Question

Year       Return

1              9%

2              11%

3              -4%

4              7%

5              6%

A) What is the geometric average? What is the arithmetic average?

B) Assume that the distribution is normal. Using the standard error, calculate the 95.4 percent confidence interval for the true return.

Answer 1

A)

Use excel to calculate arithmetric average Year Return 1 9% 11% -4% 7% 6% Arithmetic Average 5.80% Geometric average ((1+r1)*(1+r2........ (1+rn))^(1/n) - 1 Wherer is the rate of return and n is the time period 5.67%

B)

The formula for creating confidence interval is Year Return (X) +/- t* S/(n)^(1/2) where X is the mean value S = standard deviation N = number of data t = confidence level 9% 11% -4% 7% 6% Standard deviation = 0.058052 mean 5.8 5.81 2.78 hence the confidence interval would be 5.8-2.78*5.81/(5)^(1/2) -1.4233 5.8+2.78*5.81/(5)^(1/2) 13.0233 hence the confidence interval would be - 1.42 to 13.02