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

Calculation of Standard Deviation : Treasury Bills Year Rate Deviation Deviation Square A B =A-Average C =B*B 1 10.45 -0.7250 0.5256 2 11.36 0.1850 0.0342 3 9.06 -2.1150 4.4732 4 8.34 -2.8350 8.0372 5 8.88 -2.2950 5.2670 6 11.23 0.0550 0.0030 7 14.11 2.9350 8.6142 8 15.97 4.7950 22.9920 Total 89.4 Sum of C = 49.9466 Average = 89.4/8= 11.175 Sum of C /(N-1)                       7.1352 Standard Deviation = (Sum of C/N)^(1/2)                       2.6712 (N=8) Inflation Year Rate Deviation Deviation Square A B =A-Average C =B*B 1 12.55 0.7063 0.4988 2 16 4.1563 17.2744 3 1.29 -10.5538 111.3816 4 7.97 -3.8738 15.0059 5 10.29 -1.5538 2.4141 6 12.77 0.9263 0.8579 7 16.98 5.1363 26.3811 8 16.9 5.0563 25.5657 Total 94.75 Sum of C = 199.3796 Average = 94.75/8= 11.84375 Sum of C /(N-1)                     28.4828 Standard Deviation = (Sum of C/N)^(1/2)                       5.3369 (N=8) Calculation of average real return for Treasury bills Using the formula : Real Rate = [(1+ Nominal Rate)/(1+ inflation rate)]-1 Year T. Biil Rate Inflation Real Rate A B = [(1+A)/(1+B)]-1 1 10.45% 12.55% -1.87% 2 11.36% 16.00% -4.00% 3 9.06% 1.29% 7.67% 4 8.34% 7.97% 0.34% 5 8.88% 10.29% -1.28% 6 11.23% 12.77% -1.37% 7 14.11% 16.98% -2.45% 8 15.97% 16.90% -0.80% Total -3.75% Average Real rate = -3.75%/8 -0.47%

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