Question

6. Suppose that continuously compounded returns are normally distributed. A stock currently trades for $100, with an expected return of 12% and standard deviation of 20%. What is the probability distribution for the rate of return (with continuous compounding) to be earned over a one-year period?

Answer 1

Given, Expected Return = μ = 0.12

Standard Deviation = σ = 0.20

the probability distribution for the rate of return over a one-year period with continuous compounding is:

Ф(μ - σ²/2, σ²)

= Ф(0.12 - 0.20²/2, 0.20²)

= Ф(0.10, 0.20²)

The expected value of the return is 10% per annum and the standard deviation is 20% per annum