Question

1. Monthly returns for portfolio A follow normal distribution with mean 7% and standard deviation 3%. Monthly returns for portfolio B follow normal distribution with mean 3% and standard deviation 1.5% In February, the return on portfolio A was 11%, and the return on portfolio B was 5%. (a) Which of the two portfolios had a more unusually successful month? (b) What percent of months do you expect portfolio A to perform even better than this February? What percent of months do you expect portfolio B to perform even better than this February?

Answer 1

a) To find out which portfolio performed better we need to find the z scores of the two. The one with the higher z score would be more successful.

z= x-mean/sd

So, z for Portfolio A= 0.11-0.07/0.03= 1.333

z for Portfolio B= 0.05-0.03/0.015= 1.333

Since the z scores of both the portfolios are the same, none was more successful.

b) We want, P(X>0.11)  

Using standard normal approximation,

P(z>0.11-0.07/0.03) = P(z>1.33) = 1- P(z<=1.33) = 1-0.9082= 0.0918

Similarly, for Portfolio B, P(X>0.5) = P(z>1.33) = 0.0918

So for both portfolios we except them to perform better than February 9.18% of months.