2004 CFA L3 – Study Tips

Schweser CFA Level 3 Study Tips 2004

Test Format

As you no doubt are aware, your Level 3 examination will be 50 percent essay and 50 percent multiple choice (item set), with the essay portion in the morning and the multiple choice in the afternoon. Since AIMR® doesn’t release old multiple choice questions, it’s very difficult to predict what you’ll see in the afternoon session. However, we have provided many old AIMR® essay questions, as well as new ones we’ve written, to help you prepare. You’ll find these questions in our study notes.

Your 2004 Level 3 Study Guide states that 10 percent of the exam will be Ethics and Professional Standards, 0 to 10 percent will be quantitative analysis, 30 to 40 percent asset valuation (Equity, Debt, and Derivatives), and 40 to 60 percent Portfolio Management. Remember that AIMR reserves the right to test material in either essay or multiple choice format. For example, the new material on behavioral investing is quite suitable as a portion of an essay or multiple choice question. Even Ethics, which is an odds-on favorite for item set format, could show up as part of an essay.

Content

There is a lot of new material this year, much of it in derivatives. If I were making my CFA®-season study plan (I’ve included a sample 18-week plan in book one of our study notes), I would definitely plan extra time at the end to go back and re-study that material. Also, the behavioral/psychological investing material isn’t particularly difficult, but I would read it thoroughly and be familiar with it. Study Session 18 (global investing) is new this year, but it doesn’t really add much to the curriculum. Much of it was already covered in material that was removed from other study sessions for 2004.

Strategy

DO NOT take Level 3 lightly! I strongly recommend that you make a study plan and follow it throughout the season. And don’t deviate from your plan assuming you can “make it up” in the coming weeks. I realize this is very tempting, but I speak from experience in saying it’s very difficult to make up for lost time!

If at all possible, maintain a steady exercise program. Try to eat right and get plenty of sleep, especially in the 6 – 8 weeks before the exam. Keeping yourself in good shape will help keep your mind and body sharp under the stress of the exam.

Quantitative Methods: Study Session 3

Quantitative methods is always a sure thing for the exam. Look for a regression output that you will have to utilize/analyze. You will probably be asked to forecast the value of a dependent variable using the coefficients, as well as evaluate the significance of the individual coefficients and the overall model. I strongly feel that you will be asked to “fill in the blanks” in an ANOVA output. Here is a sample regression output including the ANOVA output with the relationships of the various cells, so you can get a start on feeling comfortable with the process:

(The model is trying to estimate a home building company’s annual sales as a function of GDP and changing interest rates.)

df = degrees of freedom; SS = sum of squares; MSS = mean sum of squares; n = total observations;
k = number of independent variables

Estimated model: annual sales = 6.0 + 0.004(GDP) – 20.5(Change I)
Fcritical at the 5% level of significance with dfnumerator = 2 and dfdenominator = 19 is 3.52.
Tcritical at the 5% percent level of significance (two-tailed t-values with df = 19) = 2.093

Conclusions:

  • F is highly significant, meaning at least one of the independent variables is statistically significant.
  • The r-square is marginal; the model explains 67% of the company’s annual sales.
  • The adjusted r-square adjusts for the number of independent variables, because as the number of independent variables increases, the r-square will increase whether or not the model is better.
  • In this model only change in interest rates is significant in explaining the company’s sales (t = –5.758). However, for the exam remember that even though GDP is not found to be significant (t = 1.327 < 2.093), you would use all the model’s coefficients in forecasting the company’s future sales (the dependent variable).

Quantitative methods will most likely be tested in item set format during the afternoon session of the exam, and can be extremely challenging. Look for quant concepts overlapping other sections (e.g., factor models, portfolio theory).

