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Suppose that you have estimated the expected returns and betas of the following five stocks using annual data available for the last 10 years:

Stock Market Size ($M) Beta Expected Return (%)
A 360 0.6 8
B 23 0.8 10
C 250 1.2 11
D 10 1.3 12
E 500 1.4 12

The risk-free rate of interest and the expected return on the market are 5% and 10% . You are also told that the market size of the companies in this market is normally distributed with a mean of $400M and a standard deviation of $150M.

a. Explain carefully the extent to which these data are consistent with the Capital Asset Pricing Model and whether there is an optimal investment strategy.

b. What would you advise an investor who would like to hold a portfolio with a beta equal to 1?

c. 'The risk of a company depends upon much than how well the stock market is doing. Beta only captures the co-movement of a company's share price with the market; and hence fails to capture various sources of risk.'

Critically assess the validity of the Capital Asset Pricing Model and its use as a benchmark for project appraisals.

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Bunny Greenfelder
Bunny GreenfelderLv2
28 Sep 2019

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Related questions

Market portfolio has an expected return of 11% and volatility of 20%. Risk-free rate is 3%. Security X and Y have betas of 1.4 and 0.9 respectively.

a) According to CAPM, what are the expected return of X and Y?

E(rm)-rf = 11% - 3% = 8%

3% +1.4*8% = 14.2%

3% +1.4 *8% = 10.2%

b) What should be X worth today, if X pays a dividend of $1.2 one year from today and is priced at 30 one year from today? The required rate of return is the expected return using CAPM from part a).

c) If security X has expected return of 15%, is it underprice/overprice/fairly priced according to CAPM? What is its alpha?

d) Plot SML and label X, Y and Market portfolio on the line.

e) What is the beta of a portfolio with 50% in X and 50% in Y?

f)What is the beta of a portfolio with 55% in Market portfolio and 45% in risk-free asset?

g) You are investing in a complete portfolio. The complete portfolio is composed of risk-free asset and a risky portfolio, P, constructed with 20% in X and 80% in Y. It turns out that your complete portfolio has an expected rate of return of 9.4%. What is the beta of your complete portfolio? (hint: you may or may not use all information to solve this problem)

Q2. Stock A has a beta of 1 and standard deviation of 50%. Market portfolio has a standard deviation of 20%. What is the correlation of stock A with the market portfolio? How much of stock A’s total risk is due to market risk?

Q3. Assume the risk-free rate is 8% and the expected rate of return on the market is 18%. A stock has an expected return of 6%. What is its beta?

Question 1-1

Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of -0.3, and a beta coefficient of -1.5. Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?

Problem 1-2

Assume the risk-free rate is 6% and that the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7?

Problem 1-3

Suppose rRF = 5% rM = 10%, and rA = 12%

Calculate stock A’s beta.

If stock A’s beta were 2.0, then what would be A’s new required rate of return?

Please forgive me, I posted the first part of this question (the main body) but forgot to post the rest of the question. So here is the full question. Thank you.

Problem 1:

You invest in a portfolio of 5 stocks with an equal investment in each one. The betas of the 5 stocks are as follows: .75, -1.2, .90, 1.3, 1.5. The risk free return is 4% and the market return is 9%. (Not a multiple choice problem)

A. Compute the beta of the portfolio

B. Compute the required return of the portfolio

Problem 2:

You are given the following probability distribution for a stock: (Not a multiple choice problem)

Pr. Outcome.5
.4 10%
.1 -6%
.5 12%

A. Compute the expected return of this stock

B. Compute the standard deviation

Problem 3:

You are given the following probability distribution for a stock: (Not a multiple choice problem)


Pr. Outcome.6
.4 -4%
.6 12%

A. Compute the expected return

B. Compute the standard deviation

C. Presuming the stock returns are normally distributed, what do these results indicate?

Problem 4:

A stock has a beta of 0.8. The market return is 14% and the risk free return is 3%. Compute the required return for this stock.

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