Question

Given the following data for a stock: beta = 1.2; risk-free rate = 3%; market rate of return = 13%; and expected rate of return on the stock = 17%. Then the stock is:

-overpriced

-correctly priced

-underpriced

-cannot be determined

Answer 1

The Correct Answer is Underpriced

Alpha of a stock is the difference between the expected return from the stock and the required return from the stock. When alpha is positive it means that the stock is Underpriced and when alpha is negative it means that the stock is Overpriced. When a stock is fairly priced its alpha will always be zero.

Expected Return of the Stock is the return provided by the stock.

Required Rate of Return of the Stock is the return required by the investor.

As per Capital Asset Pricing Model (CAPM)

Re = Rf + (Rm-Rf) β

Where Re = Required Rate of Return

Rf = Risk free rate of return

Rm – Market Return

β – Beta of the stock

Calculation of Required Rate of Return of stock

Rf = 3%

Rm = 13%

β = 1.2

Using the formula Re = Rf + (Rm-Rf) β

Re = 3 + (13 - 3) 1.2

Re = 3 + 10 * 1.2

Re = 3 + 12

Re = 15%

Calculation of Alpha

Expected Return of the Stock - Required Rate of Return of the Stock

= 17% - 15%

= 2%

Since Alpha is positive the stock is underpriced.