Question

1.     You are investing in two stocks: A and B, with normally distributed stock returns. Given the information on these two stocks, please use simulation to find the returns for A, B, and the portfolio for 20 years. Compute the theoretical and simulated mean and standard deviation of the portfolio return.

 

StockA

StockB

Mean

15%

8%

Sigma

30%

15%

Correlation

0.3

Proportion of A

60%

Summary of portfolio returns

Theoretical

Simulated

Answer 1

Given data are summarized below as shown-

correlation coefficient $r_{AB}=0.3$

Theortical mean is given for the two assets as shown in the table.

The simulated mean = (15%$\times$ 60%)+(8%$\times$ 40%)$=\dfrac{900+320}{10000}$ =12.2%

The standard deviation of the portfolio return-

$\sigma=\sqrt{W_A^2\sigma_a^2+W_B^2\sigma_B^2+2\sigma_AW_AW_B\sigma_B r_{AB}}$

$=\sqrt{(60)^2.(30)^2+(15)^2.(40)^2+2.(30).(60).(15).(40).(0.3)}$

$=\sqrt{3240000+360000+648000}=\sqrt{4248000}=2061.06=20.61$ %