Question

Check In 2011-2015, mutual fund manager, Diana Sauros produced the following percentage rates of return for the Mesozoic Fund. Rates of return on the market index are given for comparison. 2011 2012 2013 2014 2015 -1.4 +24.7 +40.7 +11.7 +0. -0.7 +15.0 +31.7 +11.0-0. Fund Market index Calculate (a) the average return on both the Fund and the index, and (b) the standard deviation of the returns on each. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Market Mesozoic Fund Return Portfolio Return Average return Standard deviation

Answer 1

	Fund	Market Index
2011	-1.4	-0.7
2012	24.7	15
2013	40.7	31.7
2014	11.7	11
2015	0.5	-0.5

Average Return

Average return is calculated using the formula:

Average Return = E[R] = (R₁+R₂+R₃+R₄+R₅)/n

Sample size = n = 5

Average Return for the fund = E[R_F] = (-1.4+24.7+40.7+11.7+0.5)/5 = 76.2/5 = 15.24

Average Return for the Market Index = E[R_M] = [-0.7+15+31.7+11+(-0.5)]/5 = 56.5/5 = 11.3

Variance of the sample is calculted using the formula:

Varaince = [(R₁-E[R])²+(R₁-E[R])²+(R₁-E[R])²​​​​​​+(R₁-E[R])²+(R₁-E[R])²]/(n-1)

Standard Deviation of Fund

Variance of the fund = σ_F² = [(-1.4-15.24)²+(24.7-15.24)²​​​​​​​+(40.7-15.24)²​​​​​​​+(11.7-15.24)²​​​​​​​+(0.5-15.24)²​​​​​​​]/4 = 1244.392/4 = 311.098

Standard deviation is the square-root of the variance

Standard deviation of the Fund = σ_F = 311.098^1/2 = 17.637970404783 ~ 17.64 (Rounded to two decimals)

Standard Deviation of Market Index

Variance of the Market Index = σ_M² = [(-0.7-11.3)²+(15-11.3)²​​​​​​​+(31.7-11.3)²​​​​​​​+(11-11.3)²​​​​​​​+(-0.5-11.3)²​​​​​​​]/4 = 713.18/4 = 178.295

Standard deviation is the square root of the variance

Standard deviation of the Market Index = σ_M = 178.295^1/2 = 13.3527150797132 ~ 13.35 (Rounded to two decimals)

Answer

	Mesozoic Fund Return	Market Portfolio return
Average Return	15.24	11.30
Standard Deviation	17.64	13.35