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徐威廉 · 2024年04月12日

这个相关系数计算出的beta=0.7583是谁的beta?难道不是hedge工具的吗?现货的beta应该=1啊

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.

5mx1+0.758*150000*Nf=0,这才是正确的公式啊

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已采纳答案

pzqa39 · 2024年04月13日

嗨,努力学习的PZer你好:


β是portfolio的β

可以当作一元线性回归理解: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,hedge ratio其实没区别)



5m(portfolio的价值)x0.758(portfolio的β)+1*150000*Nf=0

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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.这里公式直接负贝塔,是因为目标贝塔为0,贝塔*是0,所以直接代公式看结果正负就行了,这么理解对吗?

2023-10-14 19:33 1 · 回答

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