Suppose that the equation for the SML is Y = 0.05 + 0.07X, where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.07 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 of 7 percent?

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Business

Shiloh Rollins

13 January, 23:30

Suppose that the equation for the SML is Y = 0.05 + 0.07X, where Y is the average expected rate of return, 0.05 is the vertical intercept, 0.07 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 of 7 percent?

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Dayton Stanton · Answer 1

Risk free interest rate is 5%

Y is 15.5% at a Beta of 1.5

X is 0.29 when Y is 7%

Explanation:

Risk free interest is 0.05 which 5% as given in the equation

The average expected return is given by Y

Y=0.05+0.07X

Since Beta is the same as X, when equals 1.5, Y is calculated thus

Y=0.05+0.07 (1.5)

Y=0.05+0.105

Y=0.155

Y=15.5%

The value of Beta at an average return of 7% is computed thus:

7%=0.05+0.07X

where X is the unknown

0.07=0.05+0.07X

0.07-0.05=0.07X

0.02=0.07X

X=0.02/0.07

X=0.29

The scenario illustrates that the Beta, which is the risk of investment and the Y, the expected average return are positively correlated.