开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

Tina · 2022年03月30日

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 R~p=2Rp\widetilde R_p = 2R_p, what is the optimal hedge ratio for the Rp? Hint: Use the formula for the OLS estimator of β\beta.

解释:

The OLS β\beta is Cov(Rp,Rh)Var(Rh)\frac{Cov(R_p, R_h)}{Var(R_h)}. Scaling RpR_p by a leverage v, the optimal hedge would be Cov(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\beta, where β\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?
1 个答案
已采纳答案

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。