ps5_capm

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Economics 372/572 Intermediate Finance Spring 2013

Problem Set 5: CAPM, Performance Measurement & Forward Rates

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Question 1:

Assume that we are in a CAPM economy that is, equity prices are generally corrected valued

using the CAPM model.

a. If the T-bill (riskless) rate is 6% and the market return is 15%, draw the Security Market Line

(SML) graph for this economy. Remember that the SML is on a graph with E[r] on the vertical

axis, and on the horizontal axis. Be sure to indicate the expected market return and riskfree

rate.

b. Consider two stocks: Stock A has a beta of 2, while Stock B has a beta of 0.25. What are the

expected returns to these two stocks, assuming they are priced according to CAPM? Plot the two

stocks on the SML graph.

c. Suppose a particular analyst disagrees with the CAPM predictions for expected returns on

Stocks A and B. In particular, the analyst believes that the expected return on A is 18%, and the

expected return on B is 9.5%. In the market, however, these stocks are correctly priced

according to CAPM (i.e., their market prices are consistent with the CAPM returns that you

calculated in part (b) above).

Define alpha as the difference between the markets view of the expected return and the view of

this particular analyst. Specifically, alpha is defined by the following formula:

Ea[rk] = E[rk] +

where Ea[rk] represents security analyst's view of the stock's expected return

E[rk] represents the stock's expected return if CAPM holds.

What is each stocks alpha, according to this analyst? If you agree with the analysts predictions,

will you buy or short-sell these stocks?

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Question 2. See ps5_CAPM.xls, which gives you weekly closing levels on the S&P500 index, as

well as weekly closing prices on three stocks: a pharmaceutical company, an auto company, and

a food & beverage company, over a recent 5 year period.

a. Calculate weekly rates of return on both the S&P500 and the three stocks over the entire

sample period. Then calculate the average annualized return on the index and all three

stocks over the sample period. Report only the average annualized returns; you do not

need to print out all of the week-by-week rates of return on the index and the three

stocks.

[HINT: Should you annualize each weekly return and then calculate the average of the

annualized returns, or calculate the average weekly return and then annualize the weekly

average?]

Calculate the beta of each stock relative to the S&P500 (i.e., assume the S&P500 is the

"market" portfolio). Use the formula for beta [i =i,m / m2 ]. You can use the "covar" and

"var" functions in excel for this.

b. Comment on the results to parts a. and b. Do the average annual returns look plausible

relative to the market portfolio (and each other), based on what you know (in very general

terms) about the three industries? What about their betas? Do any of the results surprise

you? If so, why?

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Question 3

(a) Suppose that the 2yr and 5yr riskless spot rates for borrowing and lending are 1% and 1.8%

respectively (where the interest rate is quoted on an annual basis, with no compounding).Suppose also that you can also arrange a contract to borrow or lend at 1.9% for a 3 year term,

starting 2 years from now. Complete the table below, indicating how much you will borrow/lend at

each point in time (assuming that you initially borrow and lend $2,000), to ensure a risk-free

arbitrage. How much free money will you have at the end of 5 years?

Time (yrs) Action

T =0 Borrow $2,000 at ____ [interest rate] for ____ [years]

T =0 Lend (i.e., invest) $2,000 at ______ [interest rate] for ______ [years]

T =2 You owe $________ on the 2 year loan that you took out at T =0

T =2 Borrow at ____ [interest rate] for ___ [years] to pay off this loan.

T =5 You owe $__________ on your ___ [year] loan

T =5 You receive $___________ on your __[year] investment

T =5 Once you have paid off the loan with your investment income, you are left with

$__________

(b) Now suppose the following: The 2yr spot rate is still 1%, and the 5yr spot rate is still 1.8%, but

both are compounded semi-annually. Also, the 3 year forward rate starting in 2 years is now

2.5% annual, also with semi-annual compounding. (So you can lock in today a 3 year borrowing

or lending contract starting 2 years from now, with 1.25% interest every 6 months.)

You do not need to complete an arbitrage table for this section. J ust report how much free money

you will have at the end of the 5 years, assuming that you initially both borrow and lend $2,000 as

before.

ps5_capm

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