Question

# 1. Consider an economy with four possible economic states: Boom, Normal, Slow Growth, and Recession which...

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%.)

 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.