考试的时候计算器设置几位小数比较好？

问题如下：

Question Based on the following historical data, which is closest to the standard deviation for the two-asset portfolio shown in the table?

选项：

A.6.50% B.5.00% C.5.50%

解释：

Solution

C is correct. The standard deviation of a two-asset portfolio is calculated as follows:

σ_p = √w21×σ21+w22×σ22+2w1w2ρ1,2σ1σ2$\sqrt{w_1^2\times {\sigma }_1^2+w_2^2\times {\sigma }_2^2+2w_1{w}_2{\rho }_{1,2}{\sigma }_1{\sigma }_2}$

= √0.42×4.7%2+0.62×7.7%2+2×0.4×0.6×0.3×4.7%×7.7%$\sqrt{{0.4}^2\times 4.7{\%}^2+{0.6}^2\times 7.7{\%}^2+2\times 0.4\times 0.6\times 0.3\times 4.7\%\times 7.7\%}$

= 5.5%

A is incorrect. This is the simple weighted average of the standard deviations of the assets: w₁ × σ₁ + w₂ × σ₂ = 0.4 × 4.7% + 0.6 × 7.7% = 6.5%.

B is incorrect. This is the portfolio standard deviation when the asset correlation is ignored or set equal to zero.

√w21×σ21+w22×σ22=√0.42×4.7%2+0.62×7.7%2=5.0%$\sqrt{w_1^2\times {\sigma }_1^2+w_2^2\times {\sigma }_2^2}=\sqrt{{0.4}^2\times 4.7{\%}^2+{0.6}^2\times 7.7{\%}^2}=5.0\%$