FINS2624 Chapter Notes - Chapter 9-12: Risk-Free Interest Rate, Capital Asset Pricing Model, Risk Premium

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16 May 2018

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Chapter 9

- The CAPM assumes that investors are single-period planners who agree on a common input

list from security analysis and seek mean-variance optimal portfolios

- The CAPM assumes that security markets are ideal in the sense that: they are large and

investors are price takers, there are no taxes or transaction costs, all risky assets are publicly

traded, investors can borrow and lend any amount at a fixed risk free rate

- With these assumptions all investors hold identical risky portfolios. The CAPM holds that in

equilibrium the market portfolio is the unique mean-variance efficient tangency portfolio.

Thus a passive strategy is efficient

- The CAPM market portfolio is a value weighted portfolio. Each security is held in a proportion

equal to its market value divided by total MV of all securities

- If the market portfolio is efficient and the average investor either borrows nor lends, then the

risk premium on the market portfolio is proportional to its variance and to the average

coefficient of risk aversion across investors

- The CAPM implies that the risk premium on any individual asset or portfolio is the product of

the risk premium on the market portfolio and the beta coefficient, where it is equal to the

covariance of the asset with the market portfolio as a fraction of the variance of the market

portfolio

- When risk-free investments are restricted but all other CAPM assumptions hold, then the

simple version of the CAPM is replaced by its zero-eta potfolios epeted ate of etu

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Document Summary

The capm assumes that investors are single-period planners who agree on a common input list from security analysis and seek mean-variance optimal portfolios. With these assumptions all investors hold identical risky portfolios. The capm holds that in equilibrium the market portfolio is the unique mean-variance efficient tangency portfolio. The capm market portfolio is a value weighted portfolio. Each security is held in a proportion equal to its market value divided by total mv of all securities. If the market portfolio is efficient and the average investor either borrows nor lends, then the risk premium on the market portfolio is proportional to its variance and to the average coefficient of risk aversion across investors. When risk-free investments are restricted but all other capm assumptions hold, then the simple version of the capm is replaced by its zero-(cid:271)eta po(cid:396)tfolio(cid:859)s e(cid:454)pe(cid:272)ted (cid:396)ate of (cid:396)etu(cid:396)(cid:374)

Related Questions

Choose the correct answer:

The beta of an efficient portfolio: a. must be 1 since an efficient portfolio is perfectly positively correlated with the market portfolio.

b. is proportional to 1, depending on the proportion invested in the market portfolio.

c. is equivalent to the portfolio's standard deviation, since standard deviation is the measure of risk for an efficient portfolio.

d. is always less than 1.

Security A has a greater level of systematic risk than security B. The expected equilibrium return for A must be greater than that for B because:

a. B's price will fall as investors realize that B offers lower returns.

b. if it is not, then A's price will fall and B's price will rise as investors sell A and buy B.

c. the Security Market Line is negatively sloped.

d. the standard deviation of A's return is greater than B's.

In case of a simple CAPM being used to estimate a time series data:

a. the mean of a residual risk should be equal to zero.

b. the regression coefficient should be equal to zero.

c. the difference between the market return and the riskfree rate of return should be equal to zero.

d. the beta of the portfolio should be equal to zero.

In a CAPM framework, prohibiting short sales:

a. will prohibit investors from holding the market portfolio in equilibrium.

b. will make the security market line steeper.

c. will encourage investors to hold more riskless assets.

d. will not change the equilibrium.

Please answer all of the following questions

1) In a CAPM framework, prohibiting short sales:

a. will prohibit investors from holding the market portfolio in equilibrium.

b. will make the security market line steeper.

c. will encourage investors to hold more riskless assets.

d. will not change the equilibrium.

2) The beta of an efficient portfolio:

a. must be 1 since an efficient portfolio is perfectly positively correlated with the market portfolio.

b. is proportional to 1, depending on the proportion invested in the market portfolio.

c. is equivalent to the portfolio's standard deviation, since standard deviation is the measure of risk for an efficient portfolio.

d. is always less than 1.

3) Which of the following is not a general conclusion of studies of stock prices?

a. The serial correlation in daily returns in U.S. stocks is positive.

b. The serial correlation in longer period returns (monthly, annual) in U.S. stocks is negative.

c. Filter rules greater than 1% generally do not make money.

d. Stocks that have done well in the past are also likely to do well in the future.

e. There are more runs in daily stock prices than we would expect to find under a random walk.

4) In case of a simple CAPM being used to estimate a time series data:

a. the mean of a residual risk should be equal to zero.

b. the regression coefficient should be equal to zero.

c. the difference between the market return and the riskfree rate of return should be equal to zero.

d. the beta of the portfolio should be equal to zero.

5) The fact that superior returns can not be made by selling stocks that cut dividends is evidence of:

a. weak-form efficiency.

b. semi-strong-form efficiency.

c. strong-form efficiency

6) Which of the following is an implication of market efficiency?

a. Resources are allocated among firms that put them to the best use.

b. No investor will do better than the S&P 500 in any time period.

c. No investor will do better than the S&P 500 consistently after adjusting for risk.

d. No investor will do better than the S&P 500 consistently after adjusting for risk and transactions costs.

7) Which of the following is an attribute of futures contract?

a. There are no limits on the size of the position that any investor can take in financial futures markets.

b. Futures contracts are marked to the market on a daily basis

c. Margins for futures are more relative to other types of markets.

d. Almost all futures positions are settled by delivery.

Consider the following statement to answer Questions i-iv: You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of27%. The Treasury-bill rate is 7%. (i) One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill moneymarket fund. What is the expected value and standard deviation of the rate of return on yourclientâs portfolio?(2 marks) (ii) Suppose that your client decides to invest in your portfolio a proportion y of the total investmentbudget so that the overall portfolio will have an expected rate of return of 15%. (a) What is the proportion y? (Hint: Use CAPM formula) (b) Further suppose that your risky portfolio includes the following investments in the givenproportions: Stock A (27%), Stock B (33%), and Stock C (40%). What are your clientâsinvestment proportions in your three stocks and the T-bill fund?(2 marks) (iii) Now suppose that your client prefers to invest in your fund a proportion ythat maximizes theexpected return on the overall portfolio subject to the constraint that the overall portfolioâsstandard deviation will not exceed 20%. (a) What is the investment proportion, y? (b) What is the expected rate of return on the overall portfolio?(2 marks) (iv) Suppose that your clientâs degree of risk aversion is A = 3.5. What proportion, y, of the totalinvestment should you suggest that he invest in your fund?(2 marks) (v) The market price of a security is $40. Its expected rate of return is 13%. The risk- free rate is 7%and the market risk premium is 8%. What will be the market price of the security if itscovariance with the market portfolio doubles (and all other variables remain unchanged)?Assume that the stock is expected to pay a constant dividend in perpetuity.(2 marks) QUESTION 2: OMEGA Currently Omega Corporationâs shares are selling at $60 per share and company is paying $5 per share dividend. Dividends are expected to grow at an annual rate of 3% for foreseeable future. Required rate of return for investors is 12% At the same time, Heller Corporationâs shares are selling at $58 per share and company is paying $4 per share dividend. Dividends are expected to grow at an annual rate of 5% for foreseeable future. Required rate of return for investors is 12% a) Calculate the current value of each stock on the basis of Dividend Discount Model. b) On the basis of above calculation, determine either each stock is overvalued or undervalued. (5 marks)

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FINS2624 Chapter Notes - Chapter 9-12: Risk-Free Interest Rate, Capital Asset Pricing Model, Risk Premium

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