关于IR的选择

问题如下：

The benchmark portfolio is the S&P 500. Which of the following three portfolios can be combined with the benchmark portfolio to produce the highest combined Sharpe ratio?

选项：

A.

Portfolio A

B.

Portfolio B

C.

Portfolio C

解释：

B is correct.

The active portfolio that is optimal is the portfolio with the highest Information ratio, the ratio of active return to active risk. The IRs for the three active portfolios are:

$IR_A$= 1.0/10.0 = 0.10

$IR_B$ = 0. 5/3.0 = 0.167

$IR_C$= 0/2.0 = 0.00

Portfolio B has the highest IR and is the best active portfolio; it is therefore the best portfolio to combine with the benchmark.

考点：Sharpe ratio

解析：$SR^2=SR_B^2+IR^2$，benchmark的Sharpe ratio对于每个Combined portfolio都相同，因此information ratio最大的组合将会得到最大的Combined Sharpe ratio。

ABC组合的IR分别为：0.1，0.167，0。 组合B的IR最大，因此， combined Sharpe ratio 最大。