Question

Suppose that the equation for the SLM is Y = 0.05 + 0.04X, where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk level as measured by beta. What is the risk-free interest rate for this SML? What is the average expected rate of return at a beta of 1.5? What is the value of beta at an average expected rate of return is 7 percent?

Short answer

The risk-free interest rate will be 5%.

The average expected rate of return will be 11%.

The value of beta will be 0.5.

Step-by-step solution

Step 1. Explanation

The risk-free rate will be the intercept of SLM, i.e., 0.05. Thus, the risk-free rate will be 5% (=0.05*100).

The average expected rate of return is calculated below:

$$\begin{gathered} Y=0.05+0.04X \\ X=1.5 \\ Y=0.05+0.04(1.5) \\ Y=0.05+0.06 \\ Y=0.11 \\ ExpectedRateofReturn=Y\times 100 \\ =0.11\times 100 \\ =11\% \end{gathered}$$

The average expected rate of return will be 11%.

The value of beta is calculated below:

$$\begin{gathered} Y=0.05+0.04X \\ Y=7\% \\ 0.07=0.05+0.04X \\ 0.04=0.07-0.05 \\ X=\frac{0.02}{0.04} \\ X=0.5 \end{gathered}$$

The value of beta will be 0.5