问一道题：NO.PZ2019042401000044β计算的公式是哪里来的？

问题如下：

Portfolio B’ s expected return is 9% and its volatility is 20%.  At the same time, the  expected return and the volatility of  the index is supposed to be 7% and 15%, the correlation bettwen portfolio B and market is supposed to be 0.9. We observe that the risk-free rate is 3%. Calculte Jensen’s alpha for portfolio B.

选项：

1.2%.

1.5%.

2%.

0.8%.

解释：

A is correct.

考点：Jensen’s alpha.

解析：

$\alpha={\text{E(R}}_\text{P})-{\{{\text{R}}_\text{F}+\beta{\lbrack{{\text{E(R}}_\text{M})-{\text{R}}_\text{F}}\rbrack}\}}$

$\beta=\frac{\rho\sigma_p}{\sigma_m}={\textstyle\frac{0.9\times0.2}{0.15}}=1.2$

$\alpha=9\%-\lbrack3\%+1.2(7\%-3\%)\rbrack$

$\alpha=9\%-7.8\%$

$\alpha=1.2\%$