Question

Albert estimates that there are three possible return outcomes for a stock he is considering for purchase. He thinks that there is a 35% chance the economy will boom and his stock will return 25%, a 50% chance the economy will continue at its current pace and the stock will return 8%, and finally, that there is a 15% chance that the economy will falter and the expected return on his stock will be -10%. Given these probabilities and conditional expected returns, what is Albert's expected return on the stock he is considering for purchase?

Answer 1

State of Economy	Probability	Return on stock
1	35%	25%
2	50%	8%
3	15%	-10%

Suppose that the economy will boom is denoted by state 1, the economy will continue in its current pace is denoted by state 2, and the economy will falter is denoted by state 3

Probability of state 1 = p₁ = 35%, Stock return when state 1 = R₁ = 25%

Probability of state 2 = p₂ = 50%, Stock return when state 2 = R₂ = 8%

Probability of state 3 = p₃ = 15%, Stock return when state 3 = R₃ = -10%

Albert's expected return on the stock (given the probabilities and conditional expected returns) is computed using the formula:

Expected Return = p₁*R₁ + p₂*R₂ + p₃*R₃ = 35%*25% + 50%*8% + 15%*(-10%) = 8.75% + 4% + (-1.5%) = 11.25%

Answer -> Albert's expected return on the stock = 11.25%