可编辑 精品文档，欢迎下载 For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will have a $100,000 position (either long or short) in each stock. Net market exposure is zero, but firm-specific risk has not been fully diversified. The variance of dollar returns from the positions in the 20 stocks is: 20 [(100,000 0.30)2 ] = 18,000,000,000 The standard deviation of dollar returns is $134,164.
b.
If n = 50 stocks (25 stocks long and 25 stocks short), the investor will have a $40,000 position in each stock, and the variance of dollar returns is: 50 [(40,000 0.30)2 ] = 7,200,000,000 The standard deviation of dollar returns is $84,853. Similarly, if n = 100 stocks (50 stocks long and 50 stocks short), the investor will have a $20,000 position in each stock, and the variance of dollar returns is: 100 [(20,000 0.30)2 ] = 3,600,000,000 The standard deviation of dollar returns is $60,000. Notice that, when the number of stocks increases by a factor of 5 (i.e., from 20 to 100), standard deviation decreases by a factor of 5= 2.23607 (from $134,164 to $60,000).
8. a.
)e (22M 22σ+σβ=σ 88125)208.0(2222A =+?=σ 50010)200.1(2222B =+?=σ 97620)202.1(2222C =+?=σ
b.
If there are an infinite number of assets with identical characteristics, then a well-diversified portfolio of each type will have only systematic risk since the non-systematic risk will approach zero with large n. The mean will equal that of the individual (identical) stocks.
c. There is no arbitrage opportunity because the well-diversified
portfolios all plot on the security market line (SML). Because they are fairly priced, there is no arbitrage.