Bill Bostic, Sue Chung, and Sam De Felice were assigned the task of explaining the elements of financial management to PNC's board of directors. One session has been held thus far, and it covered an introduction to financial management. The team is now preparing for Session 2, which will take up the nature of financial risk and the relationship between risk and rates of return. Later sessions will cover fixed income securities, common stock, the cost of capital, capital budgeting, capital structure, dividend policy, financial forecasting, leasing, and merger analysis.

The risk and return session is important for three reasons:

(1) The company wants to maximize its stock value, and risk is a major determinant of value. If risk can be reduced, other things held constant, then the stock's required rate of return will fall and its value will rise. Thus, the directors need to know how investors evaluate and relate risk to required returns so that the directors can judge how their actions will affect the stock's risk and therefore its price.

(2) The rate of return investors require on different types of securities depends on their risks. PNC needs to know the required return (cost) of its different types of capital so it can determine if potential capital budgeting projects are likely to earn their costs of capital.

(3) The company's retirement program is based on a 401(k) plan in which individual employees direct their own pension asset allocations between common and preferred stocks, bonds, mutual funds, and PNC's own stock. The directors also participate in the plan, and Bill wants to make sure that they know about the risks inherent in various types of investments; in the benefits of creating diversified portfolios of bonds, stocks, and other assets, and in how optimal portfolios can differ among different investors depending on their age, risk tolerance, and other characteristics.

All of the directors invest in the stock and bond markets, and know that different types of securities hold different risks. However, the individual directors' knowledge varies considerably, and that makes it difficult to decide what to cover and how deep the coverage should go.

After much discussion, the team concluded that they should concentrate:

(1) on the difference between stand-alone risk and risk in a portfolio context;

(2) on how those two types of risk can be measured;

(3) on the differences between expected, required, and realized returns, and

(4) on how different types of risk affect different types of returns.

As in other sessions, they plan to use an Excel model both to illustrate the discussion and to help the directors become more familiar with Excel.

Bill also noted that several directors have expressed concern about the relationship between inflation and interest rates, and the risks posed by sharp changes in interest rates. Bill plans to discuss the effects of inflation on interest rates, and hence on bond prices.
As Table 1 in the background document shows, Ray Reed owns 19.6% of PNC's stock, and the officers and directors own over 50% of the shares. Most of the directors also own other securities, but Ray's personal wealth is concentrated in PNC stock, as is that of the other officers. Ray and the other officers maintain high holdings in PNC stock for three reasons:

• First, they are confident that PNC's stock will "beat the market" in the future, so they don't want to sell any of their shares.

• Second, Ray believes that managers perform better if their wealth is tied to the wealth of the company, and he invests heavily in PNC and expects his officers and directors to do likewise.

• Third, the company uses stock options in its executive compensation plan, and shares received under the plan must be held for 10 years.

Bill wonders how to handle this concentration of wealth in the risk session.

Bill provided the directors with the latest edition of a well-known finance textbook, and he informs them of the relevant chapters for each session. Most do not spend much time with this material before the sessions, but several were very much interested in the risk session and sent him some e-mail questions relating to the up-coming session:

o Director 1:

In reading the background material you provided for the risk session, I notice that the "experts" believe risk should be considered in a portfolio context. However, a number of major PNC stockholders have most of their wealth tied up in PNC stock-we are not as well diversified as the theorists assume we are. Should this fact affect the way we consider risk at the corporate level?

o Director 2:

In reading the background material, I was struck by the assumptions used to develop the CAPM. Since many of those assumptions are patently wrong, how can anyone rely on the CAPM for anything? Wouldn't it be misleading for me to use it to make personal investment decisions, and wouldn't it be misleading for the company to use it in its financial decisions?

o Director 3:

After going through the background materials for the next session, I came away with the feeling that the CAPM is probably useful for individual investors' decisions, but that it cannot be applied to the capital budgeting decisions that PNC itself must make. Am I wrong?
These three issues will be addressed in the session.

