questions about what goes up and down as other variables move. C is correct, but can also apply to widening. D is the best answer, B is close but a trap, A is a trap.

These are all determinants of income:
I. Wages
II. Interests
III. Rents
IV. Profits

Which determine the inequality of personal income distribution?
A. I only
B. All four
C. I, II and III
D. I and II only

90% of our online and classroom practice test students pick A or C. Why? Perhaps because the correct answer (B) seems too free of trickery! Moral: sometimes thinking too deeply gets us in trouble. Moderation helps balance every question on every exam: not too cursory or too deep for question analysis is the right approach. Think of the three bears, too big, too small, just right. If your gut tells you something is too easy or on the other hand youre working too hard, you are probably about to choose a wrong answer. Staying relaxed and confident relieves enormous stress. If too many people trip over a question, it wont survive on the exam for long, as AIMR wants you to trip, but not fall.

Statistics and Econometrics

These are frequency statistics:
1. Range
2. Skew
3. Median
4. Variance
5. Standard Deviation

Which do not measure dispersion?
A. 4 and 5
B. 2 and 3
C. 1,2 and 3
D. 3 only

60% of students pick C. The answer is B (range is the ringer here). Range is a crude evolutionary step toward 4 and 5, except in Q/C where it is of some value).

Both the 12C and the BAII (manual included with purchase plus many others available), have outstanding statistics capabilities and they will get a workout on all three levels.  We need to be able to:

  • Group data points
  • Analyze variance and calculate standard deviations
  • Test hypotheses and understand type I vs. II errors
  • Analyze given regression statistics. (Both calculators perform regressions although you must use the programming mode (P/R) to nudge the 12C into cooperating).
  • In general it is not as important to have the "mechanics" of regression down as to know the differences between ANOVA, r-squared, ts and what various coefficients and goodness of fit indicators really mean (or more importantly, dont mean)

Heres a table of the most frequent "trip terms" that trip candidates up on the LI and LII:

Trip Term

Trip Defense


One variable is the expression of the other


The error variance is not constant for all X values


Error term in one time period is correlated with another time period

Variable error

Measurement errors in regression variables

Error types

I and II in hypotheses refer to false positives vs. false negatives in trying to separate signal from noise

Structural equations

Behavior variables (of consumers, producers, other acting agents)


Descriptive of a population (Dont confuse with regression parameters of the same name from the concept)


Descriptive of a sample (not "a chance number")


Relates parameters to statistics

Efficient estimator

Like an OLS, a process with the smallest variance

Dont bite on "getting an answer the fastest" etc.

Consistent estimator

As the sample approaches infinity, the distribution collapses neatly on the true parameter. (Its "asymptotically unbiased" which is a fancy way of saying it doesnt lean and fall in the wrong place)!


The one and only, take a bow. From 1 to +1 in range, shows the proportion of Ys variation explained by your regression on X. NOT as important as what it doesnt show: Causality or dependence. Many traps here.


OLS counterpart for simultaneous equation models, used when Ordinary Least Squares has too high a variance


The sum of AX+BX+CX (etc) where A+B+C=100%

Important in portfolio theory, moving weighted averages, and a valuation model well explore in Level II.



Level II Introduction:

In this level, we will focus on valuation of firms and how that relates to valuation of securities. Since bonds are covered extensively in the Series 7 exam guide, we will focus more closely here on the firm and its securities.

Some goodies: we will take an initial look at a next level of ratios, tie them together with several models, and provide a proprietary valuation model you can load on your own PC to test various levels of risk and return.

In Level III, which focuses on portfolio management, there are additional diagrams and models of ratios at an even higher and more integrated level than presented here or in Level I; it is worth the time to visit those for a full understanding of how it all ties together.

Also notable is the clinic on this site on Ratio Analysis in Featured Tutorials at:

Speaking of ratios, the "DuPont Model" (more on this here and in the exhibits in Level III) is still heavily featured in the CFA Level I and II exams and in some problems and questions on the level III.

In its simplest form, a firm has 4 primary activities:

1. Converts inputs (labor and materials) into outputs, with a goal of market share leadership, or monopoly control, where protection of that advantage is possible.
2. Attempts to beat the risk-adjusted cost of capital (known as "k" or "required return).
3. Receives funds from customers and investors and attempts to achieve the highest return on equity possible
4. Leverages assets, talent, and debt to multiply ROE and achieve "abnormal" (excess) earnings over the required return rate

These activities create flows of numerous quantities including cash, assets, customer opinions, goods and services.


Also in its most basic form, Valuation means the total value of the firm, or the price of its ownership units (shares) times the quantity of such units.  Valuation in a cash flow sense means the present value of the flows back to the investor (dividends) or fueling growth (retained earnings) minus the cost of the investment, in todays currency.

The hypothesized per-unit value might be more or less than:

  • The current stock price
  • What an investor is willing to pay
  • The value in the opinion of other interested parties, including potential acquirers of the firm

There are numerous methods for determining a firms value, including:

  • Add debt and investment and divide it into all shares fully diluted
  • Multiply revenue by a factor (from industry or underlying math as well see below)
  • Multiply earnings by a factor
  • Divide dividends by growth minus the required return
  • Multiply P/E by earnings per share
  • PV each expected revenue stream and add them together, adjusted for risk and the cost of capital
  • Value assets and leave liabilities behind
  • Correlate a probability table or model comparing the firms risk and return to other investments and their value

With assets, the cost of funds, and "abnormal" earnings being such an important part of valuation, it is no wonder that the CFA Level II exam spends numerous questions on these ratio areas.

Please look for a moment at the following "Ratio Web" diagram:

This basic "firm valuation" ratio web summarizes the DuPont ratio flows as well as more current models such as CFROE and EVA. Market share drives both price and volume, which drive margin along with cost of goods sold to produce a Return on Sales. Assets are needed and used to achieve and maintain market share, and these plus the return on sales "engine" drive operating leverage or asset turns.  Debt is needed to maintain share and these long and short term funds both pay for assets and share gain as well as creating the other "feeder" ratio into return on equity (ROE): LEV, or financial leverage.  All these produce the "excess" or abnormal earnings (defined as earnings above WACC or the required return or the risk adjusted cost of capital, which in turn drives growth, P/E and ROE, the key inputs to any valuation model.

As seen in the classifications of the Investopedia tutorial, ratio classes form into categories called "liquidity, solvency, efficiency, return..." etc. But for valuation purposes, which is the focus of the CFA level II exam and much of the Level III, we move beyond the "run the firm" and tools/inputs value of ratios to the motion of the numbers together to produce a valuable entity in the firm being analyzed.  Analysts drill-down on these ratios to the underlying entries in the financial statements to find business weakness indicators and evidence of under or over-valuation as seen in the price of the firms equity.

Specifically, here are example drill-downs that appear frequently on CFA exam questions:

  • Asset drill-down includes items like the quality of receivables, level and market-ability of inventories, durability of patents and contracts, age and condition of plant and equipment, quality of management, etc.
  • Revenue drill-down includes sustainability of sources, growth prospects, price erosion, market size and share assumptions, etc.
  • Profit drill-down includes FIRST AND FOREMOST whether the firms "excess profits" (or "abnormal earnings") are beating the risk-adjusted cost of capital! In detail it also includes cost analysis, margin analysis and sensitivity to market conditions and economic/industry changes and evolution, stage of company development, etc.
  • Strategic analysis includes examination of risks and SWOT (strengths, weaknesses, opportunities and threats), as well as competition and market strategy for sustainable earnings growth.
  • Business financial health includes many of the fundamental analysis points made in the Investopedia Ratio Tutorial, and the relationship of the elements in the "Ratio web" diagram above. These funds flows, and the ratio relationships in the web are the basis of the DuPont model and many questions on Level II relating a group of statement inputs to ratio relationships and motion.

These elements are a piece of valuation, but when the LII and LIII CFA exams speak of valuation, only one piece of the analysis applies to firm fundamentals. The other major element is equity analysis with a subset of technical analysis.

The Equity Element in Valuation

The following are additional elements of fundamental analysis that also apply to equity analysis:

  • Financial statement analysis with a focus on over and under valuation
  • Statistical weightings (see model example in following pages)
  • Return on capital
  • Growth (Sustainable growth= ROE * the earnings retention rate. This is a key to value compared to required return - as in D/(g-k) etc - as well as one of the most important connections between ROE and P/E. When you have an accurate P/E, one huge piece of valuation clears up)
  • Competition
  • Sustainable earnings over the required return rate (remember this one!)
  • Industry environments
  • Erosion of position and renewal
  • Predictability, accuracy, sustainability, time from of financial and economic information
  • ROE, EVA, WACC and firm value via DCF of returns via cash flows
  • P/BV (price to book value) and abnormal future earnings horizon
  • The venerable P/E and earnings growth over long horizons

Remember that excess or "abnormal" earnings are just earnings above the firms risk adjusted WACC - weighted average cost of capital - from analysis and the CAPM or capital asset pricing model.

Can a large, profitable firm continue to grow P/E indefinitely?

Answer: P/E as a function of growth and the expected and present values of present and future abnormal earnings reaches a theoretical limit of 1/k where k is the firms risk adjusted cost of capital.  The inverse nature of any ratio means a decimal in the denominator becomes a "multiplier" such that 1/.05, 1/.10, 1/.20 produces P/E walls of 20,10,5, etc.  As the cost of capital goes up, both real and potential P/E go down.

For smaller growth companies, the expectation is that P/E will "break through" the wall as abnormal earnings exceed the required return rate.

Since large mature firms have little or no abnormal future earnings, the roundabout answer to the question is "usually, no." These valuation topics augment the traditional economic ratio discussion where leverage (both financial and operating) "magnify" profits above break even between the variable cost line and revenue per unit (known as "contribution margin").

More fundamental inputs to valuation

In Dupont and other traditional analyses "ROE is king," and for good reason.  In the diagram, you can see it is at the top of the "Ratio food chain" and drives valuation directly as analysts create connections to P/BV and P/E, examine beta (risk) and create a line below which the firm is undervalued and above which the firm is overvalued.

