Consider a portfolio that consists of an equal investment in 20 firms.For each of these firms,there is a 70% probability that the firms will have a 16% return and a 30% probability that they will have a -8% return.Each of these firms' returns is independent of all others.The standard deviation of this portfolio is closest to:
A)2.5%.
B)4.2%.
C)8.8%.
D)11.0%.

Question

Quizplus · Accepted Answer

The standard deviation of a portfolio with independent returns can be calculated using the formula for the standard deviation of a binomial distribution. The variance for each firm is calculated as: (0.7 * (16%)^2 + 0.3 * (-8%)^2 - (0.7 * 16% + 0.3 * -8%)^2). The variance of the portfolio is then the variance of one firm divided by the number of firms (20), and the standard deviation is the square root of this variance. This calculation results in a standard deviation closest to 2.5%.

Consider a Portfolio That Consists of an Equal Investment in 20