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highsix · 2020年03月07日

问一道题:NO.PZ2019012201000074 [ CFA III ]

问题如下:

Ap learns that Chiyodasenko has initiated a new equity fund. It is similar to Fund 1 but scales up active risk by doubling all of the active weights relative to Fund 1. The new fund aims to scale active return linearly with active risk, but implementation is problematic. Because of the cost and difficulty of borrowing some securities, the new fund cannot scale up its short positions to the same extent that it can scale up its long positions.

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:

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.


short position不能到long position的程度,那不是应该risk降低了吗??为啥是risk升高?
1 个答案
已采纳答案

袁园_品职助教 · 2020年03月09日

同学你好!

通常我们可以通过加杠杆的方式来放大收益,例如本来我有100元,都用来买了一只股票A,当股票A涨到110元的时候,我的收益是10%;此时如果我想double我的收益,我就可以去short 股票B获得100元,买200元的股票A,这样当股票A上涨10%的时候,我获得了220元,将其中100元买回股票B(假设股票B价格不变),我净得20元,此时我的return就是20%。

而由于实际操作中,你可以无法short100元的股票B,或者short股票B的成本非常高,借一天你就要负1块钱的利息,那么当你归还股票B的时候,依然假设股票B价格不变,你要归还的是101,净收益只有19,return = 19%。

上面这两种情况的对比你会发现,持仓是一样的,即active risk都增加了,但是由于实际操作中的限制(例如借不到票,交易成本过高等),你的实际收益并不能等比例上升,所以图中的直线越往后就越弯,即斜率(即IR)是随着active risk的增加而降低的。

 

你提到的“short position 不能到 long position的程度,那么risk降低了”这一点我没有太明白,可以麻烦你讲一下具体的思路吗?我猜你是觉得 short position 才有 risk,而short position 增加的比例低于 long position 所以对比之前risk 降低了?

long 和 short position 都是有risk的,如果还有疑问,欢迎留言继续讨论,加油!

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