The Level I guide gave a table of ratio numerators and denominator components that connect back to financial statements.  At level II, those analyses translate into valuation, and then portfolio analysis and management at Level III.  Study this chart with the movement of numerator (often price) and denominator (often return) in mind to get a feel for the relative motion of the numbers beneath the financial statements:



Overall ratio value


Stays same


Stays same




Stays same


Stays same



Increases more



Decreases more



Decreases less



Increases less




Increases more



Decreases more



Decreases less



Increases less








We saved the best two for last: the pneumonic is "inverse" because the "N" in numerator means a "D" relationship (direct) and the "D" in denominator means "iNverse." This may seem thoroughly confusing or just plain too basic, but many candidates even at level III get confused by the way the exams phrase the relative motion of various ratios. A fourth column could be added noting that when the ratio itself went "up" the indicator went down, just because the denominator was larger, even with no change in the numerator or denominator!

The purpose of this chart is to study then forget as it will save a lot of time on the exams when we encounter formulas in motion and have to discuss a "chain" of economic or portfolio or valuation effects as various statement items change. With this "Ratios in motion" thinking, the accounting entries themselves come alive since we bear in the back of our minds where they will be used.

Dupont vs. EVA
The 80-year-old Dupont ratio (not to be confused with recent-generation Dupont ratios referring to computer and legal sciences) can still hold its own, although the preponderance of WACC in the last couple of decades has eclipsed it with EVA, CFROI, RONAE and the P/E - P/BV models.

The Dupont model is actually an evolution from 2 to the 6 + ratios shown in exhibit II. The ratio web shows how these ratios interact to flow toward valuation and ROE as well as demonstrate strengths and weaknesses in the underlying financial statements.  In fact, Dupont is still used in computerized credit scoring models that are amazingly accurate at predicting when a firm will run into trouble based on use of assets, debt coverage and other mitigating factors.

Age-old critics of Dupont call it for weaknesses in these areas, which form a number of multiple choice, item set and financial statement questions on the CFA Level II exam:

  • GAAP methods are weak and slow (especially accrual accounting)
  • WACC needs more weight
  • Intangibles not well represented
  • Cost analysis weak
  • Not cash-based enough
  • Lack of forecasting power except for dire trouble
  • Confusing unimportant distractions like depreciation

For the purposes of the Level II and III exams, the model should be considered important as an overall valuation tool (nope, not kidding).

A note on leverage

Numerous students who take our online classes via run into immediate trouble over leverage. The Ratio web above and additional diagrams in the Level III study guide help explain its intricacies. First, "leverage" is both operating (ROA in the model with its various inputs) and financial (LEV or debt/equity and the cost of capital).

Operating leverage and financial leverage are multiplicative, not additive, so if our degree of financial leverage is 2.3 and operating leverage is 2.1, the degree of total leverage (DTL) is 4.8, not 4.4. This may seem trivial, but NOT SO! Above breakeven, every marginal dollar produces 5Xs more profits and below breakeven, every marginal dollar produces 5Xs more losses! With a very highly leveraged company (a power plant), above breakeven looks like printing money in the basement, below looks like a never ending nightmare of uncovered fixed costs. The contribution margin diagram in the Level III guide will further clarify this relationship.

Thus Dupont is the "machine" that still drives the abnormal future earnings so key to todays sophisticated valuation models, very appropriate for so venerable a contribution from the machine era. Will Dupont eventually go away from business and the CFA exams? Not in the near future! This link demonstrates a mathematical programming version of the Dupont model with automated inputs and results form Caterpillar tractor, very visual example of how the model ties to financial statements and extremely helpful for the CFA Level II:

The following exhibit gives the full formulas for the model as well as many others in the Level II and III exams, courtesy of the London school of business:

London School of Business formula summary: (Exhibit I)

Formula Sheet for Financial Risk Management 1

1. Compounding and Discounting

A. Compounding factor (future value of an interest factor r % for time t):

B. Discount factor (present value of an interest factor r % for time t):

C. Future annuity factor (future value of an annuity factor for r % for n periods):

D. Present value annuity factor (present value of an annuity factor for r % for n periods):

E. Net Present Value (NPV) of a project:

F. Value of the firm:

G. Dividend discount model for the share price ( ):

H. Real interest rate:

I. Spot or zero-coupon rates ( ) derived from the par yield curve:

2. Expected Value

3. Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT)


B. Capital structure effect on firm beta ( ):


4. Currency Relationships

A. Interest rate parity:

B. Purchasing power parity:

C. Expectations theory:

D. International Fisher effect:

5. Statistical Measures

A. Mean ( ):

B. Standard deviation ( ):

C. Kurtosis (K):

D. Skewness (S):

E. Covariance ( ab):

F. Correlation coefficient (ab):

6. Portfolio Model

A. Portfolio expected return p

B. Portfolio risk p for 2-asset portfolio:

C. Portfolio risk p for m-asset portfolio:

D. Minimum variance portfolio weights for 2-asset portfolio:

7. Credit Assessment Models

A. DuPont Model:

B. Altman's Z-score model (U.S.A):

C. Taffler - Tisshaw's Z-score model (

"Todays" models

The following model is a 5-tab excel model designed by your authors firm that is used by many investment banks worldwide. We have arranged to have an interactive version (no macros to bother your virus program) to be made available free to Investopedia visitors and students. Just click on the link and let us know where you want it e-mailed, hotmail or aol are fine as the abbreviated form we are offering is not a large file.

The model is used primarily to calculate a valuation for start-ups and small cap growth companies without a lot of history of dividends, earnings, etc.  These are some of the toughest firms to value due to high risk, potential high returns, and so many missing traditional factors in valuation.  The model utilizes the traditional firm value formula SUM E(NCFt)/(1+r) to compare expected risk and return with both a secured bank note and a traditional venture capital investment.

It also utilizes probability of various return weights as inputs to other parts of the DCF analysis and comes up with a comparative, risk adjusted, capital weighted valuation for both past and new investment in a newco.  When you receive the model via the link below, a complete description comes along of all cells and variables so you can practice your own valuations with financial statements found in numerous other study guides. Youll be surprised at both the similarities and differences the model produces compared to the textbooks, because not much has been done in the area of start up valuation, which is often "about what someone is willing to pay."

Heres your link:

"Newco" Valuation Model: (Exhibit II)

Code Underlying the Model: A FREE copy of the interactive model with formulas to try different values is available to visitors at:

(Note: the free model is a single page with macros disabled to make delivery via e-mail hassle-free. All values that the macros import can be entered easily, and a sample case is already loaded when you receive the spreadsheet).

How has company valuation changed since the Dupont model was formulated?

1. Focus has changed somewhat from accounting to the cost of capital
2. Has not changed significantly
3. More focus on excess earnings over the cost of funds
4. EVA and other models have eclipsed the Dupont approach

A. 2 only
B. 1, 2, and 3
C. 1 and 3
D. 4 only

The exam is looking for C here. D: Eclipsed is a bit too strong.

List and explain in essay form 4 weaknesses of the EVA approach
1. Predicting future cash flows is no easier than predicting ratios
2. Company managers are more likely to use a cost of capital "hurdle rate" in capital expenditure and program performance evaluation than take a "whole firm view" in their day to day decisions
3. Recent advances in PE theory give strong credence to the abnormal future earnings model over WACC or firm ratios alone as a key driver of valuation, which is close to the EVA idea when looked at in a cash flow sense.  However, critics of EVA contend that the older methods of watching margin and ROE/ROA achieve the same results as EVA with a friendlier user interface.
4. EVA argues that accounting drives too many business decisions under the old models, and accounting is inaccurate and out of date, as well as skewed by quarterly games and things like depreciation. But they are fighting a paper tiger, because no one today looks only at accruals without a statement of cash flows, which is in practice equal with the P and L and Balance Sheet in actual management today.

Tying it all together: from statement analysis to portfolio management

The CFA Level I exam tests the use of tools like ratio calculation from given financial statements, calculation of investment returns and yields and other underlying financial, statistical and economic concepts.

At Level II we transition those tools to inputs for statement analysis not just with a goal of business strengths and weaknesses, but firm valuation using a number of models, methods and calculations.

At Level III, and indeed the more complex questions of Level II, we again transition, to a "tie it all together" analysis of how two key components: market share and use of assets are the COMMON GOLDEN THREAD running from firm to valuation to a portfolio of securities.

The common thread is woven by two simple concepts:
1. To achieve and defend market share a firm requires continual renewal and efficient use of assets
2. A portfolio itself is a collection of assets, so, in an important sense, both portfolio and firm management are different hues of a single challenge: asset management

In order to transition from numerators and denominators in ratios and a general understanding of their importance, to integrating models like Dupont, to valuation models like the venture model above and others well explore below, to a deep understanding of portfolio relevance, three more steps are needed:

1. A better understanding of the various types and details of valuation models
2. A brief exploration of technical analysis
3. An integrating set of visual models stepping from ratios to accurate firm value, to a portfolio of firms, and then other hedging securities

The higher levels of II and III employ items sets and essays extensively that require INTEGRATING ANALYSIS. This means that our answers on these exams have to focus more and more on "THE BIG PICTURE" of the firm, first as an operating entity, then as a competitor in a sector, then as one sector competing for another in a portfolio of companies.

The macro always reflects the micro. Just as a group of competing companies sort themselves out along a continuum of ROI vs. Market Share, whole groups of companies and sectors also sort out by similar curves where ROI isnt company A, B and C, but Small, Medium, Large cap sector investments in a portfolio. The exam continually checks to see that we understand that these are not just technical or statistical realities, but also reflections of the underlying fundamental health of companies and global economies.

More on valuation models and the ubiquitous k

It is obvious that valuation stems from beating the cost of capital. But there are very different techniques needed to value a start up vs. a growth company vs. a mature dividend-issuing giant.

Beating the cost of capital in a giant relates to the natural limit of P/E of 1/k, the natural NPV of 0 in an efficient market, and the (relatively) straightforward index of the present value of the dividend stream (with the ubiquitous g and k in the denominator) determining firm value (more on this later).

In a growth company, valuation is all about a high P/E coming from a high P compared to E! With earnings of only a buck and a price of $50, what does a P/E of 50 really signify? Technically, that investors expect earnings to catch up with price. Emotionally, illogically, that demand for the companys securities far exceeds supply (which, as we all know from the .com experience, is a slippery slope).

In a mature company, weve discussed valuation as the PV of dividend cash flows whenever abnormal future earnings above the required return (or risk adjusted cost of capital) approaches zero. Another aspect is the ability of a company to "beat the market." In portfolio strategy, some sectors like healthcare do better in receding economies and others like auto manufacturers do better in growing economies, while still others like utilities have a complex web of energy costs, consumption and the value of world currencies vs. oil.

Consistently better than market returns is a time-honored benchmark, and consistently better than bond/CD returns is a key touchstone for all equities: if less risky investments earn more in an atmosphere of inflation, portfolio managers will flock to bonds and away from equities, creating a vicious cycle for companies of a higher cost of capital and thus even higher valuation benchmarks... (etc. as the spiral continues...)

For a start up or newco the problem is more access to capital than the cost of capital. Undercapitalized balance sheets abound in this venture-driven sector and this is the garden where new IPO stars as well as weeds are grown.

As an exercise in combining statistics, economics, the cost of capital and competing investments, the model uses a concept called a "risk weighted discount factor" to value the expected values of future earning streams and calculate a newco/startup firms valuation.

Although a complete explanation comes with the model, it is worth noting a few key components, as they are a hint at the higher Level II exam concepts as well as a transition to Level III by comparing a choice of investment returns:

1. The RWDF mentioned above is the required rate of return for a risky investment
2. It is the IRR/NPV and equivalent to the all-in yield to maturity of a risky bond
3. As seen in the model picture earlier, a probability chart of three competing portfolio investments (secured bank note, typical risky vc investment/risky bond, current firms distribution) OUTPUTS the probability of investment repayment from the risk weighted investment distribution as INPUTS to the RWDF denominator, which is the E(v) or expected value of the probability of repayment of the investment (the numerator is 1 plus the risk free investment rate).

If this seems a lot like the CAPM with WACC, it is. Statistics come in via the distributions of risky vs. risk free, so an "implied beta" is actually being calculated. In addition, economics come in since the market share assumptions in the small cap vs. medium/growth assumptions are present in the expected future earnings that the RWDF PVs to calculate value.

As a simple one-page model with no macros, this is a great yet very simple little demonstration tool, integrating concepts from valuation to portfolio comparison. With all macros and sub-sheets enabled, the model is able to integrate a complete set of ratios, earnings and revenue assumptions, tie to required return, and then calculate asset, leverage and market share assumptions.

If a firms valuation model drives an asset/investment requirement of a billion dollars and a market share requirement of 99%, analysts can re-iterate the model with objectives and constraints until a corner solution beats competing investments or the conclusion is "lets pass on this one."

Remember that the golden thread that changes with this iteration is the market share/asset/cost of capital triangle.

Like the old saying "Quality, service, price, ...PICK TWO... " iteration of this and similar models immediately shows the analysts (and managements) predicament of trying to keep cost of capital and cost of assets down while keeping asset turns and market share growth up. The moral to both is: pick your battle carefully, then focus!

Newco has 10 million shares outstanding. What revenue level does it need to attain a $200 million valuation with a P/E of 20, earnings of a dollar a share, and a return on sales of 10%?

A. Cannot be determined from the information given
B. $100 million
C. $200 million
D. A number of revenue levels will attain this valuation

On the surface, this question, which is very typical of CFA high Level II and Level III questions, is quite simple. Yet a majority of students at Level I studying for Level II choose A or D!

Under-reading the question will suggest that you cannot tie revenues to valuation this cleanly, so either A or D is appropriate.  Over-reading will say: wheres the cost of capital? Where is growth? Valuation takes pages of work, theres no way there is enough information here?

Two simple assumptions (and yes, the exam makes these all the time under the guise that were looking for "the best answer" not "the right answer) make this a straightforward calculation: P/E is a proxy for g and k and ROS is a proxy for earnings from revenue. From those valuation concepts, the rest is simple mechanics:

Revenue required is: E/(E/R) or E/1 * R/E = R (notice the "cross numerator/denominator" structure similar to the "tying" ratios of the Dupont model, why is this?*). So, were simply dividing "earnings required" (10 million) by the return that gets us to the 10 in earnings (10% of revenue) to get R:

R= 10 million/.10 =100 million, or "B."

A P/E of 20 times 10 million shares looks like 200 million, we wont bite.

10% of your P/E of 20 is 2, divided into valuation gives 100, why does this work? What does it say the 10% ROS is a proxy for?

*The creators of the Dupont model knew well that when you match a means/extremes pair in a ratio, you get out the original differential numerator (R here) if its indexed to 1, otherwise you integrate it with a sister ratio and index the two together (R/X).

The construct E/(E/R) is behind the fractional chain multiplications of the Dupont model, so the Assets * Sales/Assets is really A/(A/S) which immediately shows youre indexing assets as a percent of itself to either determine sales required to cover assets and vice versa, like we did revenue from earnings (only with assets we call them "turns"), when the construct is really just S (since A/A equals 1) broken into pieces. This is why the whole Dupont concept is mathematically called "iterative indexing"we are really just adding more and more factors that are a percent element in a bigger factor, all eventually rolling up to return on equity. Breaking a whole down into its component parts is the definition of a fraction, going in the other direction.


But how do you get a P/E of 3 vs. 40?  P/E is complex and includes illogical elements, but two non-controversial elements tested extensively on the Level II exam include:

1. Growth
2. AFE, abnormal future earnings, or excess earnings over the firms risk-adjusted cost of capital

Growth "drives" P/E and AFE "limits" is as 1/k previously. Growth is the abnormal future earnings engine, k (required return) is the "bogie."

Growth isnt just AAGR of revenue or earnings year to year, although these are the usual proxies in analysts minds.  Growth is actually the second derivative of earnings growth (a little calculus), or the "growth of growth"the rate at which the growth rate is growing or declining. Recalling our elementary calculus, the 2nd derivative gives the "rate of a rate." It also gives an "early warning" inflection point of whether growth (as a rate) is "slowing" (yes, we need calculus to determine that growth is slowing since its a rate!). This math is behind automated trading programs penalizing companies so dearly if they "miss" a quarter, continually trending growth, and systematically tracking earnings, the cost of capital, and changes in risk profiles.


Hundreds, if not thousands, of volumes have been written about risk.  The most famous model is the WACC model and its concept of beta - comparing the volatility of a security to the volatility of the market as a whole. An excellent explanation of beta is available in our dictionary as well as at:

Risk has its own taxonomy. There are types of risk, benchmarks of risk, components of risk, correlations of risk with other variables (especially the most important of all: higher risk=higher return up to a point of diminishing returns), etc. defines risk as the chance an investments actual return will be different than expected. This is pretty sophisticated in that it mentions the idea (from probability theory) of E(v) or the expected value of a return. It goes on to add a very significant example: "This includes the possibility of losing some or all of the original investment."

With investments and portfolios at from 10 to 60% of their original value in many swings, this is an important addition. Also, recapturing (as much as achieving a return on) the original investment is the basis of most venture models. Like the example model earlier, VCs know how easy it is to lose not only an entire initial investment, but experience a phenomenon not seen in the stock and bond markets, other than voluntary lowering of average portfolio prices: the requirement to continue to put more investment in to keep the venture afloat. VCs thus have additional models that require the "possibility of losing your entire investment" as only a partial and incomplete risk: there is the additional risk of having to invest more due to barriers to exit.

Bringing Valuation Together

We now have all the elements to value a firm, which is over half of the Level II exam:

  • Financial Statements
  • Ratios that factor in the key elements of market share, beating the cost of capital, and the asset requirements and leverage that help above break even and hurt below it
  • Risk vs. return
  • P/E and value surrogates
  • Triangulation

Say what? Triangulation, in actual practice, is one of the most common techniques of sophisticated analysts. The goal is to spot over and under valuation, so any tool, and every tool, that helps set the benchmark for this pattern recognition, or helps separate signal from noise, is important.

In triangulation, analysts use their networks as well as a combination of the tools weve explored, and others, to "hone in" on where a security is likely to go.

A logical question is: likely to go in what time frame? There is a drastic difference between enduring value, medium term value and short-term value! Fundamental analysis in about more than a snapshot in time, it is about integrating portfolio elements long, medium and short term for the purposes of safety and growth, or the preservation and creation of wealth.

After all the fundamental analysis, valuation in the short term comes down to a much simpler reality: "The price someone is willing to pay." Thats our segue into:

Technical Analysis

It can take an entire career to become an expert chartist, and the days of the generalist are seriously numbered. Commodities chartists dont cross over into equities very often, except perhaps to look at their own portfolio, and then they are just as likely to use tips as a related field of charting! (Busmans holiday and all that).

"Head and shoulders," "Turtle soup," and other pattern types have become common parlance with the advent of web day trading. But do not get the impression that chartists are only about short term movements, in fact, enduring value has a role in technical analysis in the longer term, secular movements of markets, securities and economies.

Technical analysis is a complex field based on a simple premise: the actual or historical movements of and patterns in a stock, bond, portfolio, index, etc. has built-in indications about what it might do next.

To put it in laymans terms: the past is a good predictor of the future. Whats happening "now" is a result of what happened "then." The common ground of fundamental and technical analysis is that both fields analyze change. What happens in the immediate future is most clearly indicated in the immediate present, and the past moves into the present with less and less chance of becoming an alternative outcome as we get closer and closer to the next second.

