02-05 How hedge funds use the CA

作者: 非常暴龙兽 | 来源:发表于2019-06-13 14:10 被阅读0次

Two stock scenario:

A: predict +1% over mkt, long $50, $\beta_A=1.0$
B: predict -1% below mkt, short $50, $\beta_B=2.0$
then
$\gamma_p =\gamma_A + \gamma_B = \beta_A \gamma_M + \alpha_A+\beta_B\gamma_M+\alpha_B$

若 $\gamma_M=0$ 大盘没涨也没跌
则 $\gamma_P=\alpha_A+\alpha_B=0.5+0.5= 1 dollar$
Two stock CAPM math:
$\gamma_P = \sum_i \omega_i(\beta_i \gamma_M+\alpha_i)$
$=(\omega_A \beta_A +\omega_B \beta_B)\gamma_M+\omega_A \alpha_A +\omega_B\alpha_B$
若 $\beta_P=0$ 则纯 $\alpha$ 套利。

How to allocate A and B?

$\beta_A=1.0,\ \ \ \ \alpha_A=+1\%$
$\beta_A=2.0,\ \ \ \ \alpha_A=-2\%$
Find $\omega_A$ and $\omega_B$ so that mkt risk is minimized.
$\beta_P=\omega_A \cdot 1 + \omega_B \cdot 2=0$
$\mathrm{abs}(\omega_A)+\mathrm{abs}(\omega_B)=1$
联立方程解出
$\omega_A=2/3,\ \ \ \ \omega_B=-1/3$
CAPM for hedge funds summary
Assuming: