Problem 10-22 Calculating Returns Suppose we have the following Treasury bill re

Question

Problem 10-22 Calculating Returns

Suppose we have the following Treasury bill returns and inflation rates over an eight year period:

Calculate the standard deviation of Treasury bill returns and inflation over this period. (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What was the average real return for Treasury bills over this period? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose we have the following Treasury bill returns and inflation rates over an eight year period:

Explanation / Answer

b. Mean of Treasury Bills = (10.45 + 11.36 + 9.06 + 8.34 + 8.88 + 11.23 + 14.11 + 15.97)/8 = 11.175%
Means of Inflation rate = (12.55 + 16 + 10.29 + 7.97 + 10.29 + 12.77 + 16.98 + 16.9)/8 = 12.97%

Variance of Treasury Bills = [(10.45 - 11.175)2 + (11.36 - 11.175)2 + (9.06 - 11.175)2 + (8.34 - 11.175)2 + (8.88 - 11.175)2 + (11.23 - 11.175)2 + (14.11 - 11.175)2 + (15.97 - 11.175)2] / 8 = 6.243
Variance of Inflation rate = [(12.55 - 12.97)2 + (16 - 12.97)2 + (10.29 - 12.97)2 + (7.97 - 12.97)2 + (10.29 - 12.97)2 + (12.77 - 12.97)2 + (16.98 - 12.97)2 + (16.9 - 12.97)2] / 8 = 10.04

Standard Deviation of Treasury Bills = 6.2431/2 = 2.50%
Standard Deviation of Inflation rate = 10.041/2 = 3.17%

c. Average real return for Treasury bills over this period = (1 + 0.11175)/(1 + 0.1297) - 1 = -1.59% since Inflation rate is more than Treasury Bill rate.

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