Weeks and months movements (not as much day movements and arbitrage/day trading as we would assume from all the publicity) are favored over last years cash reserves compared to this years. Remember, the CFA exams include arbitrage and even a little on day trading, but the focus is enduring value and portfolio management, favoring principles that have at least had some time to be subjected to research rigor (not analyst research, but scientific research, as in randomized blinded testing of a theory before pronouncing it worthwhile).

From a portfolio standpoint, technical analysts find over and undervalued opportunities in whole sectors as well as companies. They analyze trends according to efficient market principles and judge how sector prospects match these trends, from macro events in the world economy to news items.

If we answer an essay on the CFA exams with a focus on a companys ratios and financials, we will be penalized if we fail to notice that the buy-sell spread is large, or the stock is thinly traded, or few institutions hold it, or there is marked seasonality in its prices. One question on the exam shows a series of stock prices and tests to see if youll notice that the variance asked about is due to profit taking just before dividends are issued, a different swing for a company that has never missed a dividend vs. a company that is unpredictable in its dividend activity.

We've got a great section on nearly any technical analysis topic, if you feel you need a review, check out:

Types of charts and their assumptions

The "big 9" assumptions of technical charting are:
1. Patterns repeat
2. Supply and demand drive pattern trends
3. Value comes from competition between supply and demand
4. Trends echo, persist, repeat and contain momentum
5. Transaction charts eventually spot all supply/demand interactions
6. Emotion is as important to supply/demand competition as logic
7. Causality is not necessary to accurately predict patterns
8. The goal of technical analysis is to identify value patterns
9. The key to technical analysis is separation of signal from noise

Point and figure charts are used with line and bar charts to look at patterns with these keys and assumptions. Day traders attempt to spot patterns intra-day while technical analysts, and the Level II exam, focus on longer trends and assume that day trends (at least according to Dow theory) are random and not really predictable without special information. That kind of special information is theoretically unavailable to individuals apart from the market as a whole, which (again theoretically) is efficient via perfect information available to all participants at the same time.

So: Dow theory does not rely heavily on:
A. Daily trends
B. Weekly trends
C. Monthly trends
D. Annual trends

Some candidates choose D since A or D seem most likely, exam is looking for A.


Relative strength or weakness, or RSW, is based on the theory that it is possible to forecast which stocks/bonds/funds/portfolios will do better or will lose less, in bull vs. bear markets, and relative to whole-SIC changes.

Movements that show a firm under or outperforming its sector are typical of RSW analysis (NOT movements that compare it to underlying strengths in its financials: exam alligator/bait warning).

We need to practice computing moving averages from a chart of numbers, as several questions ask to choose and calculate moving averages.


Efficient markets theory/hypothesis is questioned on both Levels II and III. The following table is a good summary of EMT, and shows the relationship to random walk theory. Also check out our definition for an discussion of this and several excellent links.



Random walk

Rolling dice, throwing darts, flipping coins produce similar patterns to stock price patterns, suggesting random elements.  To be expected in an efficient market. Theory is CONTROVERSIAL (not: alligator) "WIDELY ACCEPTED."


Abnormal/excess earnings, neglected firm, value (high P/BV=value stock), Low P/E, January effect, weekend effect, etc.

Characteristic line

Y=mx +b where Y=firm return, mx=market return, b=% (+/-) to market

Strong, semistrong, weak efficiency


Why is NPV=0 for all investments in an efficient market?
A. NPV=benefits stream-investment cost (only + or - if not equal)
B. If price=volume, PV of future benefits=Price=NPV=0
C. Return is appropriately MATCHED to risk at NPV=0
D. All of the above

Of course, its D, since this is a convenient way to summarize a lot of the points in EMH/EMT. These have correlates in efficient portfolio theory as well since balancing risk and return to meet investment objectives is the purpose of portfolio management.  Even though the theory is controversial, the points in A, B and C above are crucial to numerous questions on the LII and LIII exams, and are worth understanding in deep detail.

For income tax purposes, what formula does a CPA use to calculate the value of options held by an investor? Explain the formula and its mathematical basis.

Black-Scholes is used to value European call options. The formula is based on the assumption that stock returns follow and underlying log-normal distribution function. Inputs are price, expiration, and standard deviation as a proxy for stock volatility.

The formula first defines a function Y=X-b to RFT where Y is the options premium (cost) and, X is the price of the underlying asset (eg. stock) and b is raised to a risk free exponent reflecting option maturity.

Each term X and b are then indexed to their respective distributions to determine the difference between the log-normal values and a normal distribution, then plugged into a proportion (a type of hedge ratio). is a link from our site that explains in more detail the origins and applications of Black-Scholes.

For purposes of the Level II and III exam, we are not expected to be able to remember the formula, but are expected to be able to apply and interpret it to a number of questions, examples, and inputs. To reach calculations even from given data visit or consult your BAII manual to be sure you understand the e and in functions (log and e, base of the natural logarithms).

Answering Exam Problems on Stock Valuation

Between understanding firm valuation, portfolio analysis and valuation, and technical analysis, we are expected to be able to independently value individual stocks from data from all fields. The key to this is the same as valuation of a company: growth and return.

Techniques questioned use the relationships weve discussed and will discuss further in diagrammatic form in the Level III guide, as inputs to a number of valuation formulas for equities, bonds, options and a brief touch on futures and currencies. Some of these techniques also are covered in the Series 7 study guide on this site.

Common elements asked about in multiple-choice questions on the Level II and some Level III include:

  • Growth rates, curves and functions
  • Prices and yields
  • Required returns and discount factors
  • Cost of spreads
  • Beta and risk, CAPM, WACC
  • Time indexes (eg: Days to maturity/360), and indexes are often expressed as factors, percents, multiples or ratios

From a stock standpoint, it is very important to understand the relative relationships (direct and inverse) between the formula elements, as numerous multiple choice questions and item sets are based on the formulas (since time limits on the exam do not permit half-hour long calculations of a single formula but DO permit partial answers, and formula explanation questions).

Among many others, heres an example of a chart you can create (try it for other variables) to memorize some key motions:

When this goes up...

This goes (U/D)?

Required return

P/E (Down)

Earnings growth

P/E (Up)

Dividends growth

Stock value (Up)

Required return

Stock value (Down)

In constant perpetual growth valuation, required return must be...

Greater or less than the dividend growth rate? (CAREFUL: greater) big, counterintuitive ALLIGATOR here!

In DCF valuation of a security, just like the venture firm valuation model we looked at, price is a summation of ratios where P=dividend/k-g where k is required return (remember, same as firms risk adjusted cost of capital) and g is the expected growth rate in dividends.  The above table is based on this ratio, which creates the inverse and direct relationships.

What is DCF? If you sum and then PV (discount) all the expected cash flows of an investment, portfolio, firm, salary, savings account, etc. you have the "present value" (which is a VALUATION by definition) of that stream.

The summation ( ) symbol seen in many formulas can be intimidating. All it really represents is shorthand for adding up a number of calculations that we do over and over in a sequence.

If we obtain a PV by raising a ratio to the power of each return period as in the previous example, in a sequence, then each period calculated has its own little "formula step" which is like adding up a column of formula results in a spreadsheet.

Instead of writing the formula out long-form with 3 to a, plus 3 to b, plus 3 to c, etc. the summation is used to summarize all those steps and give shorthand (FROM below TO above) of both the number of calculations, and a little "tag" to show what the summation is asking you to sum (the subscript letter, as in t).

NOTE: on the exams we are more likely to be asked a relationship question from within a given formula than to perform a large series of calculations. The obvious exceptions are summation functions that are pre-programmed into our BAII or 12C like bond, PV, DCF and statistical functions that only require a knowledge of where to input the variables.

Newco pays $4 a share in dividends, which grow constantly, annually at .08. Newcos cost of capital is 14%. What is its stock worth?

P=D(1+g)/(k-g)= 4(1.08)/.14-.08 = 4.32/.06= $72/share.

Say what? It cannot be possible to value an entire corporation on a one line data set? Multiplying the stock by shares outstanding would then value the whole corporation? What about management, technical analysis, Dupont ratios, cost of goods, margins and a million other variables? Is this all it takes to build a $72/share company is hitting a couple numbers like dividend growth and the cost of capital?

No.  It is quite difficult to grow when youre big, issue dividends, and still beat a burdensome cost of capital (growth and the assets to achieve it cost money).

The formula shows the extreme importance and power of returning cash, consistently, quarter after quarter, and having the confidence of investors that the flow will continue indefinitely.  This is true whether you give the cash flow back to investors, or invest it in growth (retained earnings) as long as there are abnormal future earnings above the cost of capital.

For the CFA Level III exam, and the more complex questions on the Level II, we are expected to be able to "tie this all together" in comprehensive models of the market, the firm and investment alternatives in a way that provides inputs to portfolios of assets and investments.

The Level III guide begins with a series of visuals that relates ratios, statement analysis, assets and valuation to the portfolio, and ends with some bullets on portfolio theory itself.

For the CFA Level III exam, and the more complex questions on the Level II, we are expected to be able to "tie this all together" in comprehensive models of the market, the firm and investment alternatives in a way that provides inputs to portfolios of assets and investments.

The Level III guide begins with a series of visuals that relates ratios, statement analysis, assets and valuation to the portfolio, and ends with some bullets on portfolio theory itself.

This diagram shows both portfolio and firm investment in the perspective of their environments.  The trade-offs between objectives and constraints force a balance between the cost of funds (financing) and the need for new asset investments. In a portfolio this is the equivalent of transaction costs and the cost of change. Returns on assets (ROA) from investing activity by the firm is very close to Return on Equity (ROE) because the key application of funds is leveraging assets to achieve market share and funds above the cost of funds, or a long, predictable stream of "abnormal future earnings."

