Question

The following are annual rates of return for U.S. government T-bills and U.K. common stocks. Year U.S Government T-Bills U.K Government Common Stock

Year US Govt T-bills UK Common Stock

2012 0.063 0.150

2013 0.081 0.043

2014 0.076 0.374

2015 0.090 0.192

2016 0.085 0.106

a. Compute the arithmetic mean rate of return and standard deviation of rates of return for the two series.

b. Discuss these two alternative investments in terms of their arithmetic average rates of return and their absolute risk and their relative risk.

c. Compute the geometric mean rate of return for each of these investments.

d. Compare the arithmetic mean return and geometric mean return for each investment and discuss this difference between mean returns as related to the standard deviation of each series.

Pls show calculation in Excel thx!

Answer 1

A) while using the excel formula, please put equal (=) sign before applying formula, it was slightly difficult to capture the formula with equal sign

AB H We will use the excel to calculate the Arithmetic mean as well as standard deviation UK Common US Govt. T-Bills stocks 2012 0.063 0.15 2013 0.081 0.043 2014 0.076 0.374 2015 0.09 0.192 2016 0.085 0.106 Arithmetic mean AVERAGE(D7:D11) AVERAGE(E7:E11) 0.079 0.173 Standard Deviation STDEVA(D7:011) STDEVA(E7:E11) 0.010319884 0.125179871

B)  

The averag return of UST Bills over these 5 years is 7.9%, whereas the average returns of UK common stocks over these 5 year period is 17.3%. The absolute risk of treasury bills measured in terms of standard deviation is 1.03%, whereas the absolute risk for the common stock is 12.52%. The relative risk which is measured in terms return per unit of risk, return divided by risk(standard deviation). The relative risk of T bills are (0.079/0.01031)=7.66 return per unit of risk, while for common stock (0.173/.1252)= 1.38 return per unit of risk. Common stocks have far more relative risk.

C)

We will use excel to calculate the geometric mean Year UK Common US Govt. T-Bills stocks 2012 0.063 0.15 2013 0.081 0.043 2014 0.076 0.374 2015 0.09 0.192 2016 0.085 0.106 Geometric mean GEOMEAN(D5:09) GEOMEAN(E5:E9) 0.07842601 0.137469921

D)

The arithmetic return is 7.9% and 17.3% respectively for T bills and common stocks whereas geometric returns are 7.8% and 13.75% for T bills and common stock respectively, geometric mean is less than the arithmetic mean because the geometric mean considers the impact of compounding. The relative return with reference to geometric mean can be calculated in the same way as we did for arithmetic mean. = geometric mean/ standard deviation return per unit of risk for T-Bills (0.0784/0.0103) = 7.61, for common stock return per unit of risk = (0.1375/0.1252) = 1.098, if you compare the return per unit of risk, the return per unit of risk is lower in geometric mean than arithmetic mean becasue of compounding effect.