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

 Calculate the standard deviation of returns over the​ 4-year period for each of the three alternatives

Answer 1

	Standard Deviation
Year	Asset F	Deviation	Deviation2
2016	16	-1.5	2.25
2017	17	-0.5	0.25
2018	18	0.5	0.25
2019	19	1.5	2.25
	70		5
Average Expected Return=			17.5
	Standard Deviation		=SQRT(Deviation)2
			2.236068
Year	Asset G	Deviation	Deviation
2016	17	1.5	2.25
2017	16	0.5	0.25
2018	15	-0.5	0.25
2019	14	-1.5	2.25
	62		5
Average Expected Return=			15.5
	Standard Deviation		2.236068
Year	Asset H	Deviation	Deviation
2016	14	-1.5	2.25
2017	15	-0.5	0.25
2018	16	0.5	0.25
2019	17	1.5	2.25
	62		5
Average Expected Return=			15.5
	Standard Deviation		2.236068

Alternative 1
​100% of asset F
Standard Deviation=		Standard Deviation of F
		2.236068
Alternative 2
​50% of asset F and​ 50% of asset G
Standard Deviation=		Standard Deviation of F* weights of F+ Standard Deviation of G * Weights of G
		2.236068
Alternative 3
​50% of asset H and​ 50% of asset G
Standard Deviation=		Standard Deviation of H* weights of H+ Standard Deviation of G * Weights of G
		2.236068