Monthly returns for portfolio A follow normal distribution with mean 5% and stan

Question

Monthly returns for portfolio A follow normal distribution with mean 5% 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 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) zscore for A's return =(X-mean)/std deviation =(10-5)/3 =1.6667

z score for B's return =(5.6-3)/1.5=1.7333

as z score for B is higher iit is nore unusually successful month

b) for portfolio A P(Z>1.6667) =0.0478 ~4.78 %

hence 4.78 % of months are expected to perform even better

for portfolio B P(Z>1.7333) =0.0415 ~4.15 %

hence 4.15 % of months are expected to perform even better

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