Question

The Ishares Bond Index fund (TLT) has a mean (average) and annual standard deviation of realized returns of 6% and 10%, respectively. If these are unbiased estimators of expected returns and future volatility, answer the following. (Round your answers to the nearest integer.)

(a) What is the 68% confidence interval for the returns on TLT next year (as a percent)? %to %

(b) What is the 95% confidence interval for the returns on TLT next year (as a percent)?

(c) What is the 99.7% confidence interval for the returns on TLT next year (as a percent)? % to %

Answer 1

(A). Law of 68 per cent

range = mean + /- 1(standard deviation)

= 9 + / -1(10)

= 9 - 1(10) to 9 + 1(10)

= -1 to 19

(B). Law of 95 per cent

range = mean +/- 1.96(standard deviation)

= 9 +/- 1.96(10)

= 9 - 1.96(10) to 9 + 1.96(10)

= -10.6 to 28.6

(C). Law of 99 per cent

range = mean +/- 3(standard deviation)

=9 +/- 310()

=9 - 3(10) to 9 + 3(10)

= -21 to 39