fin 3410 exam 2 chapter 7 problem set

Characterize each company in previous problem as underpriced overpriced or properly priced.

$1 discount store is overpriced Everything $5 is underpriced.

Rf=8% E(r)=18% I am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. If i think the beta of the firm is 0, when the beta is really 1, how much MORE will i offer for the firm than it is truly worth?

2If beta is zero, the cash flow should be discounted at the risk-free rate, 8%: PV = $1,000/0.08 = $12,500 If, however, beta is actually equal to 1, the investment should yield 18%, and the price paid for the firm should be: PV = $1,000/0.18 = $5,555.56 The difference ($6944.44) is the amount you will overpay if you erroneously assume that beta is zero rather than 1.

based on current dividend yields and expected capital gaines, the expected rates of return on portf a and b are 11% and 14%. The beta of a .8 while b is 1.5. Tbill is 6% E(r) is 12% S.dev a 10% b. 21% index is 20% A.If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? B. If instead you could invest only in bills and one of these portfolios which would you choose?

A. Using the SML, the expected rate of return for any portfolio P is: E(rP) = rf + *[E(rM) -rf ] Substituting for portfolios A and B: E(rA) = 6% + 0.8 * (12% - 6%) = 10.8% < 11% E(rB) = 6% + 1.5 * (12% - 6%) = 15.0% > 14% Hence, Portfolio A is desirable and Portfolio B is not. B. The slope of the CAL supported by a portfolio P is given by: S = (E(rP) － rf) /*stdev p Computing this slope for each of the three alternative portfolios, we have: S (S&P 500) = (12% - 6%)/20% = 6/20 S (A) = (11% -6)/10= 5/10 > S(S&P 500) S (B) = (14%-6%/31% =8/31 < S(S&P 500) Hence, portfolio A would be a good substitute for the S&P 500.

T-bill rate is 4% Market risk premium is 6% What should be the expected rate of return for each company, according to the capital asset pricing model? $1 discount store Everything $5 Forecast return 12% 11% s.dev 8% 10% Beta 1.5 1.0

E(r) = rf + β [E(rM) - rf ] $1 Discount Store:E(r)=4%+1.5*6%=13% Everything $5: E(r)=4%+1.0*6%=10%

Suppose investors believe that the standard deviation of the market index portfolio has increased by 50%. What does the capm imply about the effect of this change on the required rate of return on googles investment projects?

The required rate of return on a stock is related to the required rate of return on the stock market via beta. Assuming the beta of Google remains constant, the increase in the risk of the market will increase the required rate of return on the market, and thus increase the required rate of return on Google.

Rf=8% E(r)=18% A stock has an expected return of 6% what is its beta?

Using the SML: 6% = 8% + β(18% - 8%) -> β= -2/10 = -0.2

2 advisors are comparing performance. Once avg 19% return and the other 16%. However the beta of the first adviser was 1.5 while that of the second was 1. A.Can you tell which adviser was a better selector of indv stocks B.If the tbill rate were 6% and the market return durning the period were 14% which adviser would be the superior stock selector. C.What if the tbill rate were 3% and the market return were 15%

24. We denote the first investment advisor 1, who has r1 = 19% and b1 = 1.5, and the second investment advisor 2, as r2 = 16% and b2 = 1.0. In order to determine which investor was a better selector of individual stocks, we look at the abnormal return, which is the ex-post alpha; that is, the abnormal return is the difference between the actual return and that predicted by the SML. A.Without information about the parameters of this equation (i.e., the risk-free rate and the market rate of return), we cannot determine which investment adviser is the better selector of individual stocks. B.b. If rf = 6% and rM = 14%, then (using alpha for the abnormal return): α1 = 19% - [6% + 1.5 *(14% - 6%)] = 19% - 18% = 1% α2 = 16% - [6% + 1.0 *(14% - 6%)] = 16% - 14% = 2% Here, the second investment adviser has the larger abnormal return and thus appears to be the better selector of individual stocks. By making better predictions, the second adviser appears to have tilted his portfolio toward under-priced stocks. C.If rf = 3% and rM = 15%, then: α1 =19% - [3% + 1.5 *(15% - 3%)] = 19% - 21% = -2% α2 = 16% - [3%+ 1.0 *(15% - 3%)] = 16% - 15% = 1% Here, not only does the second investment adviser appear to be a better stock selector, but the first adviser's selections appear valueless (or worse).