This diagram integrates the materials from Level II with the exam focus on Level III.  Financial modeling moves progressively from funds flows and ratios toward investments and portfolio decisions.  It is important to put all these tools in perspective for the Level III exam, as it requires a broad strategic understanding of all the elements of analysis and where they fit in the broader picture.  Many candidates believe the Level III is only about statistical variances within portfolios, and are surprised to find that statement analysis, and analysis of firms, investments and equities are such a heavy aspect. This is because AIMR understands that the variability of a group of assets and equities comes from the single equities and assets within the firms managing them. On the III, statement analysis is expected to be fully understood from the standpoint of how all cash flows work together to create value and risk as the firm attempts to grow from equilibrium to a new state.

How do economics, statistics and a company portfolio of assets relate to a portfolio of companies? As companies in a portfolio struggle to achieve higher and higher share of market, this growth requires asset purchases and upgrades. Beating the cost of capital is being able to achieve that change while keeping pace with the revenues required to cover the marginal costs of those gains. There are numerous cash cycles within the business cycle and those cycles create the variability of returns measured in portfolio theory. Share growth requires asset investment, and the new capital employed requires share to beat its cost: this is the primal "machine" of return on assets, leverage (both operating and financial) and ROI. The marginal cost of share change compared to its benefit generates the firms "risk adjusted" cost of capital, and the hurdle it must clear for higher valuation and growth.

We spoke of leverage creating higher profits above breakeven and lower profits below. Many of the questions on both the II and III require an understanding of the variable cost and cash flow lines that bound these shaded areas. Asset purchases are required to maintain share, yet asset additions, to a company or a portfolio, increase the need for capital. Any new asset increases operating leverage and financial leverage if they are financed (or if a stock is purchased on margin). Higher breakevens mean higher price, volume or growth requirements, and higher growth bogies mean more work to increase firm and portfolio valuation.

Ratios that integrate market share, revenues, leverage, assets and ROI requirement are arranged here by strategy, funds flow components and measurements.  This is a step between Dupont type models and a whole firm valuation required to make portfolio decisions on a whole-firm basis. The top row is what AIMR calls "inputs", the middle is "process" and the bottom is "outputs." The "big six" of asset decisions, share, margin, use of cash profit proceeds, financing cost and investment strategy drive the thirst for new assets, new share, new cheaper funds and greater profit growth.

Those cycles in turn are the "engine" that drive valuation, PV, returns, and one of the alligators and sleeping giants of the Level III exam: interest coverage. This coverage is the "tie" between Balance Sheet and P and L, and more than just accounting, it is how the valuation bar is set to determine the abnormal future earnings requirements.

When a firm or group of firms in a sector or economy attempt to transition from todays strategic position to tomorrows goals, the tension between buying assets (here new R&D lab equipment) cycle growth and revenue requirements (circles) with debt requirements and ROE. The new assets have to be covered with new contribution margin that will pay for their cost, their use, the people that use them, the opportunity cost of missed returns on the money spent, the cost of the funds, the interest on the cost of funds (called "debt service" in the chart), all of which increast the risk of periods of variable returns, some of which make the hurdle, and some of which dont.

This is why ROE is SO dependent on ROA. The "yields" from asset renewal within the firm literally determine both the cost of capital and the new growth amount needed to cover it. Above breakeven this stimulates greater growth (the second derivative), below, it stimulates the greater GROWTH OF LOSSES. The difference: marginal new profits from greater market share, which is the goal of the "turns" of inventory and other asset investments in the first place. This is how analysts join the three types of financial statements, P & L, Balance Sheet and Cash Flows, into a comprehensive picture of the firm and its investments.

Two assets, or two companies in a portfolio, with different costs. A is the cheaper asset profit zone and B is the cheaper asset loss zone. The difference relates to mix, and incremental volume and margin from the more costly asset, thus leveraging more costly but more efficient assets. Each investment in a portfolio and within a firm has its own "investment frontier" line or curve. The "useful life" seen in depreciation is more than just an accounting convention, it (along with the cost of capital) is just like the price paid for a bond and its yield. Buying one asset vs. another is the heart of both portfolio and company management decisions, and are closely linked. The top line is known, above breakeven, as the "upside leverage effect," and its downside is the "accelerated loss" line. Risk comes from betting one use of investment capital will beat another by covering both the higher breakeven point and by achieving the "B" zone of ongoing abnormal earnings compared to the less risky but less-returning 1.2 unit investment. The Y axis is net income streams and X is log-net-asset-efficiency which is a weighted statistical measure of incremental "load" like buying a bigger bulldozer that can haul more logs per trip and lowering the per unit cost of gasoline while at the same time increasing the per unit profit. Always buying the "cheapest" asset (or bond) acknowledges the line but misses its slope, and slope is the driver of the efficiency that can create the abnormal earnings in the higher risk=higher returns "bet" placed by any investor.

This is a diagrammatic form of how the battle for additional market share results in higher margins and revenues yet costs new assets. Profits feeding into interest to fund leverage, retained earnings for growth, and dividends from increased equity value are driven by the cost of capital to fund the protection and promotion of market share. This and the next chart "reconcile" Dupont and EVA, which is a requirement on the level II and III exams in order to translate ratios into the underlying logic of individual firm valuation, then explain how its risk and returns affect the variability of a portfolio of risks and returns that can be additive, subtractive, or multiplicative. The "secret" on both the upside and downside is leverage. Leverage (both operating in the form of asset employment and financial in the higher returns on debt) is needed to generate non-zero and non-negative NPVs within the firms cash flows. A micro component factory in Northern Wisconsin consistently returns triple-digit annual ROEs, and is a cash and value "machine". The owner says "I keep my machines like they are new. They are all paid for long ago, and produce a million dollars in inventory that you can hold in two hands. We are always backlogged with orders, and my raw materials are scrap from big, wasteful manufacturers. I buy the scrap with 4% money provided by the manufacturers forgiving payables."

Many questions on the Level II and III exams transition to links between financial statement items and ratios. The tension between trying to beat the cost of capital with earnings growth, yet buy new assets that fund market share maintenance and growth create these key links as depicted above.

The Dupont model and its sisters need to be understood very deeply at the II and III exam levels. "S/A * P/S" cannot just be calculated correctly from accounting adjustments within the financial statements then multiplied to describe the answer as a value. This is why AIMR says "knowing the right answer will be of no advantage." They are talking about contexts. S/A as "asset turns" cannot just be described as "Newcos asset turns are Z, which are above their industry norm" Turns are the volume amplifier for return on sales in the model above, which is a key component in operating leverage, which is one of the major drivers of both higher risk (below breakeven) and higher return (above breakeven). This is where probability, economics and financial statement analysis all come together at Level III.

How is growth is related to asset and financing decisions?  The driving forces are staying ahead of competition and beating the cost of capital at the same time, while keeping assets current, inventory under control and the balance sheet healthy. We saw how one asset or investment vs. another can make all the difference in their statistical "log efficiency." But statistics do not drive returns, market share does. This slide is the key "essay" transition from firm efficiency via internal investments and portfolio efficiency and return.  A group of competing firms in a sector invest to enhance their position in the market share "food chain." The value equation for a portfolio is how those investments "position" the company for valuation depending on how green the grass is on the other side of that investment. As we will see following this, the share "environment" is lumpy and not uniform in its return profile, and bigger isnt necessarily better. Picking those firms "positioned" within their share/sector horizon is the analysts art and science. Building a portfolio is about knowing how type=returns.

Before we look at the shape of portfolios of companies competing for share territory, we have to understand the sources and uses of cash flows and the "siphons" that drain cash away from ROE in order to produce share, which is another key component in the risk/return equation. Dropping cash to the bottom line makes the firm look more valuable but is at the expense of future portfolio position if asset purchases and share spending causes market share to drop. EVA enthusiasts continually point to the valid need to beat the cost of capital and not let accounting issues like depreciation get in the way of "true" cash flow analysis and a focus on ROI. But depreciation, inventory and other "non-cash" engines are the heart and soul of the firm, and salty/seasoned managers who are shrewd about asset deployment can read volumes in a depreciation schedule.  A good analyst can see health or illness in a P&L, a great analyst can see enduring value or long term trouble in a balance sheet, and both have to keep an eye on sources and uses of cash.

As promised, this chart questions the linearity of the market share "field of action" within a portfolio of companies, and the next chart expands upon that idea for the portfolio analyst. Return on investment as a function of market share is not linear, but more like a "smiling face" curve. There are high ROE companies both in low share/niche market positions and dominating share positions, but "in the middle" ROE drops precipitously. This middle section is known as the "shake out zone." When analyzing a market it is a mistake to assume big is good and small is bad. A better rule of thumb (and none work very well) is that "stuck in the middle is the worst." Companies trying to transition from niche success to big-time success face a daunting challenge because "more cash requires growth, and growth burns cash fast." Growth is a risky, mixed bag. Cancer is a form of growth out of control. Building the asset and investment base ahead of the growth ("if we build it, they will come" or the "field of dreams" strategy) can mean huge losses as leverage punishes and humbles us below breakeven. Hitting the growth with the asset base too thin does the opposite, creating pandemonium and losing customers when "Ready-Aim-Fire" becomes "Ready-Fire-Aim" or in extreme cases: "Fire-Fire-Fire."

Portfolio analysis includes analyzing relative company positions with numerous parameters, including where they fall out by ROE according to market position within their industry. Remembering that variability and risk are direct, not inverse relationships with return, the X axis is BOTH high return on investment and higher risk as assets are employed to "roll the dice" for better period-to-period returns driven by new revenue, margin and share. But share increases are lumpy and investment is smooth, making the matching process precarious and causing the variations underlying what the portfolio analysis standard deviations are telling us. Economics come in as the greater investment requirements move us up the Y axis but also along the X axis and if suddenly we are in a cat fight for share in a shake out zone of less revenue than anticipated, forecasted and predicted, or become price takers through price erosion driven by competition, our NPVs dash for zero or deeply negative territory.

Margin Erosion is one of the alligators on both the LII and LIII exams. It is subtle and not easy to detect, and it signals the beginning of the deterioration of the ability to beat the cost of capital. Dont lose the forest for the trees on the Level III by focusing only on statistical analysis of variability. Candidates at this high a level must understand the asset intricacies within and outside of the firm that drive variability of return.

