1. Monthly returns for portfolio A follow normal distribution with mean 6% and s

Question

1. Monthly returns for portfolio A follow normal distribution with mean 6% and standard deviation 3%. Monthly returns for portfolio B follow normal distribution with mean 2% and standard deviation 1.5%. In February, the return on portfolio A was 10%, and the return on portfolio B was 5.6%. (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?

Explanation / Answer

a)

z-score for A = (X - mean)/sd = (10 -6)/3 = 4/3 = 1.3333

z-score for B = (5.6 - 2)/1.5 = 3.6/1.5 = 2.4

since

2.4 > 1.3333

B had a more ususually successful month

b)

P(Z > 1.3333) = 0.0912

hence 9.12 % we expect portfolio A to perform better than February .

P(Z > 2.4) = 0.0082

0.82 % we expect portfolio B to perform better than February .

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