Question

A portfolio consists of two stocks: 30% of Stock 1 with standard deviation of 39.44% and 70% of Stock 2 with a standard deviation of 47.29%. The correlation of Stocks 1 and 2 is 0.4. What is the standard deviation of this portfolio?

Answer 1

The standard deviation of this portfolio is approximately 39.36%.

Step-by-step explanation:

This can be calculated by first calculating the variance of this portfolio using the portfolio variance formula as follows:

Portfolio variance = (WS1^2 * SDS1^2) + (WS2^2 * SDS2^2) + (2 * WS1 * SDS1 * WS2 * SDS2 * CFab) ......................... (1)

Where;

WS1 = Weight of Stock 1 = 30%

WS2 = Weight of Stock 2 = 70%

SDS1 = Standard deviation of stock 1 = 39.44%

SDS2 = Standard deviation of stock 2 = 47.29%

CFab = The correlation between stock 1 and 2= 0.4

Substituting all the values into equation (1), we have:

Portfolio variance = (30%^2 * 39.44%^2) + (70%^2 * 47.29%^2) + (2 * 30% * 39.44% * 70% * 47.29% * 0.4)

Portfolio variance = 0.15491445898

The standard deviation of this portfolio can be calculated as follows:

Portfolio standard deviation = (Portfolio variance)^0.5 = 0.15491445898^0.5 = 0.393591741503807, or 39.3591741503807%

Rounding to 2 decimal places, we have:

Portfolio standard deviation = 39.36%

Therefore, the standard deviation of this portfolio is approximately 39.36%.