Important topics in quantitative methods include:

  • Multiple Regression
    Understanding how to read an ANOVA table and how to interpret the economic meaning of results from a multiple regression analysis are your keys to success in this Study Session. You should be able to calculate t-statistics for regression coefficients, calculate confidence intervals for slope coefficients or for forecasts, and calculate predicted values. Understand the relationship between R2 and adjusted R2. Understand terminology and implications associated with multicollinearity, heteroskedasticity, and serial correlation. The flow chart on page 156 of Book 1 should help you synthesize this material.
  • Time Series Analysis
    A successful candidate will be able to understand how to forecast based on an autoregressive model that may contain a seasonable lag component. Understand the difference between a trend model and a lagged model. The flow charts on page 198-199 should be extremely helpful in grasping the “big picture” flow of the material. You should know how to calculate a time series trend, determine whether a model is covariance stationary (including calculating the appropriate t-test statistic) or has a unit root, and test for lags in terms of t-statistics and autocorrelation. Make sure you can calculate one-step-ahead and two-step-ahead forecasts for out-of-sample forecasts.
  • Portfolio Concepts
    This material contains two main themes: single-factor models (e.g., CAPM) and multiple factor models (e.g., statistical factor models, macroeconomic factor models, and fundamental factor models). For single-factor models, you need to know how to calculate expected return, variance, covariance, and correlation; construct and interpret the efficient frontier and the impact of correlation on its shape; and understand the construction of and terminology associated with the capital market line and the capital asset pricing model. Remember, a capital allocation line is nothing more than the capital market line constructed from a limited number of possible assets, rather than the entire market.

The ability to exploit arbitrage relationships is a key topic for multiple factor models. Tracking error is big across the curriculum, and the topic of applications for construction of a tracking portfolio ties in nicely with portfolio management (benchmark error), debt, derivatives (tracking error of synthetic positions compared to the index), and alternative investments. Understand the difference between a factor portfolio and a tracking portfolio.

There has been some confusion over unit roots and random walks, so here is some clarification and new information that might help. First, for a simple linear regression time series (time is the only independent variable), a random walk has a unit root, so random walk and unit root are effectively the same thing. Also, the coefficient cannot be greater than 1.0.

For a multiple regression time series (several independent variables) none of the coefficients can be equal to or greater than 1.0. That is, none of the independent variables can have a unit or explosive root. Also, you cannot use a t-test to determine whether a coefficient is statistically different from 1.0. For example, a coefficient of 0.8 with a standard error of 0.2 would be significantly different from zero (t = 4.0) but insignificant from 1.0 using a t-test (t =1.0). Don’t worry about this concept. For the exam just be concerned with whether the coefficient is different from zero (t-test) and is not 1.0 or greater.

Portfolio Concepts

Arbitrage Portfolios (Book 1, Page 240)

An arbitrage portfolio has the following characteristics:

  • Factor sensitivities of zero to all factors (no risk).
  • Positive expected cash flow.
  • An initial investment of zero.

Arbitrage portfolios are formed by simultaneously going short in one portfolio and long by the same dollar amount in another. The portfolios have the same factor sensitivities, but the expected return on the short portfolio is less than the expected return on the long portfolio.

Deriving an APT Equation

An arbitrage opportunity exists if we can create an arbitrage portfolio by going long in one portfolio (positive weights) and short in another (negative weights).

Example:

The figure below shows three sample portfolios with sensitivities for a one-factor model. Determine the parameters of the one-factor model that are consistent with these expected returns and factor sensitivities.

Expected Returns and Factor Sensitivities

Portfolio / Expected Return / Factor Sensitivity (βp,1)
X / 14.35% / 1.25
Y / 11.35% / 0.8
Z / 13.60% / 1.1

Expressing the expected returns in the form of a one-factor model, we have three equations and two unknowns. We need to do a little math to solve for the two unknowns (RF and λ1). The three equations are:

  • E(RX) = RF + 1.2λ1 = 14.35%
  • E(RY) = RF + 0.8λ1 = 11.35%
  • E(RZ) = RF + 1.1λ1 = 13.60%

To solve for the value of λ1, we subtract equation 2 from equation 1:

0.4λ1 = 3.0% → 1.0λ1 = 7.50%

Plugging this value into equation 3 yields the value for RF:

RF + 1.1(7.5%) = 13.6% → RF = 5.35%

The APT equation is, therefore:

E(Rp) =5.35 + (7.50%)βp,1

Note: βp,1 is the sensitivity of the portfolio to the single factor, λ1.

