A portfolio has 30% of its value in IBM shares and the rest in Microsoft (MSFT).The volatility of IBM and MSFT are 35% and 30%,respectively,and the correlation between IBM and MSFT is 0.3.What is the standard deviation of the portfolio?

Question

Quizplus · Accepted Answer

The formula to calculate the standard deviation of a portfolio is:

Portfolio SD = sqrt(w1^2 * SD1^2 + w2^2 * SD2^2 + 2 * w1 * w2 * Corr * SD1 * SD2)

where:
- w1 and w2 are the weights of each asset in the portfolio
- SD1 and SD2 are the standard deviations of each asset
- Corr is the correlation between the two assets

In this case:
- w1 = 0.3 (IBM weight)
- w2 = 0.7 (MSFT weight)
- SD1 = 35% (IBM volatility)
- SD2 = 30% (MSFT volatility)
- Corr = 0.3 (correlation)

Plugging these values into the formula:

Portfolio SD = sqrt(0.3^2 * 35%^2 + 0.7^2 * 30%^2 + 2 * 0.3 * 0.7 * 0.3 * 35% * 30%)
= 26.15%

Therefore, the answer is B (26.15%).

A Portfolio Has 30% of Its Value in IBM Shares