A portfolio consisting of four stocks is expected to produce returns of 9%, 11%, 3% and 17%, respectively, over the next four years. What is the standard deviation of these expected returns?
A) 5.00%
B) 5.77%
C) 25.00%
D) 33.33%

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the expected returns, we first need to calculate the portfolio's expected return. We can do this by taking a weighted average of the individual stock returns, based on the portfolio weights. Let's assume the portfolio weights are 25% for each stock. Then, the portfolio's expected return would be:

Portfolio expected return = 0.25(9%) + 0.25(11%) + 0.25(3%) + 0.25(17%) = 10%

Next, we need to calculate the variance of the expected returns. We can do this by using the formula:

Variance = (weight of stock 1)(return of stock 1 - portfolio expected return)^2 
          + (weight of stock 2)(return of stock 2 - portfolio expected return)^2 
          + (weight of stock 3)(return of stock 3 - portfolio expected return)^2 
          + (weight of stock 4)(return of stock 4 - portfolio expected return)^2

Plugging in the numbers, we get:

Variance = 0.25(9% - 10%)^2 + 0.25(11% - 10%)^2 + 0.25(3% - 10%)^2 + 0.25(17% - 10%)^2 
         = 0.5625

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(0.5625) = 0.75

So the standard deviation of the expected returns for this portfolio is 0.75, or 5.77% as a percentage. Therefore, the best choice is B.

A Portfolio Consisting of Four Stocks Is Expected to Produce