Identifying Arbitrage Opportunities

Example:

Portfolio A has an expected return of 12% and a factor sensitivity of 1.07. Determine whether an arbitrage opportunity exists, and discuss how this opportunity can be exploited.

Answer:

Using the arbitrage equation we derived, we calculate the expected return for A:

E(RA) = 5.35 + (7.50%)1.07 = 13.4%

The consensus expected return for A is 12% and our APT model says it should be 13.4%, so A is overpriced relative to this risk factor.

Exploiting Arbitrage Opportunities

To take advantage of this arbitrage opportunity, we will first find a combination of portfolios X and Y that has the same factor sensitivity (1.07) as portfolio A*. Because this other portfolio will also be consistent with the APT, it should have a return equal to 13.4%. Then we can create an arbitrage portfolio by going short in A and long in the other portfolio.

Expected Returns and Factor Sensitivities

Portfolio / Expected Return / Factor Sensitivity (βp,1)
X / 14.35% / 1.25
Y / 11.35% / 0.8
Z / 13.60% / 1.1

First we find a combination of X and Y that has a factor sensitivity of 1.07. This is a combination of two-thirds (0.666) X and one-third (0.333) Y:

  • βx+y,1 = (0.666)(1.2) + (0.333)(0.8) = 1.07
  • E(Rx+y) = (0.666)(14.35%) + (0.333)(11.35%) = 13.4%.

* Note: Only portfolios X and Y were used to simplify the mathematics. You would no doubt be given the correct combination on the exam. Also, I took minor liberties in rounding.

Portfolio XY has the same factor sensitivity as A (1.07) but a higher expected return (13.4% percent versus 12%). Assume you short $50,000 of A and invest the entire proceeds in XY for one year. The net (risk-less) cash flow to this costless strategy is:

Cash Flow to Arbitrage Portfolio

Factor Sensitivity (β1) / Initial Cash Flow / Cash Flow in One Year
Short Portfolio A / –1.07 / $50,000 / –$50,000 × 1.120 = –$56,000
Long Portfolio XY / 1.07 / –$50,000 / $50,000 × 1.134 = $56,700
Total / 0.00 / $0 / $700

Factor Portfolios (Book 1, Page 243)

A factor portfolio is a portfolio with a factor sensitivity of one to one factor and zero for all other factors. It represents a pure bet on that factor. In order to create a factor portfolio, three relationships must hold:

  • The sum of the portfolios’ weights in the factor portfolio must equal one.
  • The weighted average of the factor sensitivities to the factor we want to gain exposure to must equal one.
  • The weighted average of the factor sensitivities to the other factor we do not want exposure to must equal zero.

Example: Calculating Factor Weightings for a Factor Portfolio

Assume the two-factor (real interest rates and GDP) APT equation is:

E(Rp) = 3.0% + 5.0%βp,GDP + 6.0%βp,INT

Given the factor sensitivities for each portfolio below and the APT equation, calculate the expected returns of a factor portfolio, which takes a bet on GDP growth without taking on any interest rate risk. That is, construct the portfolio with a factor sensitivity of 1.0 to GDP and 0.0 to interest rates.

Portfolio Expected Returns and Factor Sensitivities

Portfolio / Expected Return / GDP Factor Sensitivity (βp,GDP) / Int. Rate Factor Sensitivity (βp,INT)
D / 20.10% / 1.02 / 2.00
E / 14.00% / 0.88 / 1.10
F / 12.05% / 1.15 / 0.55

Answer:

  • Equation 1:wD + wE + wF = 1.0
  • Equation 2: 1.02wD + 0.88wE + 1.15wF = 1.0
  • Equation 3: 2.00wD + 1.10wE + 0.55wF = 0.0

To find the combination (weights of D, E, and F in the factor portfolio) and then calculate its required return, you would have to solve the system of equations. I find it hard to believe AIMR would ask you to do that, but you can look at the appendix for Book 1 for an example of how to solve a system of three simultaneous equations. What is more likely for the exam is that you would be asked to set up the equations as above. You will notice that equation:

  • 1 forces the weights of the portfolios to in the factor portfolio to equal 1.0
  • 2 forces the weighted average factor sensitivity to GDP equal to 1.0
  • 3 forces the weighted average factor sensitivity to interest rates to 0.0

Market IndexesGlobal Equity: Study Session 5

Know the differences in methodology for price-weighted, market value-weighted, and unweighted (equal-weighted) indexes and their built-in biases. For example:

  • Changes in the prices of higher priced stocks have more of an impact on a price-weighted index than do changes in lower priced stocks.
  • Firms with a greater market value have the greater impact on value-weighted indexes.
  • Use of the geometric average return for an unweighted index causes a downward bias.

