A stock has an expected return of 12.15 percent, its beta is 1.31, and the expected return on the market is 10.2 percent. What must the risk-free rate be

Rf=risk-free rate=3.91%

Explanation:

E(R) = Rf + ß( Rmarket - Rf )

E(R)= Expected return =12.15%=0.1215

Rf= Risk free rate = ?

ß = Beta = 1.31

Rmarket = Expected return of market = 10.2 %= 0.102

Changing to fraction before solving

0.1215= Rf + 1.31(0.102- rf)

0.1215= Rf +0.13362-1.31Rf

0.13362-0.1215= -Rf+1.3Rf

0.01212=0.31Rf

Rf= 0.01212/0.31= 0.03909 x 100%= 3.909% =3.91%

or Solving directly

12.15=  Rf +1.31(10.2-Rf)

12.15=  Rf +13.362 -1.31Rf

13.362 -12.15=-Rf + 1.31Rf

 1.212= 0.31Rf

Rf =3.909% round off to 3.91%

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