关于公式中的百分比

问题如下：

Beade uses a surplus optimization approach to liability-relative asset allocation based on the objective function U_m^LR​ = E(R_s,m) - 0.005λσ²(R_s,m)

where E(R_s,m) is the expected surplus return for portfolio m, λ is the risk aversion coefficient, and σ²(R_s,m) is the variance of the surplus return. Beade establishes the expected surplus return and surplus variance for three different asset allocations, shown in Exhibit 2. Given λ = 1.50, she chooses the optimal asset mix.

Exhibit2 Expected Surplus Return and Volatility for Three Portfolios

Based on Exhibit 2, which portfolio provides the greatest objective function expected value?

选项：

Portfolio 1

Portfolio 2

Portfolio 3

解释：

B is correct.

The objective function expected value is U_m^LR​ = E(R_s,m) - 0.005λσ²(R_s,m)

λ is equal to 1.5, and the expected value of the objective function is shown in the right most column below.

Portfolio 2 generates the highest value, or utility, in the objective function.

考点：surplus optimization

解析：surplus optimization方法下objective function的应用。将每个组合的Expected Surplus Return和Volatility代入公式，计算后比大小，选结果最大的一个。

原版书公式为U_m^LR​ = E(R_s,m) - 0.005λσ²(R_s,m)，λ=1.5, Expected Surplus Return和Volatility代入数字时不加%，举例：U₁​ = 13 - 0.005*1.5*576=8.68。

分别计算三个组合的utility，结果为8.68，9.57，8.29，因此B选项结果最大。