解释题目的意思和考点

问题如下：

A portfolio manager holds five bonds in a portfolio and each bond has a 1-year default probability of 17%. The event of default for each of the bonds is independent. What is the mean and standard deviation of the number of bonds defaulting over the next year?

选项：

A.

Mean = 0.15, standard deviation = 0.71

B.

Mean = 0.85, standard deviation = 0.84

C.

Mean = 0.85, standard deviation = 0.71

D.

Mean = 0.15, standard deviation = 0.84

解释：

中文解析：

公式计算：

Mean = E(K) = n x p = 5 x 0.17 = 0.85.

Variance = Variance(K) = n x p x (1-p) = 5 x 0.17 x (0.83) = 0.7055

Standard deviation = sqrt(0.7055) = 0.8399.

选B

Letting n equal the number of bonds in the portfolio and p equal the individual default probability, the formulas to use are as follows:

Mean = E(K) = n x p = 5 x 0.17 = 0.85.

Variance = Variance(K) = n x p x (1-p) = 5 x 0.17 x (0.83) = 0.7055

Standard deviation = sqrt(0.7055) = 0.8399.