Question

You have observed the following returns on Rogers Ltd shares over the past 5 years: (16%, 12%, -28%, -7% and 29%)

a) What was the average return on Rogers Ltd shares over this five year period? Show workings

b) What was the variance of Rogers Ltd shares’ returns over this period? What was the standard deviation?

Following from the above, suppose the average inflation rate over this period was 1.2% and the average cash rate over the period was 2.1%

c) What was the average real return on Rogers Ltd shares over this five year period?

d) What was the average nominal risk premium on Rogers Ltd shares??

e) What was the average real risk-free rate over this time period?

f) What was the average real risk premium??

Answer 1

a) Average Return = (16 + 12 - 28 - 7 + 29) / 5 = 4.40%

b) Variance can be calculated using mathematical formulas or using VAR.S function in excel

VAR.S(16%...29%) = 4.94% is variance

Standard Deviation is square root of variance = 4.94%^(1/2) = 22.23%

c) Average real return = Nominal - Inflation = 4.4% - 1.2% = 3.2% (using arithmetic method)

d) Average nominal risk premium = Return - Cash rate = 4.4% - 2.1% = 2.3%

e) Average real risk-free rate = Cash rate - Inflation = 2.1% - 1.2% = 0.9%

f) Average real risk premium = 2.3% - 1.2% = 1.1%