题目
A portfolio has an expected return of 7% with a standard deviation of 13%. For an investor with a minimum annual return target of 4%, the probability that the portfolio return will fail to meet the target is closest to:
选项
A.33%.
B.41%.
C.59%.
答案
B
解析
B is correct. There are three steps, which involve standardizing the portfolio return: First, subtract the portfolio mean return from each side of the inequality: P(Portfolio return – 7%) ≤ 4% – 7%). Second, divide each side of the inequality by the standard deviation of portfolio return: P[(Portfolio return–7%)/13% ≤ (4% – 7%)/13%] = P(Z ≤ –0.2308) = N(–0.2308). Third, recognizethat on the left-hand side we have a standard normal variable, denoted by Z and N(–x) = 1 – N(x). Rounding –0.2308 to –0.23 for use with the cumulative distribution function (cdf) table, we have N(–0.23) = 1 – N(0.23) = 1 – 0.5910 = 0.409, approximately 41 percent. The probability that the portfolio will underperform the target is about 41 percent. B正确。 有三个步骤，涉及到标准化投资组合收益:首先，从不等式的每一边减去投资组合平均收益:P(投资组合收益- 7%)≤4% - 7%)。其次，等式两边同时除以投资组合收益的标准差:P[(投资组合收益- 7%)/13%≤(4% - 7%)/13%]= P(Z≤- 0.2308)= N(- 0.2308)。第三，在左边我们有一个标准正太分布的变量，用Z和N(- x) = 1 - N(x)表示。在使用累积分布函数(cdf)表时，N(- 0.23) = 1 - N(0.23) = 1 - 0.5910 = 0.409，约占41%。投资组合表现不佳的可能性约为41%。