A stock is valued at $28.00.The annual expected return is 9.0% and the standard deviation of annualized returns is 19.0%.If the stock is lognormally distributed,what is the expected price after 4 years?
A) $28.00
B) $32.33
C) $40.13
D) $54.60

Question

Quizplus · Accepted Answer

We can use the formula for lognormal distribution to find the expected price after 4 years, which is:

Expected Price = Current Price * e^[(μ - σ^2/2) * t + σ * sqrt(t) * Z]

where:
- μ is the expected return
- σ is the standard deviation
- t is the number of years
- Z is a standard normal random variable

Plugging in the values given, we get:

Expected Price = $28.00 * e^[(0.09 - 0.19^2/2) * 4 + 0.19 * sqrt(4) * Z]
Expected Price = $28.00 * e^[-0.5016 + 0.38Z]

Using a calculator or a normal distribution table, we can find that the expected value of e^(0.38Z) is 1.4397. Therefore:

Expected Price = $28.00 * 1.4397
Expected Price = $40.13

So the best choice is C.

A Stock Is Valued at $28