Question

A financial analyst has estimated the following returns for stocks of company X and company Y under five possible states of the economy.

State of the market	Probability	Percentage Return
	P (X)	X	XP(X)	(X-µ)	(X-µ)2	(X-μ)2P(X)
Rapid growth	0.05	35	35x0.05=1.75	35-9= 26	26^2=676 26x26=676	0.05x676=33.8
Moderate growth	0.25	15	15x0.25=3.75	15-9=6	6^2=36 6x6=36	0.25x36=9
Normal	0.45	10	10x0.45=4.5	10-9=1	1^2=1 1x1=1	0.45x1=0.45
Moderate recession	0.15	0	0x0.15=0	0-9=-9	-9^2=81 -9x-9=81	0.15x81=12.15
Severe recession	0.10	-10	-10x0.10=-1	-10-9=-19	-19^2=361 -19x-19=361	0.10x361=36.1
			E(X)=μ= 1.75+3.75+4.5+0-1=9			Variance for X, V(X)= 91.5 Square root of 91.5 is 9.5
						St.dev for X=9.5
	P(Y)	Y	YP(Y)	(Y-η)	(Y-η)2	(Y-η)2P(Y)
Rapid growth	0.05	25	25x0.05=1.25	25-8=17	17^2=289 17x17=289	0.05x289=14.45
Moderate growth	0.25	20	20x0.25=5	20-8=12	12^2=144 12x12=144	0.25x144=36
Normal	0.45	10	10x0.45=4.5	10-8=2	2^2=4 2X2=4	0.45x4=1.8
Moderate recession	0.15	-5	-5x0.15=-0.75	-5-8=-13	-13^2=196 -13x-13=196	0.15x196=29.4
Severe recession	0.10	-20	-20x0.10=-2	-20-8=-28	-28^2=784 28x28=784	0.10x784=78.4
			E(Y)=η=8 1.25+5+4.5-0.75-2=8			Variance for Y, V(Y)=160.05 Square root of 160.05
						St.dev for Y=12.6

Note: In the table the expected return for X is denoted by μ while the expected return for Y is denoted by η.

a. Calculate the expected return for each stock option. Show your steps by filling out the appropriate cells in the table above.

b.Calculate and interpret the standard deviation for each stock option. Show your steps by filling out the appropriate cells in the table above.

Based on your results under (b) which stock option appears to be more risky to invest in? Is this comparison fully informative? Please explain your answer.                         

Answer 1

You have already filled out the cells of the table.

The variance of Y is higher than the variance of X. So Y is more risky to invest in.

But this comparison is not fully informative. Considering mean you have to calculate the coefficient of variation.also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as

Coefficient of variation= (standard deviation/mean)*100

So for X, C.V.=(9.5/9)*100= 105.6%

For Y,. C.V.= (12.6/8)*100= 157.5%

So as the coefficient of variation of Y is much higher than the coefficient of variation of X then Y is more risky to invest in.