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chuziyang · 2022年04月24日

1-40.90%

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.

B is correct. By using Excel's NORM.S. DIST() function, we get NORM.S. DIST((4%-7%)/13%) = 40.87%.

The probability that the portfolio willl underperform 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, 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.

請問這題爲何最終沒有用1-40.90%,謝謝

1 个答案

星星_品职助教 · 2022年04月25日

同学你好,

将X<4%做正态分布标准化后,得到的是N(-0.23)

可以直接查表得到结果0.409,也可以通过转化:N(–0.23) = 1 – N(0.23) = 1 – 0.5910 = 0.409.

0.409就是最终的答案,不需要用1再去减。

HL · 2022年05月14日

讲明白了

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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?

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