MGSC 372: Advanced Business Statistics
Practice problems on the lognormal distribution
1. A stock has an expected return of 12% per annum and a volatility of 36% per
annum. Assume the price evolves according to the geometric Brownian motion
model.
(a) What is the probability that the price of the stock triples in 10 years?
(b) What is the probability that the price of the stock is cut in half in 6 months?
(c) Repeat parts (a) and (b) for a stock with the same expected return, but a
volatility of only 16% per annum. Before doing the calculations, think about
how you expect your answers to change.
2. Mr. Jones has just bought 150 shares in a hi-tech stock that is currently valued
at $40 per share. Financial analysis indicates that the expected annual return on
the stock is 13%, and the volatility is 16% per annum. Assume that the price of
a share follows the geometric Brownian motion model. Find the probability that
Mr. Jones’ investment will be worth at least $9,000 in 3 years’ time.
3. Mr. Ricci has invested in a stock with an expected return of 11% per annum and
a volatility of 4% per annum. Assume that the price of the stock follows geometric
Brownian motion. Find a 90% prediction interval for the average rate of return over
a five year period (we will discuss the average rate of return in class on Monday
Sept. 18).