YL2023-01-22 22:06:05
Module 4-官网习题-第52题-答案中所写的:The portfolio with the highest safety-first ratio minimizes the probability that the investor’s portfolio will have a value lower than $700,000 at year end.但是教材P264所写的是,Roy’s safety-first criterion (Roy 1952) states that the optimal portfolio minimizes the probability that portfolio return, RP, will fall below the threshold level, RL. 这道题中的$700,000是threshold level RL? 另外,教材P264-Example 7上方最后一段的最后一句话,所写的:When we evaluate portfolios using the Sharpe ratio, the portfolio with the highest Sharpe ratio is the one that minimizes the probability that portfolio return will be less than the risk-free rate (given a normality assumption).这道题中的$700,000是the risk free rate(given a normality assumption)? 请问最优的Roy's Safety-First Ratio 将使什么的概率(低于什么的值)最小化?
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Evian, CFA2023-01-25 03:40:59
ヾ(◍°∇°◍)ノ゙你好同学,
(1)这道题中的$700,000是一个绝对金额,不是threshold level RL,RL是一个收益率,在这个题目中,需要用($30,000+$10,000)/$700,000求RL
(2)这道题中的$700,000不是the risk free rate(given a normality assumption),同学你说的P264这段话是在对比罗伊第一安全比率和夏普比率,如下讲义截图1
(3)如下图2所示,求RL之后,求阴影面积,它越小,概率越小,投资组合表现越好
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(1)为什么要拿Roy's safety-fist Ratio和Sharpe Ratio 作比较?
(2)答复中的截图2,为什么expected return 14%是均值?
(3)答复中的截图2,?=(5.7%-14%)/22%=-0.3773不是您所写的-0.3768?查表的话,应该查0.38的值?
- 追答
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(1)因为两个公式长得非常像,分子都是超额收益,分母都是标准差,而且这两个公式都可以衡量单位风险对应的超额回报
(2)求均值=求期望,在同学其他提问中回复过这个问题
(3)截图2中的5.7%应该是5.71%,少写了一个0.01%,(5.71%-14)/22%=-0.3768
查标准正态分布表,如下图,查“-0.3768”的近似值“-0.38”,得到“0.3520”他表示截图2阴影部分占整体的比例
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书P264-Example 7上方的最后一句话,When we evaluate portfolios using the Sharpe ratio, the portfolio with the highest Sharpe ratio is the one that minimizes the probability that portfolio return will be less than the risk-free rate (given a normality assumption). 如果portfolio return 小于the risk-free rate, 那么夏普比率的分子就变成负数了,那还怎么是minimize the probability? 并且,这个minimize the probability的夏普比率是the highest?
- 追答
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SFRatio = [E(RP) − RL]/σP
可以理解为Sharpe ratio将RL替换:Sharpe Ratio = [E(RP) − Rf]/σP
假设E(RP)和σP不变,只有Rf改变,此时Sharpe ratio↑,Rf只能↓,此时投资组合收益率小于Rf的概率就被缩小了
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