Question

1. Consider an economy with four possible economic states: Boom, Normal, Slow Growth, and Recession which have a 0.2, 0.3, 0.4, and 0.1 probability of occurring, respectively. You are considering a stock which is expected to return 12%, 9%, 4%, and 2%, respectively, in each of those states. What is the expected return on the stock?

The answer to the above is 6.9%. I need the next question answered.

2. What is the standard deviation of the above stock's return? (Assume that the expected return is 8%.)

Answer 1

Probabilty	Return	P*Return	(R -mean 8%)	(R -mean)^2	P*(R-M)^2
0.2	12	2.4	4	16	3.2
0.3	9	2.7	1	1	0.3
0.4	4	1.6	-4	16	6.4
0.1	2	0.2	-6	36	3.6
Total		6.9			13.5

Mean             %     =	Sum of( P*return)
		6.9
Standard deviation % =	squarroot of(Sum of (P* (R-Mean)^2))
		SQRT of ( 13.5)
		3.674235 3.67%

Note : Here in second part of the question specifically says to take the expected return as 8% hence in table R-8% has been take actually it has to be take as R- Mean that is 6.9 (calculated value) . i think students understood the concept here.