NO.PZ2017092702000088
问题如下：
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%
解释：
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, recognize that 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.
老师，看到这道题我第一思路是：E（Rp）=7%，方差=13%，Rl=4%，可求出SFR=23%。题目问 target fali，我理解意思是寻找SFR＞23%的数字，因为这样Rl就会＜4%，没有达到minimize的要求，我陷在这个思路里出不来了，没有想到用标准化公式。请老师帮忙指点迷津，谢谢！