Tables 1 through 4 of the background document provide some relevant information on PNC, while Table 2-2 gives data that Sue developed for illustrations in the session. She and Bill considered using PNC itself in the illustrations, but they decided to stay with hypothetical data in this early session so people would not worry about why PNC's stock rose or fell in the different years. Bill does plan to suggest, though, that PNC's structure and market conditions are similar to Games Inc., a maker of video games sold over the Internet. After much discussion, plus some conversations with PNC's investment bankers, Bill, Sue, and Sam developed a set of issues that they plan to cover in the session. These issues are listed in Table 2-1. Assume that you are Sue Chung, and you must prepare statements regarding each of the issues.

Sue plans to develop an Excel model to generate numerical results, but the focus will be on explaining the implications of the numbers.

Q1. Find the expected returns, standard deviations (sigma), and coefficients of variations (CV) for the assets in Table 2-1, then rank the assets from least risky to most risky based on their sigmas and CVs, and discuss the pros and cons of using sigma and/or CV as a measure of investment risk.

Note that Outplace Inc. does well when the economy is weak and companies are laying off employees but badly when the economy is strong. If data were shown for an index fund designed to mirror the market, would the best guess as to its expected return and _ be equal to the expected return and sigma of the market?

Q2. Now use the data in Table 2-1b to calculate the returns and standard deviations on portfolios consisting of 50% each of Games and Outplace for the period 2000-2004. Also, calculate the correlation coefficients between Games and Outplace. Then discuss the implications of your results for the investment risks of these securities.

Q3. Now use the historical returns data in Table 2-1 to calculate Market, Games, and Outplace's standard deviations, beta coefficients, correlation coefficients with the market, and R2 values. Discuss the roles of these statistics when assessing assets' risks, and re-rank the assets from least risky to most risky.

Q4. Are the probability data given in Table 2-1a consistent with the time series data given in Table 2-1b? If the securities' expected values and standard deviations as shown in the two sets of data are different, does this prove that something is wrong with the data, i.e., that one or the other data sets must be incorrect?

Q5. Use the data in Table 2-1c to establish parameters for the SML equation and then construct a graph of the SML. Calculate the required rates of return for the various securities, and then (based on the data in Table 2-1) indicate where each security lies in relation to the SML. Do the different securities appear to be in equilibrium? If not, might the problem be with the data, i.e., might the stocks actually be in equilibrium, but the data in Table 2-1 do not correctly reflect the marginal investor's expectations? (Note that thus far we have explicitly assumed that the data in Table 2-1a do reflect investor expectations, but we also implicitly assumed that investors form expectations on the basis of historical data such as that in 2-1b. These two assumptions might be in conflict.)

Q6. Would an increase in (a) expected inflation and (b) the market risk premium have the same effect on the required return on each of the securities in Table 2-1a?

Q7. What is the covariance between Outplace and the Market, and how is the covariance interpreted? What is the correlation between Outplace and the Market? How are the covariance and the correlation coefficient related?

Q8. The following equations can be used to find the expected return and the standard deviation of a portfolio of any two stocks X and Y:

Use these equations to find (a) the expected return and (b) the standard deviation of portfolios that consist of 0%, 25%, 50%, 75%, and 100% of Outplace with the balance in the Market. Then graph your results with the portfolio's return and SD on the vertical axis and the percent in Outplace on the horizontal axis. Then construct another graph with expected returns on the vertical axis and the portfolio's SD on the horizontal axis. Then discuss your results.

Q9. Why is it important to consider the R2 and the standard error of beta as well as the value of beta itself? Then consider this statement: "The CAPM is more useful for investment management, where portfolios are being formed, than for corporate finance, where the CAPM is used to estimate the cost of a firm's common stock." Do you agree with the statement?

Q10. Prepare responses to the three directors' comments about the CAPM.