Question

Suppose you observe the following situation:

Security
Beta
Expected Return
Pete Corp.

1.30


.140

Repete Co.

.99


.113



a.
Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.
What is the risk-free rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

1. According to CAPM, expected return of any asset can be calculated as follows:

$E(r) = rf+\beta*(E(rm)-rf)$

where $E(r)$ - expected return on the asset,  $rf$ - risk-free rate, $E(rm)$ - expected return on the market.

2 By plugging in figures for Pete Corp. and Repete Co. we get system of equations:

$0.140 = rf+1.3*(E(rm)-rf)\\\\ 0.113 = rf+0.99*(E(rm)-rf)$

3

$0.140-0.113=0.31*(E(rm)-rf)\\\\ E(rm)-rf = \frac{0.027}{0.31}\\\\rf=0.140-1.3*\frac{0.027}{0.31}=0.02677\\\\E(rm)=rf+\frac{0.027}{0.31}=0.140-1.3*\frac{0.027}{0.31}+\frac{0.027}{0.31}=0.140-0.3*\frac{0.027}{0.31}=0.11387$

a) Expected return on the market is 11.39 (%)

b) Risk-free rate is 2.68 (%)