Question

EXPECTED RETURN

A stock's returns have the following distribution:

Demand for the Company's Products	Probability of This Demand Occurring	Rate of Return If This Demand Occurs
Weak	0.1	(20%)
Below average	0.1	(13)
Average	0.4	16
Above average	0.3	38
Strong	0.1	53
	1.0

1. Calculate the stock's expected return. Round your answer to two decimal places.
   %

2. Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Calculate the stock's coefficient of variation. Round your answer to two decimal places.

Answer 1

Expected Ret = Sum [ Prob * Ret ]

Demand	Prob	Ret	Prob * Ret
Weak	0.1	-20%	-2.00%
Below Avg	0.1	-13%	-1.30%
Avg	0.4	16%	6.40%
Above Avg	0.3	38%	11.40%
Strong	0.1	53%	5.30%
Expected Ret			19.80%

SD = SQRT [ Sum [ Prob * ( X - Avg X)^2 ] ]

Demand	Prob	Ret ( X )	(X - Avg X)	(X - Avg X)^2	Prob * (X - Avg X)^2
Weak	0.1	-20%	-39.80%	0.158404	0.01584
Below Avg	0.1	-13%	-32.80%	0.107584	0.010758
Avg	0.4	16%	-3.80%	0.001444	0.000578
Above Avg	0.3	38%	18.20%	0.033124	0.009937
Strong	0.1	53%	33.20%	0.110224	0.011022
Sum [ Prob * (X - Avg X)^2 ]					0.048136
SQRT [ Sum [ Prob * (X - Avg X)^2 ] ]					0.2194

SD is 0.2194 i.e 21.94%

COefficient of Varaition = SD / Expected Ret

= 21.94% / 19.80%

= 1.11