Picking a success rule and sorting companies by compliance to the rule vs. size of share or revenues is another way to segment a portfolio. The rule can range from patent position to type and amount of junk bonds issued. This is simply an illustration of the numerous ways to segment a basket of companies into understandable groupings in addition to market share. Hedging portfolios with risk free investments, calculating Treynors performances (the beta in the denominator is not just a coefficient, it relates to real asset deployment), running Jensen regressions, solving simultaneous equations of portfolios with equities in disequilibrium, using betas in arbitrage pricing, creating a portfolio matrix with three variances and six covariances, all are valid BALANCING strategies AFTER the economic and firm movements underlying the statistics are thoroughly understood.

Taking five economic horizons and calculating optimal mix along efficient frontiers also requires a deep understanding of what sector competition factors drive the risk/return statistics along the frontier. Efficient assets are the heart of both company and investment portfolios.

Because, as we saw in the Level II guide, risk and return are directly correlated, portfolio strategies match the risk of higher ROI against the additional risk of the higher operating and financial leverage needed to earn the abnormal future funds to beat the cost of capital. This can be an upward spiral or a vicious circle. It is not a coincidence that both company "bets" and portfolio objectives have safety, growth and speculative elements. The investor objective to maximize expected values of returns while minimizing standard deviations or variability of returns/risk is natural but misses the variability that is "built in" to asset deployment ramp ups within the firm and the economy. There are enormous transaction costs built into launching and optimizing an investment fund or portfolio just like deploying a group of assets in a company. Assets covary in companies just like they do in portfolios, in fact the former is a key part of the latter.

In a portfolio of projects within a company or a portfolio of companies within an investment fund, each project, company and security has its own dynamic profile of probabilities of achieving various levels of NPV with the baseline in an efficient market at zero. This is a graphic representation of the firm valuation model examined in Level II, where one investment has a 25% probability of achieving a higher NPV than another, but due to risk, the probability functions can cross in a way that cannot be seen if only a single point calculation is made. This slide of NPV frontiers within the firm is where firm valuation intersects with portfolio theory. Valuation, risk and return drive a firms beta and other characteristics that are then translated into competing investments in other categories like gold, T-bills, or even shorts that bet the companys fortunes will take a turn for the worse.

Portfolio Analysis beyond firm fundamentals

The transition between firm/investment risk and analysis of the risk/quality of a portfolio of investments is a statistical transition from the variability of returns for a single security (like a share of stock) to the variability within the portfolio. A single share of stock has a rate of return defined, like a bond yield, as the price change plus any dividends divided by the purchase price at the start of the period.  Risk comes in (with standard deviations as a proxy for variability) when returns are expected to vary from period to period.

The crucial concept of covariance

The transition from a group of assets deployed within the firm to a group of portfolio assets, turns up the volume on our statistical competence. The single most important concept in portfolio analysis is the idea of COVARIANCE. The term is used all the time, but often misunderstood.

The dictionary defines covariance as:

"A statistical measure of two assets, and how their returns move in relation to each other." Statisticians generalize the definition to say, "Variance measures the amount that a set of data points varies about its mean. Covariance, on the other hand, measures how two data sets vary with respect to EACH OTHER."

Geometers compare variance and covariance by defining rectangles of data sets in a Cartesian coordinate system then describing the area of the rectangle as the variance. When the same is done for covariance the difference that becomes evident is the fact that negative distances can produce sign changes, which become a defining feature of covariances.

Covariances are also called the "mean of the product of deviations". This seems to be a language version of a formula that sums a group of positive and negative numbers, somehow weights them with an average or a probability, and multiplies the results.

This is the exact process required on the exam for entering a data set and then computing and interpreting covariances. Since computing covariances requires building a table, a couple problems give the categories and two assets and we basically have to know which to add and which to multiply. Anything beyond that would consume too much time, and neither the 12C or the BAII have covariance functions.

While were on the topic, much ado is made of the fact that the BAII has four regression functions and the 12C has only one. Honestly? Both calculators are statistically weak! Both will enter a series of X and Y values (watch out for crushing data in Registers 1 to 6 in the 12C) and run a linear regression with an r squared. Thats about all we need to know for any level of the exam. The focus on covariances in the Level III is interpretation and limits of their value vs. various market and portfolio theories.

A lot of BASIC statistical concepts are tested on all three levels and we need a picture in our minds of, especially, the concept of a standard deviation.

Recall that (assuming a normal curve) variance (and its square root, standard deviation) measures the MAGNITUDE OF DIFFERENCES in measuring dispersion in a distribution. When we say one standard deviation is .68, the question is .68 of what? In common English, 68%, or about 2/3rds of the data values are within one SD. More accurately, we EXPECT that 2/3rds of the data will fall within one SD of the MEAN (or in area under the curve terms, one Z score).

A term related to covariance and also used to measure portfolio risk is "correlation." The exam will give a couple standard deviations and a covariance and ask for the coefficient of correlation. The covariance is the SDs of the two assets multiplied together and by the CC, which ranges from -1 to +1. To get the answer, calculate: CC=Cov/SD1*SD2.

Balancing Asset Valuation vs. Portfolio exam preparation

The Level III exam transitions from firm/asset valuation to portfolio valuation. Much of this study guide has focused on the firm, and the sister study guide on this site (for the Series 7) focuses more heavily on stock, bond and derivative valuation and calculations. Both are necessary to ace the Level III!

This is our estimate of the balance of questions on the Level III for 2002 and it is just a wild guess based on 2001 exit interviews and 2002 materials and comments provided by AIMR:

1.     Professional Standards and ethics: 12%
2.     Quantitative analysis in economics and portfolio management: 13%
3.     Debt, equity, international and derivative/alternative investment valuation: 25%
4.     Performance evaluation and standards, asset allocation, investment policies for both individual and institutional investors, portfolio management of equity vs. debt derivatives, portfolio strategy and risk, and issues in portfolio valuation and management: 50%

Following is a list of topic terms that need to be understood at the conceptual level:

  • Bond immunization
  • RVA
  • Secondary trading
  • Swaps
  • Indexing
  • Duration approach vs. SD
  • Cap, call and interest rate risks
  • Correlations between emerging and developed markets
  • P/E and yields vs. inflation
  • Economic vs. market and firm valuation in sector selection
  • Limited usefulness of economic models in forecasting
  • Explaining average returns vs. predicting expected returns
  • Compare factor models (fundamental as in the charts here vs. macroeconomic)
  • How does quantitative research relate to subsequent investment decisions?
  • AIMR presentation standards
  • Performance evaluation vs. measurement
  • How do you break a fixed income portfolio into factors?
  • Be able to define Treynors measure, Jensens alpha and the Sharpe ratio
  • Performance of managers (benchmarks, attribution analysis, universes, normal portfolio comparisons)
  • Market vs. price vs. earnings, vs. "value" vs. small cap and other styles
  • VAR (value at risk) Standard deviations are not very intuitive, so the VAR has been touted as the latest and greatest (interesting that its well covered on the Level III and its only five years old). A limitation of standard deviations is that they assume symmetry. Options destroy the symmetry of a portfolio, giving SDs above and below the expected return different likelihoods.
  • Hedging
  • Psych (regret, cognition, prospect theory, self control)
  • Durations/basis point values in interest rate futures
  • Put options, how used as a hedge?
  • Contract multipliers for indexes (you dont have to check them for the time of the exam, they will be "givens" on the exam)
  • Asset allocation (this is really all about how you balance a portfolio based upon your clients situation and needs, and then change that balance as those needs change by continuing to adjust the risk/return tradeoffs.
  • Corporate risk management: the firms equities as part of its own pension fund
  • Beginning with capital market expectations, we need to be able to design a "case portfolio" for an institutional client including objectives, constraints and how they affect asset allocation choices/alternatives given your assumptions about capital markets.
  • Tax (especially pre vs. after tax ROI, the Series 7 study guide has a good discussion of EBIT vs. Net income and their alligators).
  • What are "alternative investments?" The AIMR does lip service to real estate mostly in the form of REITS. There is little acknowledgement that various "decades" in history have seen swings between real estate, gold, equities and bonds produce decade-long differences in returns. Real estate investment is an entire field that needs its own "AIMR" and AIMR itself needs more material on this important topic, since numerous clients are "betting" that their home or property will be a generational retirement asset.
  • What is the effect of getting a second mortgage to day trade? Yikes.

Special Section for the CFA Level III Exam: "Acing the Essay"

There are a number of key rules, and "dos and don'ts" for a consistently high score on CFA essay-format questions. The examples in this section are specifically tailored to the Level III topics (asset allocation and portfolio management) but many of the tips, pointers and hints apply to essay questions at all levels.

These rules derive from the fact that consistent grading by the CFA readers and professors require graders to use "guideline" answers.

The fundamental guidelines driving these rules include:

  • Thoroughness
  • Accuracy
  • Deep understanding of concepts
  • Adequate and correct justification of your position
  • Plentiful quantitative examples

Some of the "rules" that stem from the guidelines:

DO divide your answers into complete component parts and DO NOT miss a major category asked for in the question.

For a portfolio performance question, this could include (for example):

  • Long-term asset allocation policies (state, explain, give examples)
  • Short term asset choices and decisions
  • Market conditions and timing
  • Asset classes to be used
  • Security selection criteria and rationale
  • Sector performance and rotation
  • Industry selection criteria
  • International, including currency evaluation, risk and management
  • Derivatives strategy
  • Strategic match to customer needs and objectives
  • Anomalies and special conditions

For a company evaluation, this could also include:

  • General comments
  • Unique circumstances
  • Risk vs. Return
  • Time horizon of analysis and decisions
  • Management
  • Finance and Accounting factors
  • Investing factors
  • Operations
  • Environment
  • Market and competition
  • (Etc. see graphics above!)

The question may also have been set up as: "Analyst A gives ABC opinion, analyst B says XYZ, and analyst A rebuts with GHI..."

