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开泰-王飞 · 2022年12月02日

为何sortino ratio最大优选 它的maxium drawdown也是最大的,综合起来不是b好一点?

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NO.PZ201909280100000908

问题如下:

Based on the IC’s primary considerations for acombined portfolio, which simulated hedge fund strategy portfolio in Exhibit 1creates the most suitable combined portfolio?

选项:

A.Merger arbitrage

B.Systematic futures

C.Equity market neutral

解释:

C is correct. Theequity market-neutral strategy makes for a combined portfolio that has astandard deviation below the maximum specified and has the highest Sortinoratio.

The primaryconsideration is that the variance of the combined portfolio must be less than90% of that of the current portfolio. Since variance is the square of standarddeviation, the maximum variance allowed is


And standard deviation is thesquare root of variance, so the maximum standard deviation allowed is


All three portfolios are belowthe maximum specified variance.

The next consideration is thatthe portfolio should maximize the risk-adjusted return with the expectation oflarge negative events. For hedge fund strategies with large negative events,the Sortino ratio is a more appropriate measure of risk-adjusted return thanthe Sharpe ratio. The Sharpe ratio measures risk-adjusted performance, whererisk is defined as standard deviation, so it penalizes both upside and downsidevariability. The Sortino ratio measures risk-adjusted performance, where riskis defined as downside deviation, so it penalizes only downside variabilitybelow a minimum target return. Of the portfolios that meet the variancerequirement, the one with the highest Sortino ratio is the portfolio with theequity market-neutral allocation, with a Sortino ratio of 1.80. Therefore, theportfolio with the equity market-neutral allocation is the most suitableportfolio for the considerations specified by the IC.

A is incorrect because theportfolio with an allocation to the merger arbitrage hedge fund strategy, whilemeeting the variance requirement, has a lower Sortino ratio (1.35) than theportfolio with an allocation to the equity market-neutral hedge fund strategy(1.80). Although the portfolio with the merger arbitrage allocation has thelowest value of maximum drawdown (5.60), the relevant measure of downside riskis the Sortino ratio. As a result, the portfolio with the equity market-neutralallocation is the most suitable portfolio given the considerations specified bythe IC.

B is incorrect because theportfolio with an allocation to the systematic futures hedge fund strategy,while meeting the variance requirement, has a lower Sortino ratio (1.68) thanthe portfolio with an allocation to the equity market-neutral hedge fundstrategy. As a result, the portfolio with the equity market-neutral allocationis the most suitable portfolio given the considerations specified by the IC.

The equity market-neutral strategy使得组合投资组合的标准差低于指定的最大值并且具有最高的 Sortino 比率。

客户主要考虑的是合并后的投资组合的方差必须小于当前投资组合的 90%。由于方差是标准偏差的平方,因此允许的最大方差为


标准差是方差的平方根,所以允许的最大标准差是


所有三个投资组合都低于最大指定方差。所以第一条都满足。

下一个考虑是投资组合应该在预期出现大的负面事件的情况下最大化风险调整后的回报。对于具有较大负面事件的对冲基金策略,与夏普比率相比,Sortino 比率是一种更合适的风险调整回报指标。夏普比率衡量风险调整后的绩效,其中风险被定义为标准差,因此它对向上(就是价格变高)的波动和向下(就是价格变低)的波动都作为分母纳入计算。 Sortino 比率衡量风险调整后的绩效,其中风险被定义为下行偏差,因此它仅考察低于最低目标回报的下行波动。在满足方差要求的投资组合中,Sortino比率最高的是The equity market-neutral strategy,Sortino比率为1.80。因此,The equity market-neutral strategy的投资组合是最适合指定考虑因素的投资组合。

如题      

3 个答案

伯恩_品职助教 · 2023年02月06日

嗨,从没放弃的小努力你好:


老师,1、maxium drawdown只是看最大的回撤,不是看最小的回撤吧,您上面是不是说错了。——其实我是想表达的是不同基金最大回撤里最小的。表达不对,应该说最小的最大回撤。。。

2、maxium drawdown只看最大回撤,Sortino同时看最大回撤和最大回撤后的涨幅,上述表述对么——不是,sortino看的是标准差向下的波动的情况最好的回报。

sortino ratio是一种衡量投资组合相对表现的方法。与夏普比率(Sharpe Ratio)有相似之处,但索提诺比率运用下偏标准差而不是总标准差,以区别不利和有利的波动。和夏普比率类似,这一比率越高,表明基金承担相同单位下行风险能获得更高的超额回报率。索提诺比率可以看做是夏普比率在衡量对冲基金/私募基金时的一种修正方式。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

伯恩_品职助教 · 2022年12月05日

嗨,从没放弃的小努力你好:


其实没必要,题目要求的是在预期负面事件下的最大风险调整后的回报,而maxium drawdown只是看最小的回撤,这两个是有区别的,打个比方,比如有次回撤比较大,但是马上又涨起来了,而且涨幅特别大,那么这个时候Sortino比率是最高的,但是maxium drawdown不是最小的

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加油吧,让我们一起遇见更好的自己!

伯恩_品职助教 · 2022年12月05日

嗨,努力学习的PZer你好:


其实没必要。题目要求的是在预期负面时间下的最大风险调整后的回报,而maxium drawdown只是看最小的回撤,这两个数有区别的,打个比方,比如有个回撤比较大,但是马上又涨起来了,而且涨幅特别大,那么这个时候Sortino比率是最高的,但是maxium drawdown不是最小的

----------------------------------------------
加油吧,让我们一起遇见更好的自己!

cika · 2023年02月04日

老师,1、maxium drawdown只是看最大的回撤,不是看最小的回撤吧,您上面是不是说错了。2、maxium drawdown只看最大回撤,Sortino同时看最大回撤和最大回撤后的涨幅,上述表述对么

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