【正文】 as measured by its beta, is lower than the risk of A. Thus, a typical riskaverse investor will prefer stock B. b. = () + () = () () + () () = sP 2 = sA2 + sB2 + 2 () () Corr (RA , RB) sA sB = () () + () () + () () () () = sP = = c. The beta of a portfolio is the weighted average of the betas of the ponents of the portfolio. bP = () bA + () bB = () () + () () = Chapter 11: An Alternative View of Risk and Return: The Arbitrage Pricing Theory a. Stock A: Stock B: Stock C: b. c. i. ii. To determine which investment investor would prefer, you must pute the variance of portfolios created by many stocks from either market. Note, because you know that diversification is good, it is reasonable to assume that once an investor chose the market in which he or she will invest, he or she will buy many stocks in that market. Known: Assume: The weight of each stock is 1/N。 that is, for all i. If a portfolio is posed of N stocks each forming 1/N proportion of the portfolio, the return on the portfolio is 1/N times the sum of the returns on the N stocks. Recall that the return on each stock is +bF+e. a. Since Var, a risk averse investor will prefer to invest in the second market. b. Corr Since Varaverse investor will prefer to invest in the second market. c. Since , a risk averse investor will be indifferent between investing in the two market. d. Indifference implies that the variances of the portfolio in the two markets are equal. This is exactly the relationship used in part c. a. Let X= the proportion of security of one in the portfolio and (1X) = the proportion of security two in the portfolio. The condition that the return of the portfolio does not depend onimplies: Thus, P=(1,2)。 . sell short security one and buy security two.b. Follow the same logic as in part a, we have Where X is the proportion of security three in the portfolio. Thus, sell short security four and buy security three. this is a risk free portfolio!c. The portfolio in part b provides a risk free return of 10% which is higher than the 5% return provided by the risk free security. To take advantage of this opportunity, borrow at the risk free rate of 5% and invest the funds in a portfolio built by selling short security four and buying security three with weights (3,2).d. Assuming that the risk free security will not change. The price of security four ( that everyone is trying to sell short) will decrease and the price of security three ( that everyone is trying to buy ) will increase. Hence the return of security four will increase and the return of security three will decrease. The alternative is that the prices of securities three and four will remain the same, and the price of the riskfree security drops until its return is 10%. Finally, a bined movement of all security prices is also possible. The prices of security four and the riskfree security will decrease and the price of security four will increase until the opportunity disappears. E 20% 10% 5% 0 Chapter 12: Risk, Return, and Capital Budgeting a. To pute the beta of Mercantile Manufacturing’s stock, you need the product of the deviations of Mercantile’s returns from their mean and the deviations of the market’s returns from their mean. You also need the squares of the deviations of the market’s returns from their mean.The mechanics of puting the means and the deviations were presented in an earlier chapter. = / 12 = = / 12 = E( ) ( ) = rTMsTsM = ()()() = E( )2 = b = sTM/sM2 = / = b. The beta of the average stock is 1. Mercantile’s beta is slightly greater than 1, indicating that its stock has slightly greater than average risk. a. RM can have three values, , or . The probability that takes one of these values is the sum of the joint probabilities of the return pair that include the particular value of . For example, if is , RJ will be , or . The probability that is and RJ is is . The probability that RM is and RJ is is . The probability that is and RJ is is . The probability that is is, therefore, + + = . The same procedure is used to calculate the probability that is and the probability that is . Remember, the sum of the probability must be one. Probability b. i. = () + () + () = ii. = ( ) 2 () + ( ) 2 () + ( ) 2 () = iii. = = c. RJ Probability .16 .10 .18 .20 .20 .40 .22 .20 .24 .10 d. i. = .16 (.10) + .18 (.20) + .20 (.40) + .22 (.20) + .24(.10) = .20 ii. sj2 = (.16 .20)2 (.10) + (.18 .20)2 (.20) + (.20 .20)2 (.40) + (.22 .20)2 (.20) + (.24 .20)2 (.10) = .00048 iii. sj = = .02191e. Covmj = (.16 .18) (.16 .20) (.10) + (.16 .18) (.18 .20) (.06) + (.16 .18) (.22 .20) (.04) + (.20 .18) (.18 .20) (.02) + (.20 .18) (.22 .20) (.04) + (.20 .18) (.24 .20) (.10) = .000176 Corrmj = () / () () = f. bj = (.635) (.02191) / (.01265) = Chapter 13: CorporateFinancing Decisions and Efficient Capital Markets a. Aerotech’s stock price should rise immediately after the announcement of this positive news.b. Only scenario ii (the stock price jumps to $116 and remains there) indicates market efficiency. In that case, the price rose immediately to the level that eliminated all possibility of abnormal returns. In the other two scenarios, there are periods of time during which an investor could trade on the information and earn abnormal returns. The market is generally considered to be efficient up t