Question

Asset	Average	Return Standard Deviation
Canadian common stocks	13.20%	16.62%
US common stocks	15.59%	16.86%
Long bonds	7.64%	10.57%
Small-company stocks	14.79%	23.68%
Treasury bills	6.04%	4.04%

1. If the returns on small-company stocks are normally distributed, which of the following returns [-30%, -10%, 50%, 70%, 90%] would lie in a 99% confidence interval around the mean, but not in a 95% confidence interval? (70%)
2. Assume the return on T-bills is normally distributed. Assuming a 68% probability, what is the highest return you would expect to earn on T-bills? (10.08%)

Answer 1

1.

95% confidence interval: 14.79%-1.96*23.68% to 14.79%+1.96*23.68% i.e., from -31.62% to +61.20%

99% confidence interval: 14.79%-2.58*23.68% to 14.79%+2.58*23.68% i.e., from -46.30% to +75.88%

Hence 70% would lie in 99% confidence interval but not in 95% confidence interval

2

=6.04%+0.99446*4.40%=10.08%