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如此_AnnieCcc · 2021年02月05日

问个问题

  1. CFA I
  2. Quantitative

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.

我真的看不懂看了答案也不知道在说啥子。。。。这道题我用的sfr是错的。。。要用标准正态分布，标准正态不是x-均值除以标准差吗？均值不知道啊。。。只知道标准差啊。。。return又不是均值。。。

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1 个答案

星星_品职助教 · 2021年02月06日

同学你好，

这道题要求“ the probability that the portfolio return will fail to meet the target ”，而return target=4%，所以要求的就是P(X＜4%)。

P(X＜4%)是没法直接查表求的，所以需要将其转化到标准正态分布进而查表进行求解，此时需要代入正态分布标准化的公式，

问题就转化为求P[Z＜（4%-7%）/13%]的概率，即P（Z＜-0.2308），原版书后表可以查负数，最多小数点后两位。所以P（Z＜-0.23）查出来是0.4090，即40.90%，选择B选项。

这道题不需要计算SFR。

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NO.PZ2017092702000088 问题如下 A portfolio hexpectereturn of 7% with a stanrviation of 13%. For investor with a minimum annureturn target of 4%, the probability ththe portfolio return will fail to meet the target is closest to: A.33%. B.41%. C.59% B is correct.B is correct. using Excel's NORM.S. ST() function, we get NORM.S. ST((4%-7%)/13%) = 40.87%. The probability ththe portfolio willl unrperform the target is about 41%.本题要求的P(X＜4%)的概率。第一步先做标准化后才能查表。然后代入标准化的公式即可。-------------------------------------------------------------------------There are three steps, whiinvolve stanrzing the portfolio return: First, subtrathe portfolio mereturn from easi of the inequality: P(Portfolio return – 7%) ≤ 4% – 7%). Secon vi easi of the inequality the stanrviation of portfolio return: P[(Portfolio return – 7%)/13% ≤ (4% – 7%)/13%] = P(Z ≤ –0.2308) = N(–0.2308). Thir recognize thon the left-hansi we have a stanrnormvariable, noteZ anN(–x) = 1 – N(x). Rounng –0.2308 to –0.23 for use with the cumulative stribution function (c) table, we have N(–0.23) = 1 – N(0.23) = 1 – 0.5910 = 0.409, approximately 41 percent. The probability ththe portfolio will unrperform the target is about 41 percent. 求问这道题0.59是不是要靠查表啊？题目没有给出表是不是就无法求出0.59?

2022-07-19 07:53 1 · 回答

NO.PZ2017092702000088 问题如下 A portfolio hexpectereturn of 7% with a stanrviation of 13%. For investor with a minimum annureturn target of 4%, the probability ththe portfolio return will fail to meet the target is closest to: A.33%. B.41%. C.59% B is correct.B is correct. using Excel's NORM.S. ST() function, we get NORM.S. ST((4%-7%)/13%) = 40.87%. The probability ththe portfolio willl unrperform the target is about 41%.本题要求的P(X＜4%)的概率。第一步先做标准化后才能查表。然后代入标准化的公式即可。-------------------------------------------------------------------------There are three steps, whiinvolve stanrzing the portfolio return: First, subtrathe portfolio mereturn from easi of the inequality: P(Portfolio return – 7%) ≤ 4% – 7%). Secon vi easi of the inequality the stanrviation of portfolio return: P[(Portfolio return – 7%)/13% ≤ (4% – 7%)/13%] = P(Z ≤ –0.2308) = N(–0.2308). Thir recognize thon the left-hansi we have a stanrnormvariable, noteZ anN(–x) = 1 – N(x). Rounng –0.2308 to –0.23 for use with the cumulative stribution function (c) table, we have N(–0.23) = 1 – N(0.23) = 1 – 0.5910 = 0.409, approximately 41 percent. The probability ththe portfolio will unrperform the target is about 41 percent. 請問這題爲何最終沒有用1-40.90%，謝謝

2022-04-24 23:31 1 · 回答

NO.PZ2017092702000088 老师，题目中的7%为预期回报，怎么就把他当做公式中的均值了呢？

2021-11-24 16:54 1 · 回答

NO.PZ2017092702000088 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！

2021-04-04 18:12 1 · 回答

NO.PZ2017092702000088 我想问的是u为什么是百分之7，u是均值，这里的%7不是return吗？？？

2021-02-05 16:56 2 · 回答