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花卷喵 · 2023年09月01日

加杠杆会降低information ratio

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NO.PZ201809170400000505

问题如下:

Relative to Fund 1, Chiyodasenko’s new equity fund will most likely exhibit a lower:

选项:

A.

information ratio.

B.

idiosyncratic risk.

C.

collateral requirement.

解释:

A is correct. As the new fund scales up active risk by doubling active weights, it will face implementation constraints that will prevent it from increasing the weights of many of its short positions. The information ratio (IR) is defined as the ratio of active return to active risk. If there were no constraints preventing the new fund from scaling up active weights, it could scale up active risk by scaling up active weights, proportionally increase active return, and keep the IR unchanged. Implementation constraints experienced by the new fund, however, such as the cost and difficulty in borrowing securities to support the scaled-up short positions, will prevent the active return from proportionally increasing with the active risk. Therefore, the IR would most likely be lower for the new fund than for Fund 1. As the following chart illustrates, as active risk is scaled up, implementation constraints create diminishing returns to scale for active returns, thereby degrading the IR.

可以解释一下推导过程吗?

1 个答案

笛子_品职助教 · 2023年09月01日

嗨,从没放弃的小努力你好:


Hello,亲爱的同学~

这里不是推导的,是直接根据原理写出的公式。

也就是基础讲义下,红框里的公式。


因为波动率越高,就越可能在某一次波动中,亏损大额本金。

而且复利计算中,亏损和盈利的比例是不对等的。

例如亏损33%,盈利33%,还是净亏损。亏损33%,要盈利50%才能回本。


因此才有波动率越高,复利的收益率越低。

根据这个原理,写出了以上公式。

以上二次函数曲线公式,会呈现出凹性特征:也就是说,随着风险的增加,收益并不会等比例增加。


本知识点考点有两种形式。

一是概念题,例如本题。

二是计算题,掌握下图例题即可。


协会本身并没给出推导过程,也不会要求推导过程。



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