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刘季松 · 2022年09月07日

老师,有个地方没理解

NO.PZ2016082404000024

问题如下:

You have a portfolio of USD 5 million to be hedged using index futures. The correlation coefficient between the portfolio and futures being used is 0.65. The standard deviation of the portfolio is 7% and that of the hedging instrument is 6%. The futures price of the index futures is USD 1,500 and one contract size is 100 futures. Among the following positions, which one reduces risk the most?

选项:

A.

  Long 33 futures contracts

B.

  Short 33 futures contracts

C.

  Long 25 futures contracts

D.

  Short 25 futures contracts

解释:

ANSWER: D

To hedge, the portfolio manager should sell index futures, to create a profit if the portfolio loses value. The portfolio beta is 0.65×7%6%=0.758.0.65\times\frac{7\%}{6\%}=0.758.The number of contracts is N=βSF=(0.758×5,000,000)1,500×100=25.3N\ast\text{=}-\beta\frac SF=\frac{-{(0.758\times5,000,000)}}{1,500\times100}\text{=}-25.3 or 25 contracts.

为什么0.758是portfolio的beta呢,这不应该是hedge ratio 吗,原portfolio的beta应该和对冲工具没有关系啊,谢谢

2 个答案

品职答疑小助手雍 · 2022年09月08日

一般默认期货和现货完全正相关,相关性为1,所以期货的beta等于1,所以这里portfolio的beta也可以认为是capm里的beta(其实应该按你追问里说的,不能完全等同)

品职答疑小助手雍 · 2022年09月07日

同学你好,还记得一元线性回归么,0.65是ρ,6%和7%分别是y和x的标准差,现在求Y=a+bX里的b。b就是beta。(相当于把期货合约看成X,作为benchmark来计算portfolio的beta,和你所说的hedge ratio其实没区别。)

现在用两者的线性关系连降低风险就看需要short多少份期货合约就可以了。

刘季松 · 2022年09月07日

老师,那讲义里面的那个合约数量=(β*-β)Va/Vf这个公式中的右面的β其实是期货为X,portfolio为Y这样的一个线性关系中的β,而不是CAPM中的那个β对吗

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NO.PZ2016082404000024问题如下 You have a portfolio of US5 million to heeusing inx futures. The correlation coefficient between the portfolio anfutures being useis 0.65. The stanrviation of the portfolio is 7% anthof the heing instrument is 6%. The futures priof the inx futures is US1,500 anone contrasize is 100 futures. Among the following positions, whione reces risk the most?   Long 33 futures contracts   Short 33 futures contracts   Long 25 futures contracts   Short 25 futures contracts ANSWER: o hee, the portfolio manager shoulsell inx futures, to create a profit if the portfolio loses value. The portfolio beta is 0.65×7%6%=0.758.0.65\times\frac{7\%}{6\%}=0.758.0.65×6%7%​=0.758.The number of contracts is N∗=−βSF=−(0.758×5,000,000)1,500×100=−25.3N\ast\text{=}-\beta\frSF=\frac{-{(0.758\times5,000,000)}}{1,500\times100}\text{=}-25.3N∗=−βFS​=1,500×100−(0.758×5,000,000)​=−25.3 or 25 contracts.5mx1+0.758*150000*Nf=0,这才是正确的公式啊

2024-04-12 16:29 1 · 回答

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