Question

Stock Y has a beta of .9 and an expected return of 11.2 percent. Stock Z has a beta of .5 and an expected return of 7.2 percent. What would the risk-free rate have to be for the two stocks to be correctly priced

Answer 1

Required risk free rate for two stocks to be correctly priced would be 2.20%.

Step-by-step explanation:

In order to determine this, the Capital Asset Pricing Model (CAPM) formula is used as follows:

Rs = Rf + (Beta * MR) .................................... (1)

Where;

For Stock Y:

Rs = Expected return on stock = 11.2%, or 0.112

Rf = Risk free return = ?

Beta = 0.9

MR = Market risk premium = ?

Substituting the values into equation (1), we have:

0.112 = Rf + (0.9 * MR) ................................. (2)

For Stock Z:

Rs = Expected return on stock = 7.2%, or 0.072

Rf = Risk free return = ?

Beta = 0.5

MR = Market risk premium = ?

Substituting the values into equation (1), we have:

0.072 = Rf + (0.5 * MR) ................................. (3)

If we deduct equation (3) from equation (2) and solve for MR, we have:

(0.112 - 0.072) = (Rf - Rf) + (0.9MR - 0.5MR)

0.04 = 0 + 0.4MR

MR = 0.04 / 0.4

MR = 0.10, or 10%

Substituting MR = 0.01 into equation (2) and solve for Rf, we have:

0.112 = Rf + (0.9 * 0.10)

0.112 = Rf + 0.09

Rf = 0.112 - 0.09

Rf = 0.022, or 2.20%

Therefore, required risk free rate for two stocks to be correctly priced would be 2.20%.