Question

Suppose stock X has a price of $100 today. There are three possible scenarios one year later as detailed below. Let R denote the one-year return of stock X (today to one year later).

Scenario 1 Probability 20%, Stock price $80, Dividend $0

Scenario 2 Probability 50%, Stock price $105, Dividend $5

Scenario 3 Probability 30%, Stock price $140, Dividend $5

Calculate: (a) R in each of these three scenarios, and(b) The volatility of R.

Answer 1

Formulae used-
Holding period return = (Price at year end +dividend -Price at year beginning)/Price at year beginning
Expected Return = Sum of Holding period returns
Standard deviation= sqrt(Variance)
Variance = probability *Sum of (Holding period return -Expected return)^2