v？

NO.PZ2020010801000015

问题如下：

How does adding leverage (borrowing at a risk-free rate, which is not random) to a portfolio change the optimal hedge ratio? For example, if the portfolio returns were doubled so that $\widetilde R_p = 2R_p$ , what is the optimal hedge ratio for the Rp? Hint: Use the formula for the OLS estimator of $\beta$ .

解释：

The OLS $\beta$ is $\frac{Cov(R_p, R_h)}{Var(R_h)}$ . Scaling $R_p$ by a leverage v, the optimal hedge would be $\frac{Cov(vR_p, R_h)}{Var(R_h)} = v\frac{Cov(R_p, R_h)}{Var(R_h)}=v\beta$ , where $\beta$ is the ledge ratio from the unlevered portfolio.

Levering up increases exposure to risk that can be hedged and to the hedge ratio must account for this.

老师，请解释一下这道题，还有，这里v是2吗？

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品职答疑小助手雍 · 2022年03月31日

同学你好，这题其实就是解释了一下回归里面，把因变量扩大V倍，对系数beta的影响，结论是beta也会等比例扩大。

2只是对v举的例子。

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NO.PZ2020010801000015 问题如下 How es aing leverage (borrowing a risk-free rate, whiis not ranm) to a portfolio change the optimhee ratio? For example, if the portfolio returns were ubleso thR~p=2Rp\witil R_p = 2R_pRp=2Rp, whis the optimhee ratio for the Rp? Hint: Use the formula for the OLS estimator of β\betaβ. The OLS β\betis Cov(Rp,Rh)Var(Rh)\frac{Cov(R_p, R_h)}{Var(R_h)}Var(Rh)Cov(Rp,Rh). Scaling RpR_pRp a leverage v, the optimhee woulCov(vRp,Rh)Var(Rh)=vCov(Rp,Rh)Var(Rh)=vβ\frac{Cov(vR_p, R_h)}{Var(R_h)} = v\frac{Cov(R_p, R_h)}{Var(R_h)}=v\betaVar(Rh)Cov(vRp,Rh)=vVar(Rh)Cov(Rp,Rh)=vβ, where β\betis the lee ratio from the unlevereportfolio.Levering up increases exposure to risk thcheeanto the hee ratio must account for this. 可以说下这题用到的对冲的知识吗

2024-05-09 19:37 2 · 回答

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