投资学第六版第7章课后答案

1. Because very few securities will exhibit perfectly positive correlation,diversification will tend to reduce portfolio risk. Thus, for any given level of expected return, one would expect that portfolios will exhibit lower risk (lie further to the west in the feasible set) than individual portfolios (which will therefore lie to the east in the feasible set).2. Diversified portfolios are more efficient than individual securities. That is,diversified portfolios provide the investor with higher expected returns for given levels of risk and/or lower risk for given levels of expected return when compared with individual securities.Diagrammatically, individual securities will lie in the eastern portion of the feasible set. Hence they are dominated by diversified portfolios, which lie in the northwestern portion of the feasible set, including those on the efficient set.3. The macroeconomic forces that impact the U.S. economy tend to have a strongeffect on the earnings (and, hence, stock prices) of all domestic corporations, although the magnitude of this effect will vary among industries and specific firms.For example, a recession causes most companies to experience a downturn in earnings. While some companies may be more severely affected than others, nevertheless, the broad influence of a recession on general economic activity likely results in most companies' stocks performing poorly.Companies whose stocks would be expected to have a high positive covariance are auto and steel companies. When auto sales are strong (weak), the demand for steel generally rises (falls). The earnings of companies in both industries would rise and fall at roughly the same time and this movement would likely be anticipated by the earlier rise and fall of their stocks' prices.Companies whose stocks would be expected to have a low covariance are banks and gold mining firms. Rising interest rates and poor business conditions generally produce declining bank earnings. At the same time, a pessimistic economic outlook often causes investors to increase their demand for gold, which increases the price of gold and, therefore, the earnings of gold mining firms. The result is that the stock prices of banks and gold mining firms will not likely move in the same direction.4. It is the fact that all stocks do not have high positive covariances that causesdiversification to benefit the investor. That is, by diversifying, investors can reduce portfolio risk and thereby create more efficient portfolios. If stocks did have high positive covariances, then holding a well-diversified portfolio would not result in meaningful reductions in risk relative to holding individual securities.5. If the security in question had significant negative correlation with the rest of thesecurities in the portfolio, Mule might consider purchasing it even though it had anegative expected return. The diversifying nature of the security might reduce the risk of the portfolio sufficiently to make it attractive despite its inferior return potential.6. Given the expected returns and variance-covariance estimates for all securities, aninvestor can construct the efficient set. This information, combined with the unique risk-return preferences of the investor, allows the investor to determine his or her optimal portfolio. Diagrammatically, this optimal portfolio lies at the point of tangency between the investor's indifference curves and the efficient set.7. The standard deviation of a two-security portfolio is given by:[]σσσρσσp A A B B A B AB A B X X X X =++22122/In Dode's case:= [(.35)²(20)² + (.65)²(25)² + 2(.35)(.65)(20)(25)12]½= [49 + 264 + 22812]½The portfolio's standard deviation will be at a minimum when the correlation between securities A and B is -1.0. That is:= [49 + 264 - 228]½= 9.2%The portfolio's standard deviation will be at a maximum when the correlation between securities A and B is +1.0. That is: = [49 + 264 + 228]½= 23.3%17. The beta of a portfolio is defined as the weighted average of the componentsecurities' betas. In the case of Siggy's portfolio:ββP i i i X ==∑13= (.30 ⨯ 1.20) + (.50 ⨯ 1.05) + (.20 ⨯ 0.90)= 1.07Further, the standard deviation of a portfolio can be expressed as:()σβσσεp P I p =+22212/= [(1.07)²(18)² + (.30)²(5.0)² +(.50)²(8.0)²+ (.20)²(2.0)²]½= [370.9 + 2.3 + 16.0 + 0.2]½= [389.4]½ = 19.7%18.The total risk of a portfolio can be expressed as: σβσσεp p I p =+222Further, the unique risk (σεp 2) is the weighted average of the unique risks of the portfolio's individual securities. In the case of the first portfolio with four equal-weighted securities:()()σεp i 2221430025=⨯=∑..= 56.25 ⨯ 4 = 225.0Therefore the total risk of the first portfolio is:0.225)20()00.1(2221+⨯=σ= 625.01 = 25.0%In the case of the second portfolio with ten equal-weighted securities:()()σεp i 22211030010=⨯=∑..= 9.0 ⨯ 10 = 90.0Therefore the total risk of the second portfolio is:σ222210020900=⨯+(.)().= 490.02 = 22.1%。