Adjusting the divisor to calculate the value of a price-weighted index is unlikely for the exam, but know why it is done. Also, be able to determine the proper type of benchmark index to use, given the construction of the managed portfolio.

I can’t imagine you’ll have to actually calculate an index or the return on an index for the exam. I would be more concerned with knowing the construction methodologies and any biases incorporated into the indexes. Remember, for benchmarking you need to select an appropriate index (i.e., one constructed in the same manner as your managed portfolio).

Global Equity

You should be able to discuss the following topics:

  • The arguments for and against international diversification.
  • The difference between country and industry factors as they relate to portfolio diversification.
  • Barriers to global investing, such as political barriers, inefficient markets, differing market regulations, low trading volume, and lack of information.
  • Benefits and difficulties associated with investing in emerging markets.

Check out the summary table on page 315 of Book 1 of the Schweser Study Notes.

The return to an international investment is approximately the sum of the return on the investment in its currency (the local currency) and the currency return. This is a fairly easy concept and is covered on page 288 of Book 1. International investing barriers are important for the test (page 298). There seems to be a move toward global and away from international (i.e., be able to discuss why it’s not enough to diversify by country alone). Industry factors are becoming more and more important. The emerging markets material is always popular, but of course evidence about whether correlations increase or decrease in crisis is conflicting. Be able to discuss how international economies are becoming more correlated over time.

Debt Securities: Study Session 6-7

Debt Securities will comprise about 10 percent of the exam and will probably be tested in the item set format in the afternoon session of the exam. Prior to entering the exam center, you should be familiar with the following:

International Bond Portfolios

Be prepared to calculate the local bond excess and currency returns as part of an analysis to determine which strategy should be used in the international bond markets (i.e., no hedge, full hedge, proxy hedge, cross-hedge).

Start by determining which bond promises the greatest excess return above its local risk-free rate and then determine the optimal hedging strategy using that bond. See Book 2, pages 135 – 142.

Breakeven Analysis

Be able to conduct a breakeven analysis to determine the necessary change in the spread between two bonds, either both domestic or one domestic and the other foreign. You should be able to perform this calculation from the perspective of either bond.

When performing the calculation, don’t worry about whether the sign of the numerator is positive or negative. The sign has no effect on the absolute size of the yield change. Just remember this: For the bond at the disadvantage, the necessary price change is positive, meaning its yield change must be negative. For the bond at the advantage, the necessary price change is negative, meaning its yield change must be positive. In either case, you’ll find the spread must widen for the total return on the two bonds to be equal (breakeven). See Book 2, pages 144 – 150.

Downside Risk Measures

Downside risk measures as applied to bonds include target semivariance, shortfall risk, and value at risk. Be able to discuss the benefits and criticisms of each. I have a gut feeling VAR will be on this year’s exam. Be able to calculate and interpret historical and statistical VAR (using Z-values). See Book 2, pages 42 – 49.

Debt securities will comprise about 10 percent of the exam and will probably be tested in item set format during the afternoon exam session. Prior to entering the exam center, you should be familiar with the topics of bond management techniques, duration and leverage, and managing funds against liabilities.

Bond Management Techniques

You should know the pros and cons of various bond management techniques, especially bond indexing (Book 2, page 88) and enhanced indexing (Book 2, page 95), and know the conditions that lead to increased tracking error risk (Book 2, page 32).

The benefits to indexing include diversification, lower costs, and stable performance. Be able to discuss the effects on these characteristics as you move from pure bond indexing to full blown active management.

Duration and Leverage

Be able to calculate the effects of leverage (Book 2, page 58) on the duration of both domestic and international bond portfolios. You will want to read and know the fixed-income review in Book 2, starting on page 41.