An investor holds a portfolio with the following weights: 20% in T-bills, 50% in

Question

An investor holds a portfolio with the following weights: 20% in T-bills, 50% in the S&P500 equity index, 10% in Google and 10% in Amazon. The actual returns on these assets over the last 5 years are as follows:

What is the arithmetic average return on each of the assets? What is the geometric average return on each of the assets? What is the sample variance for each of the assets? What is the sample standard deviation for each of the assets? What is the arithmetic average return across the 4 assets (ignoring the relative weights the investor has in each asset within her portfolio) for each of the 5 years? What is the return on the portfolio (i.e., the weighted average return across the 4 assets) for each of the 5 years?

Year T-bills S&P equity index Google Amazon 1 0.01 0.06 0.12 0.01 2 0.01 0.09 0.08 -0.20 3 0.02 0.01 -0.02 0.16 4 0.01 -0.02 0.06 0.14 5 0.01 0.03 0.20 -0.02

Explanation / Answer

Arithmatic mean formula = (return of year 1 +  return of year 2 +  return of year 3 +  return of year 4+  return of year 5)/5

Geometric mean formula = ((1+return of year1)*(1+return of year2)*(1+return of year3)*(1+return of year4)*(1+return of year5))^(1/5)

sample variance = ((arithmetic mean - return of year 1)^2 + (arithmetic mean - return of year 2)^2 + (arithmetic mean - return of year 3)^2 + (arithmetic mean - return of year 4)^2 + (arithmetic mean - return of year 5)^2)/(5 -1 )

sample standard deviation = root(sample variance)

Year T-bills S&P equity index Google Amazon Artihmetic Average return(ignore weight) Artihmetic Average return(consider weight) 1 0.01 0.06 0.12 0.01 0.05 0.050 2 0.01 0.09 0.08 -0.2 -0.005 0.039 3 0.02 0.01 -0.02 0.16 0.0425 0.026 4 0.01 -0.02 0.06 0.14 0.0475 0.013 5 0.01 0.03 0.2 -0.02 0.055 0.039 Arithmetic return 0.012 0.034 0.088 0.018 Geometric return 0.011992 0.033293 0.085603 0.009253 Sample Variance 0.00002 0.00183 0.00652 0.02102 Sample std. Dev 0.004472 0.042778 0.080747 0.144983

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