With this type of setup the focus should be to use EACH category and its facts and calculations to SUPPORT our STANCE in agreeing with A vs. B (YES there is a "correct" guideline answer for the graders, but well see in a minute that we can also get FULL CREDIT for a "wrong" answer if we play our cards right!).

The greater degree of support we give to our position from referenced literature, definitions (again, our dictionary is helpful for a passing score), concept explanations and, of course, calculations, the more likely we will have no problem with the essay questions and even the new item sets.

Remember, the grading process on essay questions is fair and consistent. Although AIMR has gotten a lot of (undeserved) criticism for the format, it really is not subjective at all. Numerous checks and balances are built into the grading, like the same highly professional CFA recipient or university professor grading each question, and focusing on just that one, as well as numerous "eyeballs" reviewing answers that did not receive full credit. These reviewers are looking for the exact mix well be suggesting here: Calculations, Creativity and Judgment. In fact, your synthesis could easily bring out a brilliant new point the original test question writers did not think of, and your answer and/or unique points will then be considered in the evaluation of all other answers for that question!

So even though there is a guideline correct answer, other than quantitative answers like the yield on a bond or convert ratios of a debenture (lots of examples on those in the sister Series 7 guide), many "close" answers with unique and strong supporting principles also get the cigar.

  • DO use pro-formas, tables, charts, bullets, embedded calculations, English versions of formulas, output from the 12C, and even partial but not directly related calculations.
  • DO take a pro/con approach stating both advantages and disadvantages EVEN IF THE QUESTION ONLY ASKED FOR ADVANTAGES, with underlying definitions and principles stated clearly
  • If you take a position that a portfolio adjustment is necessary or beneficial, be prepared to give deep DETAIL on how youd execute the changes, including the differences between alternative PVs and yields, derivatives vs. converts and all transaction costs, opportunity costs, loss of interest, change of risks, tax and other consequences
  • DONT make a point you cant explain in detail and just leave it hanging there, play to your own strengths as a professional analyst
  • DONT ever BS by giving a "spin" to the question, then answering the spin because you know it better than the real question. This is a guaranteed bomber. Better to take on the question directly and use other methods to get at your position, do that well, and come out with partial credit than receive no credit (at a point a minute!) for trying to fake it
  • DONT get too broad and run out of time for the necessary calculations of yield, put/call differences, price and dividend calculations, or an important valuation. Giving a 30 minute answer to a 15 minute question gains us nothing
  • Do quote articles, textbooks, principles and definitions

Remember that the graders are both professional like yourself, but also live in a world of theories and looking at problems from a number of angles, in a word, scientific, meaning somewhat irreverent about absolutes.

Balancing scholarly concepts and theories subjected to rigor with real life examples and factual calculation will win you to the graders side immediately. Some "key word" TRIGGERS that help your professionalism show through:

"There are three common approaches to scenario forecasting..."

"It is widely recognized that numerous large trades are not reported..."

"A more formal approach to this problem than simple trending would be to subject the data to econometric analysis..."

"High yield bonds should be evaluated with a number of parameters, but liquidity is always a key consideration..."

"The reasons that high grade corporate bonds and Treasury Bonds have such a high regression coefficient include..."

"Currency exposure is a major performance evaluation factor, suggesting a hedge strategy of..."

In general, it is not enough to answer essay questions on the Level III with good facts, good calculations and good positions alone. The answers MU.S.T be sprinkled with PRINCIPLES of analysis (even to the point of being preachy) to support (or, better, give pro/cons for) a position.


The more our answers look like a case history in a textbook, the better! That means that exhibits, tables, sections and subsections, and parenthetical calculations are all winners.  A brief OUTLINE is a must for the longer questions and even more complex item sets. An example outline could include:

  • Make a point and state a position
  • Support it with pro/con concepts and principles
  • Support THOSE with references and explanation
  • Support those further with calculations, giving back question data and facts
  • Define and expand your calculations with English versions and definitions
  • Create a synthesis and take a judgmental stand based on your analysis
  • THEN, analyze the differences between the choices and the CONSEQUENCES OF YOUR STANCE (THIS is where we get a HUGE gimmee: even if we are "wrong" but CRITIQUE OUR OWN POSITION ENOUGH WITH THE CON SIDE OF OUR OWN ARGUMENT, WE CAN GET FULL CREDIT!).

Say what?...

Again, subtle point here: Lets say we agree with a convert to common rather than staying with a covered call. We could just come right out and say: this is the way to go. A better choice, though, would be to give all sides of both arguments with the PVs, lowered risks (and consequent limit on return), etc. and then pick your choice (you have to if its a judgment question) BY A SLIM MARGIN. This way, if we picked wrong, weve given a dynamic argument (and good pro/con thinking, which is real world as well as scientific) for the opposite choice, and if it turns out to be "right" (a lot of these are close calls) we can still get full credit.

Examples (This is important!):

  • Choice A carries more risk via option contract obligations
  • Choice B carries a negative tax effect
  • Choice C has a better PV (demonstrate)
  • Choice D is a wash due to a convert vs. the bond yield and call feature
  • Choice E has interest rate parity with the Yen and is well hedged, yet carries other risks...

So, even though well get slammed for NOT ANSWERING a question, we DO NOT get dinged for looking at many sides. Even if we chose "wrong" compared to the sample correct answer, our thoroughness can win us full credit. This is especially true if we quote theory, use examples from our own deep experience, call on definitions and concepts/calculations for support and MOST IMPORTANTLY: PROVIDE OUR OWN DEFT CREATIVE SYNTHESIS THAT MAY HAVE ASPECTS THE WRITERS DID NOT CONSIDER.

Choosing The Right Process

Does the divestiture of subsidiary XYZ enhance or decrease the value of ABC? (These questions almost always include dividend aspects!)

Which PROCESS best fits this question?
a. Calculate a value for each and subtract the sub from the parent
b. Use a dividend discount t decide via the sustainable growth model
c. PV both parent and subsidiary and see if parent ROE is enhanced

All of these have merit, but the exam expects you to quote the literature and choose B as the most appropriate process (but if you do a great job on all three, using the value in a and the PV/ROE in c to support b, youll get credit even if you thought c was most appropriate (and who wouldnt with cash flow being King, even of sustainable growth!?).


  • Obtain g via ROE * (1-DP/O ratio) (wow, we included all 3!)
  • Obtain ROE from given financials as pre and post divestiture = common/SE for each and put in a cool table format
  • Find the 2 estimated dividends for the coming year = D(1+g)
  • K=D/(k-g)
  • P=D/(k-g)

The comparison will then show if the sub has p and g higher or lower than the parent (this is why subtraction alone doesnt work, it is really a mixing problem, with a rate influencing a rate, to either make it accretive or dilutive like any acquisition).


REALLY show your expertise (see the graphics in the main CFA III study guide) with the comment: "Examining the ROAs of both units gives a quick instinctive answer that the divestiture will be a good idea, and the analysis bears this out..." (How could that eyeball do so much?).

If NO dividend is given, even though sustainable growth is still the touchstone, enough data may have been given (no dividend information is the clue) to calculate accretion/dilution directly. In that type of question, what variables WOULD have to be given? (The amount of shares or enough info to calculate them for BOTH divisions; separable EPSs for both divisions (or conversion/compression ratios or factors that will get us to the same number) and the transaction cost impact on earnings to separate the two. We then do a "mini schedule" to see if over the question horizon (say 3 years, a usual parameter), the new companys earnings are accretive or dilutive without the sub in place. Know that theoretically this is inferior to the sustainable growth model, even if retained earnings is a proxy for dividends, but if all the "GIVENS" in the problem point to a dilution analysis, go for it! ROA of the two is a huge key either way, because it point not only to ROE, but shows whats going on structurally in operations in the two divisions, beneath the numbers.

How do analysts get around the difficult problem of valuing intangibles?

First, clarify the problem with a WHY: "This IS a problem (we just agreed with the exam writers), because valuation relates to abnormal earnings and these are difficult to determine directly for intangible assets."

HOW: "Analysts back into intangible value (IV) for intangible assets (IA)" - because normal earnings are relatively easy to determine for tangible assets (TA).  Knowing that the total earnings (TE) = abnormal earnings (AE) + normal earnings (NE), analysts can:

  • Determine TE
  • Determine NE for TA
  • Calculate AE as TE-NE
  • Assign AE to IA
  • Calculate IV from the AE

How could this outline be handled as an essay? First, practice building logical outlines like the above, then flesh them out with explanatory principles, definitions and calculations! AN OUTLINE will relax you, make sure you dont miss any points, and assure you are covering most of the "best answer" template even if you miss or blow a few calculations (everyone does, if perfection were required, there would be no CFA initials after anyones name).

Also: give a quick "Who, what, where, when, why, how, how much" test to every answer to be sure there isnt an aspect you could enhance. "When," for example, might suggest time frame, timing, and duration issues you havent covered yet.

Action verbs/command words

There are a number of action/command words woven throughout the CFA Level III exam questions, and AIMR is kind enough to warn us that these terms carry special importance.

In essence, they are HINTS! (Youre kidding, AIMR would put a word in bold, set neon around it, and point a flashing arrow at it, and its a hint??).

Yep. There are just too many possible variations unless AIMR is either really nasty, or really helpful, and in this instance the board is clearly setting the focus for the candidate on what the question is really looking for.

The following chart pulls the curtain back on some of these clues. (The "C" category is for Create, "J" is for Judge).






Create a policy



Crunch numbers



SWOT analysis/pro-con

Identify (choose)


Trade-off analysis



Concept exposition



Selection criteria



Focus on alternatives



Bring it all together



Compare concepts

It helps our focus, and takes greatest advantage of the hints, to organize our thinking around EXACTLY what the question wants, and to first ask if the question has a heavier focus on calculation, creative solutions, or supported judgments (or all three in proportion, or by the "partial" answer requested in each section of a larger scenario/case history/item set backgrounder).

