Level I Review: Quant Methods, Building Blocks going Forward

This week we begin our review of some of the most important topic areas for the Level 1 exam. We may not cover every study session before the December exam but we will hit the most important areas and try to make sure you get all the points possible.
You’ll notice that we are skipping over one of the most important topic areas in the exam, Ethics and Professional Standards. If you’ve been following the blog, you know how important this topic is but also that it does not change much from year to year. We’ve covered the Ethics section several times and you can find the most recent post by clicking here. Remember, don’t just read through the material on Ethics and the Standards. You really need to be practicing those end-of-chapter and test bank problems to get a feel for how it will be tested on the exam.

Quantitative Methods: Lower points but absolutely essential

The Quant Methods topic area may represent one of the secondary topics by points on the first exam, only accounting for 12% of your total score, but the material is absolutely critical to your success across the exams and as a professional. You may be able to get through the exams and your career with just a basic understanding of other topics (i.e. derivatives) but try being an analyst without mastering discounted cash flows and statistical concepts and it will be a short career.
Unfortunately, the section is avoided by many candidates. As someone who never really liked math in school, I can relate to the desire to avoid quant methods. Realize as I did though, you are in an analytical field and you need to embrace mathematics. Trust me, math can actually be enjoyable and you can learn to love it. Spend a little time and you will be amazed at how quickly you start understanding more complex concepts. A little effort to break an old perspective will go a long way and will help you immensely.
Quant methods are covered in two study sessions in the Level 1 exam, Basic Concepts and Application, with four readings in each study session. The first study session will be repeat material for anyone with an educational background in finance and should be fairly easy to understand for just about anyone else. Study Session 3 is a little more difficult but still manageable. Of the readings, I would say all but technical analysis are equally important and testable. Ideas like time value of money, probability and quant testing are fundamental to the curriculum and you’ll need to be able to do the math in just about every other topic area.
Make sure you have a basic understanding of technical analysis but it is probably the least important. The Institute has never really put much faith in technical analysis so you will likely only see basic questions on the exam, if at all.

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.
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.

The future value of cash flows is
FVN=PV(1+r)N
i.e. if your savings account earns interest at a 5% rate and you have $100 deposited, how much will it be worth in 20 years?
FV20=$100(1+.05)20
=$265.33
This is a fairly basic calculation with no payments and you’re more likely to see something more difficult on the exam. It is relatively easy to work through but learn to do it on your time value buttons,
PV = 100
I/Y = 5
PMT = 0
N = 20
CPT –>FV
Whether you input the present value as a negative or not doesn’t matter much here since there are no payments. For other problems, just remember that outflows (deposits and payments into an investment or account) should be negative while inflows (money you receive or value) should be positive. One of the cash flows must be negative (outflow).
The future value of a series of cash flows is only slightly more difficult but easily understandable if you think of each payment as a single future value calculation. Don’t forget the note on changing your calculator for an annuity due.
Example: The same savings account as above has $100 deposited but you plan on depositing an additional $100 per year at the end of the year. What will the balance be at the end of 20 years?
PV= -100
PMT = -100
N = 20
I/Y = 5
CPT–>FV
FV = $3,333
Make sure you understand how to solve for each variable in the equation when given the other variables.
Note: I set my calculator to four decimal places which is usually more than you will need for the exam.

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.
Both NPV and IRR are found easily with the calculator. Remember that a key assumption of IRR is that cash flows are reinvested at the rate, which may not be realistic. Also, if there are multiple cash outflows, there will be multiple IRRs or none at all. There may be a conflict between NPV and IRR when projects are mutually exclusive or when there are multiple cash outflows. In this case, NPV is preferred.
Using the calculator is relatively easy,
The initial project cost or investment is a negative (outflow) as CF0
CO1 through x are the stream of cash flows and entered as a positive (inflow)
If cash flows are an equal amount, you can enter them as F (frequency)
Press the NPV button and enter the interest rate
Down arrow
CPT–> NPV
For IRR, just press the IRR button and CPT
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 material on measures of dispersion is extremely important and will feed into the concept of risk. Even though you will be able to calculate variance and standard deviation on your calculator, spend the time to learn the formulas.
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 is the covariance divided by the product of the two standard deviations.
Correlation = COV(X,Y) / STDev (x) STDev (y)
Correlation ranges from -1 (perfect negative relationship) and +1 (perfect positive relationship).

Common Probability Distributions

Most of the introductory material here is fairly unimportant as it isn’t used much in other parts of the curriculum. The binomial distribution is a little more important because it relates to some of the derivatives material. The normal distribution is really where you want to spend your time.
Remember that 90% of the distribution will be between 1.65 standard deviations, 95% within 1.96 deviations and 99% within 2.58 deviations. You will be given a z-table but need to know the formula and the applicable number of standard deviations. You need to pay attention to the question and look for which part of the curve you are being asked to measure. Do you need an interval around the mean or just one side? All the stuff around the z-score (the formula and finding probabilities) is fairly basic so spend some time and master it.
The information covering Monte Carlo simulations is important but just definitional and advantages/disadvantages against other analytical methods.

Sampling and Estimation

Again, fairly unimportant material but it is mostly conceptual so it should be easier to remember. You won’t need much in the way of formulas but will want to understand the ideas and differences between the different sampling plans. Remember that a good estimator is unbiased, efficient and consistent.

  • Understand the difference between simple random, systematic and stratified sampling as well as advantages/disadvantages around each.
  • A carryover from the previous reading, be able to calculate and interpret confidence intervals for the different distributions. Remember, if the sample size is larger than 30 then the z-score can be used as a proxy for the t-score.
  • Probably the most important material in the reading is that on data mining, sample selection, survivorship, look-ahead and time-period biases. Understand these and the different situations in which they might occur.

Hypothesis Testing

  • Understand the difference between the null and alternative hypothesis and be able to calculate the test statistic. The p-value is the lowest level of significance at which the null hypothesis is rejected.
  • Understand the difference between a Type I and Type II error
    • Type I is where you reject the true null hypothesis (i.e. saying that the statistic falls outside of the confidence interval in a normal distribution when it does not)
    • Type II is where you do not reject a false null hypothesis (i.e. saying that the statistic lies within the confidence interval when it does not)
    • Remember the rules for setting a low or high level of significance (1% or 10%) depending on the penalty for committing either error (i.e. 1% significance if you do not want to make Type I error, 10% significance if you do not want to make Type II error)

Technical Analysis

Again, not as important as the other readings but make sure you have a basic understanding in case you see something on the exam. Understand the assumptions, especially how they relate to the theory of efficient markets, and the comparison to fundamental analysis. It does look like the Institute is putting in more charting information in the curriculum so understand the basic definitional ideas around the vocabulary (i.e. head and shoulders, double tops, neckline, etc.)
Understand what volume says about technical analysis, i.e. intensity of confidence in an up or down move.
The technical indicators are of relatively more importance than the material on charting. Understand the concept behind the price-based indicators, momentum oscillators, sentiment and flow-of-funds indicators and whether an indicator is giving a bullish or bearish signal.
That is a lot to take in for one week so you will probably want to cover one study session per week. It is pretty basic stuff if you have at least an understanding of basic statistics and algebra. We’ll start on the Financial Reporting material next week.
‘til next time, happy studyin’
Joseph Hogue, CFA

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