Question

Congo Plc is considering two assets which are mutually exclusive for the expansion of its investment portfolios. Details of the assets are as under:

ASSET A

Condition	Probability	Possible return
Sunny	0.1	10%
Windy	0.36	11%
Rainy	0.24	9%
Dry	0.16	7%
Humid	0.09	10.2%
Cloudy	0.05	6.8%

ASSET B

Condition	Probability	Possible return
Sunny	0.14	10.1%
Windy	0.39	12%
Rainy	0.21	11%
Dry	0.15	8%
Humid	0.03	7.7%
Cloudy	0.08	13%

Required

Which asset will be selected? Use an appropriate risk measure

Answer 1

Expected return of asset A=E= sum of (probability*return of condition)

=.1*10+.36*11+.24*9+.16*7+.09*10.2+.05*6.8 =9.498%

Variance of asset A= sum of (probability*(E-returns)^2)

=.1*(9.498-10)^2+.36*(9.498-11)^2+.24*(9.498-9)^2+.16*(9.498-7)^2+.09*(9.498-10.2)^2+.05*(9.498-6.8)^2

=2.303596

Std dev A= sqrt(variance) = sqrt(2.303596) =1.517%

--

Expected return of asset B=E= sum of (probability*return of condition)

=.14*10.1+.39*12+.21*11+.15*8+.03*7.7+.08*13=10.875%

Variance of asset B= sum of (probability*(E-returns)^2)

=.14*(10.875-10.1)^2+.39*(10.875-12)^2+.21*(10.875-11)^2+.15*(10.875-8)^2+.03*(10.875-7.7)^2+.08*(10.875-13)^2

=2.484475

Std dev B= sqrt(variance) = sqrt(2.484475) =1.576%

--

Coefficient of variation= std dev/return

coefficient of variation asset A=1.517/9.498= .1597

coefficient of variation asset B=1.576/10.875=.145

----From Coefficient of variation; lowest value asset is selected which is Asset B