Question

The following probability distributions of returns for two stocks have been estimated:

Probability; Stock A; Stock B

0.3; 12%; 5%

0.4; 8; 4

0.3; 6; 3

What is the coefficient of variation for the stock that is less risky (assuming you use the coefficient of variation to rank riskiness).

3.62

0.28

0.66

5.16

0.19

Answer 1

Stock A

Probability (P)	Return(%)	P*Return	Deviation form expected return (D)	PD^2
0.3	12.00	3.60	3.40	3.47
0.4	8.00	3.20	(0.60)	0.14
0.3	6.00	1.80	(2.60)	2.03

Expected Return =P*Return

= 3.6+3.2+1.8

= 8.60%

Variance = PD^2

= 3.47+.14+2.03

= 5.64

Standard Deviation = Variance

= 5.64

= 2.37%

Coefficient of Variation (CV) = standard deviation / expected value

= 2.37/8.6

= 0.28

Stock B

Probability (P)	Return(%)	P*Return	Deviation form expected return (D)	PD^2
0.3	5.00	1.50	1.00	0.30
0.4	4.00	1.60	-	-
0.3	3.00	0.90	(1.00)	0.30

Expected Return =P*Return

= 1.5+1.6+.9

= 4.00%

Variance = PD^2

= .3+0+.3

= .60

Standard Deviation = Variance

= .60

= .77%

Coefficient of Variation (CV) = standard deviation / expected value

= .77/4

= 0.19

The lower the ratio, lower the risk.So answer is 0.19