It also helps to re-slice the judging and creating functions by answer types that fit their domains--

Judgment Commands

Creation Commands

Both have calculations


Formulas in English


Pro/con analysis


Decision analysis, fact finding


Quantitative solutions

Synthesized solutions

Make choice from close alternatives


Decide which behavior is ethical


Apply principles to alternatives

Historical and scientific wisdom

Our Dictionary Can Help!

OK, OK, so we've plugged our dictionary about a dozen times now throughout these guides. But, under "rationale support", graders are looking for underlying concepts to support the position you are (J) choosing or (C) taking/creating. Our definitions are good examples of how to demonstrate a deep command of underlying concepts. In fact, many of the "correct" answer templates are filled with defining concepts that illustrate and substantiate the choices made.

For example, you might have judged that a security will increase more in value due to a longer duration/lower coupon.

After your calculations, analysis and conclusions-recommendations, you can add:

"Duration is a measure of a securitys cash flows, calculated in such a way that each cash flows PV is a weighted percent of the PV of all cash flows. Comparing two bonds, one with a higher, and one with a lower coupon, the lower has more "duration" due to the weight of its cash flows being end-loaded. More duration generally means greater sensitivity to interest rate swings."

Using a "formula in words" in this fashion is an outstanding way to ace essays on the III.  It shows a command of the concept and quantitative facts at the same time.

Also, be sure to include a couple other enhancements with the definition format:

  • "Formula in words" is very close to many of the best example answers
  • Specify what moves in what direction
  • Pro/con and cost/benefit are crucial ("risk is lowered with this strategy, but upside gain potential also is reduced" etc.)
  • Lecturing is even good, if its accurate, relevant, scholarly, etc. ("As we know, a long position held with a hedge is different than the hedge alone...")
  • Uncovering trends and non-obvious or hidden facts and relationships is a real winner. ("Newcos top ten indicators are all positive, but creeping inflation in the cost of capital and last quarters softening of excess earnings suggest an underlying, less obvious, weakening trend...")

If we introduce a technical strategy to hedge, replace, or balance a portfolio, we also have to REMEMBER TO INCLUDE THE EFFECT in addition to the RATIONALE AND CALCULATIONS! This may seem obvious, but it really isnt. Like the company who wins a great new market share segment but fails to calculate the competition the success will draw, the "echo" or "rebound" effect HAS to be projected to truly reach seasoned professional analysis from the exams perspective.

"With liabilities in Newcos balance sheet requiring matching, a portfolio structured component combination of

  • Immunization
  • Indexing

...would represent diversification of the total portfolio, with a number of the traditional downsides of both such as (etc.)..."

So far, so good. BUT, we need to remember the finish line and not stop short on that 1 yard line! What is the expected EFFECT?

  • Indexing, for example, assures market movement correlation...
  • Immunization "solidifies" the probability of meeting Newcos targets
  • Together, they open the door for active portfolio management at a higher level of risk than would be possible without their stabilizing EFFECTS on cash flows...

Other ENHANCING steps:

  • Definitions, Investopedia style
  • Deep explanation of concepts EMPLOYED in the analysis or judgment
  • Effects in time sequence
  • Stating scholarly, scientific and proven principles
  • Turning the exams own charts, graphs, tables, statements, etc. into CRITERIA for our judgments ("These factors suggest the potential for an LBO: strong management, low seasonality and cyclicality, strong financials, and a track record of abnormal earnings and excess cash flows...")


An analyst and university professor who has graded exams for many years said:

"The biggest cause for losing credit on an otherwise good answer on the CFA exams is missing one of the main issues, because we have to get the feeling a candidate is in control of the process, hitting at least the main story pegs in our ideal answer, showing a deep mastery of most of the concepts, and giving back quite directly what the question is asking for."

There are several ways to avoid this "thoroughness" alligator:

  • Answer the questions in the order presented
  • Give answers that touch on EVERY issue raised in the question itself BEFORE you start raising additional issues

The "impression of control" comes from balancing breadth with depth and overlaying your points on top of the ideal answer like two normal curves without too much kurtosis or skew (are these two different?).

  • Dont spend too much time on one issue to the point where you dont at least touch on ALL the issues raised by the question
  • Frequently re-read the question and its supporting exhibits to be sure there isnt a key that you havent covered

After that,  read over your entire answer quickly, did you:

  • Re-state the issue youre answering
  • Judgment: take a position (WITH pro/con!)
  • Support the judgments (pro and con) with calculations, charts, tables, rules, principles and definitions
  • Synthesize your data and conclusions into an overall creative strategy of solutions, trade-offs, new asset allocations, detailed change steps, resulting portfolio position, etc.
  • WEAVE concepts into your DEBATE WITH YOURSELF on the alternatives with frequent ties back to your calculations
  • Express your calculations in sentences that explain and interpret them and their relevance to the key issue (NOTE this one!)

In our practice essay feedback sessions at we often find that AIMR loves concepts like:

  • A covered call in a hedge
  • Bond decisions with a competing derivative
  • Derivatives and equities with the same underlying security
  • A currency risk
  • Fate of a pension plan in a company experiencing a downturn (hint, how many of the firms own shares are in the plan?)
  • A real estate investment with a hidden declining rent trend problem
  • An asset class return imbalance
  • A portfolio problem where the clients objectives are in conflict, such as the need for immediate income vs. long term growth
  • The TRICKY distinction between YIELD and TOTAL RETURN

Issues like these can DISTRACT us into detours that are TIME BURNERS, as we sweat over a subtle problem, when the question is really asking for something much more basic.

  • NEVER spend 30 minutes on a 15 minute question
  • Always state the obvious even if means restating the question itself in different words with new explanatory definitions included
  • Sometimes all that is being asked for is a slight fleshing out of the question with the correct principles from the references - the exam is not just testing our knowledge, IT IS ALSO TRYING TO DETERMINE IF WE DUG INTO THE SUGGESTED TEXTS
  • Show even indirectly related and exploratory calculations in your answer booklet, not just scratch paper. If an answer is marginal and the committee could go either way, a calculation showing you were on the right track could push the answer over the top!

On longer questions, an outline is mandatory.

Some Successful Formats

  • "The six key ratios are..." (then explain each)
  • "The four relevant portfolio techniques are..." (then give references and apply each to the situation)
  • "The comparison techniques include..." (then build a choice table with risk, return, unusual circumstances, tax, regulatory, ethics, liquidity, solvency, timing components, with your calculations, or even the exams own parameters, filled in)
  • "The advantages of the 5 potential strategies are..." (Do NOT show only disadvantages if a question asks for advantages even if a technique has known flaws- e.g. indexing, include highest return for each parcel of risk..." not just limited returns, and do show both sides of each issue)

A question is exploring the price fluctuations in a technical problem and brings up, and asks about, the idea of elasticity.

In addition to explaining variability of demand or supply in response to price movements, we could draw three simple downward-sloping curves (nothing fancy, just a scribble):


Then, note that the top is elastic, the middle is normal, and the bottom is inelastic (picture worth a thousand words?). Enhancements could include labeling Y with Price and X with Quantity, but DONT switch the two curve explanations though! This may seem rinky-dink for a level III analyst, but in combination with a good quantitative analysis of the elasticity itself, shows a deeper understanding and costs little time.

Judgment vs. Process

With the changes made on the 2001/2002 exams, not every question is looking for a judgment. Many item sets and shorter essays are looking as much for PROCESS.

xyz portfolio needs to be shifted from convertible debentures and bonds, to common. Demonstrate how this is done, and compute the resulting profile

There are numerous "trick" concepts on the I and II, especially in subtleties within item sets and multiple choice options, but these diminish greatly on the III. Reading too much for tricks into the III, in fact, can get us into an over thinking problem. Because focus is so crucial and there is a lot to get done in little time, take the exam questions on III for what they aregood background data and honest set-ups for whats being asked for. The exam will not mislead you with misstatements of facts or data on essay questions like it will on multiple choice or item sets.

Take a question like the above at face value and believe the exam that the change is needed as a going-in assumption. We will certainly TEST that assumption with a lot of pro/cons, but dont over sweat the question. In fact, if its obvious that the adjustment is a GIVEN, forget about the IF of the change and get into the HOW:

  • Yields of both categories of investment (see S7 guide for examples)
  • Conversion ratios (S7 too)
  • PVs
  • People involved in the transactions and what they cost
  • Detailed process steps (sell A before you buy B)
  • "ABC can be converted, FGH will have to be sold on the open market..."

Then, build a cost/return table of the cash flows and PV the differences

In addition to the value differences, comment (quantitatively) on differences and similarities between the two portfolios in conversion features, credit risk, match to client objectives and appetite for risk, offsets, tax differences, etc. if applicable (meaning: the data was given in the question or supporting exhibits that would allow a comment).

A Final Key Practice Exercise

We spent a lot of time in the previous study guides on formulas, calculations and tables that showed English versions and graphic diagrams of formulas, as well as how ratio denominators go up/down, etc. The reason for this emphasis is now clear: at level III we are not only required to be able to do the calculations, but our word-explanations of the results interwoven with principles is the key to acing the essay format!

Calculate a formula like a yield and then practice writing it out in words. Several competing assets over a fixed time frame with variations of different periods (as in a mathematical period or frequency like a metronome) can be more simply described as:

"Money market funds usually have a lower yield but are safer, Stocks have the least predictable periodic payments and regular yields but appreciation can make total return attractive, and bonds offer higher returns than money market funds but fluctuate in opposition to interest rates, risking decreased value with interest rate inflation..."

This may look extremely basic and obvious, but it is only so because the advanced analysts brain has been so conditioned to translate ratios effortlessly. Underneath the simple statement are a ton of ratios, formulas and mathematical relationships. Moving comfortably between the formula and word versions of a concept is the essence of translating complex models into reports that are useful to, and understandable by, private and institutional investors.


"The harder you work, the harder it is to surrender. Dont just tell someone something, show them the reasons"

-Vince Lombardi

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