Question

Consider the following possible outcomes for the economy (first column) with the associated probabilities (second column) and the return of stock A for the different states of the world. Outcome Probability Return Recession 25% -30% Expansion 40% 15% Boom 35% 55% What is the expected variance of stock A?

a.

11%

b.

6%

c.

29%

Answer 1

Correct answer is option (a). 11%

Explanation;

Condition	Probability	Return	Expected return (Probabilty * Return)
Recession	0.25	- 30%	- 7.5%
Expansion	0.40	15%	6%
Boom	0.35	55%	19.25%
Expected return			17.75%

Probability	Return	Deviation from Expected Value	Square	Probability * Square
0.25	- 30%	(-.30 – .1775) = - .4775	0.2280	0.057
0.40	15%	(.15 – .1775) = - .0275	0.00076	0.000304
0.35	55%	(.55 – .1775) = .3725	0.1387	0.0485
Variance				0.1059

Variance is 10.59% (Approx.) OR 11%