Question

g You invest 56% of your money in Stock A and the rest in Stock B. The standard deviation of annual returns is 49% for Stock A and 49% for Stock B. The correlation between the two stocks is 0.2. By how many percentage points does diversifying between these two stocks reduce your risk? Go out three decimals - for example, write 5.6% as .056.

Answer 1

The risk will be reduced by 0.109

Step-by-step explanation:

Standard deviation for stock A = 49%

Standard deviation for stock B = 49%

Correlation = 0.2

Let's use the standard deviation of portfolio equation:

`= √(w_A^2 \sigma _A^2 + w_B^2 \sigma _B^2 + 2w_A w_B \sigma _A \sigma _B * C)`

Where
`w_B` = 100% - 56% = 44%

`= √((0.56^2 * 0.49^2) + (0.44^2 * 0.49^2) + (2*0.56*0.44*0.49*0.49)0.2)`

= 0.381 = 38.1%

The risk will be reduced by:

(0.56*0.49)+(0.44*0.49)-0.381

= 0.109