Question

you have been given the expected return data shown in the first table on three

assetslong dash—​F,

​G, and

H long dash—over

the period​ 2016-2019:

	Expected Return
Year	Asset F		Asset G		Asset H
2016	16​%		17​%		14​%
2017	17​%		16​%		15​%
2018	18​%		15​%		16​%
2019	19​%		14​%		17​%

Using these​ assets, you have isolated the three investment alternatives shown in the following​ table

Alternative		Investment
1		​100% of asset F
2		​50% of asset F and​ 50% of asset G
3		​50% of asset F and​ 50% of asset H

a.  The expected return over the​ 4-year period for alternative 1 is

17.50​%.

​

The expected return over the​ 4-year period for alternative 2 is

16.50​%.

The expected return over the​ 4-year period for alternative 3 is

16.50​%.

b.  The standard deviation of returns over the​ 4-year period for alternative 1 is

1.29​%.

​

The standard deviation of returns over the​ 4-year period for alternative 2 is

0.00​%.

​

The standard deviation of returns over the​ 4-year period for alternative 3 is

1.29​%.

Use your findings in parts a and b to calculate the coefficient of variation for each of the three alternatives

Answer 1

Coefficient of variation is a statistical measure which compares the expected return that is mean and volatility of return that is standard deviation to calculate the risk-return trade off of investments. From the investor’s point of view, a lower coefficient of variation is desirable.

Use information of mean and standard deviation of alternative 1 to compute the coefficient of variation for alternative 1 using the equation as follows:

Hence, coefficient of variation for alternative 1 is 7.37%.

Use information of mean and standard deviation of alternative 2 to compute the coefficient of variation for alternative 2 using the equation as follows:

Hence, coefficient of variation for alternative 2 is 0%.

Use information of mean and standard deviation of alternative 3 to compute the coefficient of variation for alternative 3 using the equation as follows:

Hence, coefficient of variation for alternative 3 is 7.82%.