Question

A stock has an expected return of 12.4 percent and a beta of 1.37. The market expected return is 10 percent. What must the risk-free rate be?

Fill in the values in the spreadsheet.

	Input area:
	Stock E(R)	12.40%
	Stock beta	1.32
	Market E(R)	10.00%
	Output area:
	Risk-free

Answer 1

Note: Beta value is different in the question and in the table. Assuming Beta = 1.37 as in question.

This is an application of CAPM, which is mathematically expressed as:

Expected Return on Equity = Risk Free Rate + Beta * (Expected Market Return - Risk Free Rate)

Substituting the values given in question,

12.40% = Risk free rate + 1.37 * (10% - Risk Free Rate)

12.40% = Risk Free Rate + 13.7% - 1.37 * Risk free Rate

1.3% = 0.37 * Risk free rate

=> Risk free rate = 3.51%

Had Beta been 1.32 as given in table, Risk free rate by same methodology above would have been 2.5%