Question

A stock’s return has the following distribution:

Demand for Products                           Probability of Occurrence of Demand              Return if

Demand Occurs

Weak                                                             0.1                                                                 -40%

Below Average                                             0.2                                                                  -5

Average                                                         0.4                                                                   12

Above Average                                             0.2                                                                   21

Strong                                                            0.1                                                                   50

Calculate the stock’s expected return and standard deviation.

Answer 1

Stock Expected Return
	P	R
	Probability of Occurance of Demand	Return if Demand Occurs	Probability* Return*100
Weak	0.1	-40%	-4
Below Average	0.2	-5%	-1
Average	0.4	12%	4.8
Above Average	0.2	21%	4.2
Strong	0.1	50%	5
			9
Stock Expected Return = 9%
Standard Deviation
	Assume P as Probability	Assume R as Return	Assume X is Expected Return	(R-X)^2	P*[(R-x)^2]
Weak	0.1	-40.00	9.00	2401.00	240.1
Below Average	0.2	-5.00	9.00	196.00	39.2
Average	0.4	12.00	9.00	9.00	3.6
Above Average	0.2	21.00	9.00	144.00	28.8
Strong	0.1	50.00	9.00	1681.00	168.1
					479.8
	Standard Deviation = Square root of Probabilty * [ (Return - Expected Reurn)^2] for all lines
	Standard Deviation = Square root of 479.8 i.e 21.9