# Level I Review, Quantitative Methods

Quant methods can either be fairly easy points or it can be a constant struggle. The material is very basic and worth some significant points across all three CFA exam levels. The study session is worth 12% of the Level I CFA Program and between 5-10% of the second test. While there is no new material in CFA Level III, you will need to use the material learned in the other two tests to work through the essay section.
Many candidates, having convinced themselves that they hate math, neglect the topic and pay for it with a failing score. Yes, most of this stuff will be performed by computer in your daily responsibilities but an understanding of the concepts will not only move you closer to those three little letters, it will make you a better professional. Embrace the horror that you now work in an analytical field and need to know how to calculate basic quantitative formulas.
Time Value of Money
The most important thing here is be able to use your calculator to solve for any one of the missing variables. Note that the Institute usually keeps problems within the realm of possible reality so if you get an answer that seems extremely high or low then you need to go back through the calculation to make sure you did it correctly. Remember that payments
Make sure you divide the annual rate by the number of times it is compounded within your formula. (i.e. \$100 at 8% compounded quarterly for two years = \$100 (1.02)8  is different than simply \$100 (1.08)2
Most calculators calculate cash flows as an ordinary annuity, where payments come at the end of the period. Make sure you set the “begin” key for any annuity due problems where payments come at the beginning of the period. Also, remember that the payment and present value inputs will have opposite signs (i.e. since the payment represents an outflow use a negative sign).
**Important** Get in the habit of clearing out your calculator before or after you work a problem. It is as easy as two quick keystrokes (2nd and Clr Wk) and can save you points on the test.
Discounted Cash Flow
This is arguably the most important reading in the study session and you will see the concepts across all three exams.
The first section covers NPV and IRR which are really two sides of the same coin. NPV is the value today of the series of cash flows at a discount rate. IRR is the discount rate at which NPV is zero. Either one can be used in a budgeting decision. As with much of the material, understand the situations where each is more appropriate and the strengths/weaknesses of each concept.
Time-weighted returns measure the rate of growth over a defined period between cash flows. It should be used when the portfolio manager does not control cash in and out of the account (as is usually the case). Money-weighted returns can be done easily using the cash flow function on your calculator but may not be as applicable unless you have discretion on cash flows.
Know the difference and how to calculate the material in money market yields section (i.e. money market yield, bond equivalent yield, and HPY). These are good formulas for flash cards if you’re having problems.
Statistical Concepts and Market Returns
As with much of the quant methods material, you should start with an understanding of the basic concepts before worrying too much about the different variations. It is much more important to master the concept of standard deviation than to work through the material too quickly trying to get a vague idea of everything.
Geometric and Arithemetic averages are important. The arithmetic mean is simply the sum of observations divided by the number of observances while the geometric mean is the compound return by taking the nth root of the product.
The Sharpe ratio is a key concept throughout the curriculum and you need to understand what it means as well as how to calculate it. It measures the excess return on an investment or portfolio and can be used to rank opportunities. You will use iterations of this formula in many other concepts (i.e. Roy’s Safety First). The drawback is that, since it uses standard deviation as a measure of risk, it is most applicable for symmetric distributions and may overstate risk-adjusted performance.
Understand that the mean, median and mode are the same in a normal distribution but different with skewness. Don’t worry too much about calculating kurtosis or skewness, just understand the their implication. (i.e. how it affects dispersion and returns)
Probability Concepts
The most important material here is covariance, correlation and being able to do the calculations for expected value, variance and standard deviation for a two-asset portfolio. The formulas can get kind of long but they are pretty basic. This is the material that will be used most through the other levels of the exams as well.
Remember, the expected return is just the weights of each asset times their respective expected returns. Correlation between two assets ranges from -1 (perfect negative relationship) and +1 (perfect positive relationship).
Besides outright learning the material (always best) you need to put yourself in the shoes of the CFA exam developer. Within a multiple choice format it is far easier to test list-type questions (advantages and disadvantages of different options) and calculable answers than it is to dig deeply into the material.
Study session three in the CFA level I curriculum is also quant methods, so we will revisit it next week. If you didn’t see it, make sure to check out the posts on study session one.
‘til next time, happy studyin’
Joseph Hogue, CFA

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