Question

(TCO 2) Given the data below, calculate the expected return, variance, and standard deviation of the following company. In a recessionary economy, which is expected to occur with a 30% probability, the expected returns would be -5%. In an expanding economy with an expected probability of occurrence of 20%, the expected return would be 10%. In a normal economy, expected to occur 50% of the time, the expected return would be 5%.

Answer 1

Expected returns are considered as X, and probabilities are considered as P.

X, %	P	Expected return (%), PX	X^2	PX^2
-5	0.30	-5 × 0.30 = -1.5	(-5)^2 = 25	0.30 × 25 = 7.5
10	0.20	10 × 0.20 = 2	(10)^2 = 100	0.20 × 100 = 20
5	0.50	5 × 0.50 = 2.5	(5)^2 = 25	0.50 × 25 = 12.5
Total	1.00	3		40

Expected return = 3% (Answer)

Variance = (PX^2) – (PX)^2

                = 40 – 3

                = 37% (Answer)

Standard deviation = Square root of variance

                                    = Square root of 37

                                    = 6.08% (Answer)