Question

Stock a has a beta of 1.47 while stock b has a beta of 1.08 and an expected return of 13.2 percent. what is the expected return on stock a if the risk-free rate is 4.5 percent and both stocks have equal reward-to-risk premiums

Answer 1

Using the Capital Asset Pricing Model and the given information, the expected return on Stock A is calculated to be 16.3417% when both stocks have equal reward-to-risk premiums.

Step-by-step explanation:

The question asks for the expected return on Stock A given the expected return on Stock B, the beta values of both stocks, and the risk-free rate, assuming both stocks have equal reward-to-risk premiums. To calculate the expected return on Stock A, we can use the Capital Asset Pricing Model (CAPM), which states that the expected return on a stock is equal to the risk-free rate plus the stock's beta times the market risk premium (the difference between the market return and the risk-free rate). However, the market return is not provided directly. Instead, we are told that the reward-to-risk premiums of the stocks are equal, meaning that the excess return per unit of beta is the same for both stocks. Thus, we can calculate the expected return on Stock A by maintaining the same reward-to-risk premium as Stock B.

To calculate Stock A's expected return, we need to find the risk premium for Stock B by subtracting the risk-free rate from Stock B's expected return:

• Risk premium Stock B = Expected return Stock B - Risk-free rate
• Risk premium Stock B = 13.2% - 4.5%
• Risk premium Stock B = 8.7%

Now, we calculate the reward-to-risk premium for Stock B by dividing its risk premium by its beta:

• Reward-to-risk premium Stock B = Risk premium Stock B / Beta of Stock B
• Reward-to-risk premium Stock B = 8.7% / 1.08
• Reward-to-risk premium Stock B = 8.0556%

Since Stock A has the same reward-to-risk premium, we multiply this value by Stock A's beta to find Stock A's risk premium and add it to the risk-free rate to find Stock A's expected return:

• Risk premium Stock A = Reward-to-risk premium Stock B * Beta of Stock A
• Risk premium Stock A = 8.0556% * 1.47
• Risk premium Stock A = 11.8417%
• Expected return Stock A = Risk-free rate + Risk premium Stock A
• Expected return Stock A = 4.5% + 11.8417%
• Expected return Stock A = 16.3417%

Therefore, the expected return on Stock A is 16.3417% assuming equal reward-to-risk premiums with Stock B.

Answer 2

The expected return of stock A is 16.34%.

The formula for computing expected return according to CAPM is:

Expected Rate of Return = Rf +β (Rm-Rf)

The underlined term (Rm - Rf) in the equation above is known as the reward-to-risk premium. This represents the excess return earned by an investment over and above the risk free rate.

From the data given in the question, we can arrive at the reward-to-risk premium of stock b.

Let the reward to risk premium (Rm - Rf) be 'x'.

Substituting the values in the CAPM equation we get,

0.132 = 0.045+1.08x

Solving for x we get,

0.087= 1.08x

x = 0.080555556 (0.087/1.08)

Now, we substitute this value of 'x' again in this CAPM, but this time with stock a's beta.

Expected Return = 0.045+ (1.47 × 0.080555556 )

= 0.045 + 0.118416667

= 0.163416667 or 16.34%