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Zunniyaki · 2023年05月05日

为什么B和C不对?

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NO.PZ202206140600000202

问题如下:

Based on the client’s investment mandate, the most appropriate appraisal measure for McNeil to use is the:

选项:

A.Sortino ratio. B.Treynor ratio. C.information ratio.

解释:

Solution

A is correct. Given that the fund mandate requirement is for a short-term return in excess of the risk-free rate, the Sortino ratio is a more appropriate measure because it penalizes returns below a specific return—in this case, 1.5% above the risk-free rate.

B is incorrect. The Treynor ratio penalizes returns below the risk-free rate. It will not measure the fund’s ability to meet the requirement of a short-term return in excess of the risk-free rate.

C is incorrect. The information ratio evaluates the portfolio return relative to a benchmark. It will not measure the fund’s ability to meet the requirement of a short-term return in excess of the risk-free rate.

1.5%above the risk free rate不就是相当于一个benchmark么?这道handbook题目有讲解嘛?

2 个答案

笛子_品职助教 · 2023年07月03日

嗨,努力学习的PZer你好:


老师你好,C选项虽然公式里没有risk-free,但就像题主问的,不能把r_B看为Rf+1.5%吗? 本质上也就是一个benchmark而已,rf+1.5%不能当作benchmark吗?


即便如此,C也不选的。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

笛子_品职助教 · 2023年05月07日

嗨,从没放弃的小努力你好:


1.5%above the risk free rate不就是相当于一个benchmark么?这道handbook题目有讲解嘛?


如果把1.5% + risk free rate理解为Benchmark,B也是不正确的。

我们从Treynor ratio的公式可以看出,Treynor ratio的benchmark,并不是1.5% + risk free rate,而是一个index。



注意公式,分母是portfolio的Beta,而portfolio的Beta是基于一个index指数(benchmark)算出来的。如果benchmark是risk - free rate,是计算不出Beta的。


因为Beta公式为:贝塔系数 = (Cov(rp,rm)) / (σp * σm)


而risk free rate的波动性为0,也就是公式的σm =0,分母为0,无法除。


至于C选项,信息比率的公式:

公式里没有risk - free,因此体现不出1.5%above the risk free rate的要求。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

IVALAINE · 2023年07月02日

老师你好,C选项虽然公式里没有risk-free,但就像题主问的,不能把r_B看为Rf+1.5%吗? 本质上也就是一个benchmark而已,rf+1.5%不能当作benchmark吗?

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