Is this situation possible? Portf E(r) Beta Risk-free 10% 0 Market 18% 1.0 A 16% 0.9

Not possible. The SML is the same as in Problem 18. Here, the required expected return for Portfolio A is: 10% + (0.9 * 8%) = 17.2% This is still higher than 16%. Portfolio A is overpriced, with alpha equal to: -1.2%

T/F a. Stocks with beta of zero offer an expected rate of return of zero. b.The capm implies that investors require a higher return to hold highly volatile securities. C.you can construct a portfolio with a beta of 0.75 by investing 0.75 of the investment budget in t-bills and the remainder in the market portfolio.

A.False. According to CAPM, when beta is zero, the "excess" return should be zero. B.False. CAPM implies that the investor will only require risk premium for systematic risk. Investors are not rewarded for bearing higher risk if the volatility results from the firm-specific risk, and thus, can be diversified. C.False. We can construct a portfolio with the beta of .75 by investing .75 of the investment budget in the market portfolio and the remainder in T-bills.

Mkt Return Aggress sk Defensive stk 5% 2% 3.5% 20 32 14 A.what are the betas of the two stocks B.what is the expected rate of return on each stock if the market return is equally likely to be 5% or 20% C.if the t-bill rate is 8% and the mkt return is equally likekly to be 5 or 20% daw the sml for this economy D.Plot the two securities on the sml graph. what are the alphas of each. E.What hurdle rate should be used by the management of the agressive firm for a project with the risk characteristics of the defensive firm's stock.

A.The beta is the sensitivity of the stock's return to the market return, or, the change in the stock return per unit change in the market return. We denote the aggressive stock A and the defensive stock D, and then compute each stock's beta by calculating the difference in its return across the two scenarios divided by the difference in market return. betaA = (2 － 32)/(5 － 20) = 2.00 betaD = (3.5 － 14) /(5 － 20) = 0.70 B.With the two scenarios equally likely, the expected rate of return is an average of the two possible outcomes: E(rA) = 0.5 * (2% + 32%) = 17% E(rD) = 0.5 * (3.5% + 14%) = 8.75% C. The SML is determined by the following: Expected return is the T-bill rate = 8% when beta equals zero; beta for the market is 1.0; and the expected rate of return for the market is: 0.5 * (20% + 5%) = 12.5% The equation for the security market line is: E(r) = 8% + β(12.5% - 8%) D. The aggressive stock has a fair expected rate of return of: E(rA) = 8% + 2.0 *(12.5% - 8%) = 17% The security analyst's estimate of the expected rate of return is also 17%. Thus the alpha for the aggressive stock is zero. Similarly, the required return for the defensive stock is: E(rD) = 8% + 0.7 *(12.5% - 8%) = 11.15% The security analyst's estimate of the expected return for D is only 8.75%, and hence: αD = actual expected return-required return predicted by CAPM= 8.75% - 11.15% = -2.4% The points for each stock are plotted on the graph above. E. The hurdle rate is determined by the project beta (i.e., 0.7), not by the firm's beta. The correct discount rate is therefore 11.15%, the fair rate of return on stock D.

"If we can identify a portfolio with a higher sharpe ratio than the s&p 500 index portfolio, then we should reject the single-index. Agree or disagree?

An example of this scenario would be an investment in the SMB and HML. As of yet, there are no vehicles (index funds or ETFs) to directly invest in SMB and HML. While they may prove superior to the single index model, they are not yet practical, even for professional investors.

Is this situation possible? Portf E(r) st.dev Risk-free 10% 0 Market 18% 24 A 16% 22

Possible. Portfolio A's ratio of risk premium to standard deviation is less attractive than the market's. This situation is consistent with the CAPM. The market portfolio should provide the highest reward-to-variability ratio.

Rf=8% E(r)=18% share of stock is selling for $100. it will pay dividend of $9 per share att the end of the year. the beta is 1. what must investors expect the stock to sell for at the end of the year?

Since the stock's beta is equal to 1.0, its expected rate of return should be equal to that of the market, that is, 18%. E(r) = D+P1-P0/P0 0.18 = 9+P1-100/100 = $109

What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%? A.15% B.more than 15% C.Cannot be determined without the risk free rate.

a. 15%. Its expected return is exactly the same as the market return when beta is 1.0.