Question

A. Fair, Inc. is considering an investment in one of two common stocks. Given the information
that follows, which investment is better, based on risk (as measured by the standard deviation)
and return?

Stock	A	Stock	B
Probability	Return	Probability	Return
0.3	12%	0.2	15%
0.4	16%	0.3	6%
0.3	18%	0.3	13%
0.2	21%

Answer 1

Calculation of Risk and return for Stock A :

Probability (P)	Return (x)	PX	DX = x- X	DX2	PDX2
0.3	12	3.6	-7.6 (12-19.6)	57.76	17.328
0.4	16	6.4	-3.6(16-19.6)	12.96	5.184
0.3	18	5.4	-1.6(18-19.6)	2.56	0.768
0.2	21	4.2	1.4(21-19.6)	1.96	0.392
		X(Return)=19.6			23.672

Risk = = PDX²

Risk = = 23.672

Risk = = 4.8654

Calculation of Risk and return for Stock B :

Probability (P)	Return (x)	PX	DX = x- X	DX2	PDX2
0.2	15	3	6.3 (15-8.7)	39.69	7.938
0.3	6	1.8	-2.7(6-8.7)	7.29	2.187
0.3	13	3.9	4.3(13-8.7)	18.49	5.547
		X(Return)=8.7			15.672

Risk = = PDX²

Risk = = 15.672

Risk = = 3.9588

Coefficient of variation(CV) : CV tells us about how much risk we are taking to earn 1% of return

When we have to decide which stock is preferred we apply CV concept

Formula of CV = Risk / Return or  /X

CV for Stock A = 4.8654/19.6 = 0.248

CV for Stock A = 3.9588/8.7 = 0.455

Decision Rule of CV : Lower of CV is preferred, because lower CV means we have to take less risk to earn same 1% of return

As per above calculatio of CV and decision rule we will prefer lower CV i.e of stock A.Hence stock A is better and we shold invest in it.