Using the annual returns for years 3–5 in Spreadsheet 5.2:

a. Compute the arithmetic average return.

b. Compute the geometric average return.

c. Compute the standard deviation of returns.

d. Compute the Sharpe ratio, assuming the risk-free rate was 6% per year.

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B Implicit E F 1 Year Probability HPR (decimal) Squared Deviation Gross Return Wealth =1+ HPR Index* 2 3 4 123. 0.20 -0.1189 0.0196 0.8811 0.8811 0.20 -0.2210 0.0586 0.20 0.2869 0.0707 0.7790 0.6864 1.2869 0.8833 5 6 4 5 0.20 0.1088 0.0077 0.20 0.0491 0.0008 1.1088 0.9794 1.0491 1.0275 7 Arithmetic average = AVERAGE(C2:C6) 0.0210 8 Expected HPR 9 Variance 10 Standard deviation 11 Standard deviation 12 Std dev (df 4) SUMPRODUCT(B2:B6, D2:D6) SQRT(D9) STDEV.P(C2:C6) SUMPRODUCT(B2:B6, C2:C6) 0.0210 0.0315 0.1.774 0.1.774 13 Std dev (df = 4) SQRT(D9*5/4) STDEV.S(C2:C6) 0.1983 0.1983 0.0054 14 Geometric avg return F6^(1/5)-1 15 16 The wealth index is the cumulative value of $1 invested at the beginning of the sample period. Spreadsheet 5.2 Time series of holding-period returns