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A stock has a beta of .75, the expected return on the market is 11 percent,...

A stock has a beta of .75, the expected return on the market is 11 percent, and the risk-free rate is 4 percent.

              a.           What must the expected return on this stock be?

              b.           Draw the Security Market Line (SML) -be sure to label all relevant points-

              c.           Suppose the risk free rate falls to 3%. What is the expected return on this stock? Redraw the SML. How has the shape of the curve changed?

              d.           Suppose the expected return on the market is now 14 percent and the risk free rate is 4%. What is the expected return on his stock? Redraw the SML. How has                  the shape changed from the first graph you created?

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Answer #1

A) We need to solve the CAPM equation to calculate the Expected return of the given stock:

E_{r} = R_{RF}+\beta(R_{M}-R_{RF})

  • E_{r} = Expected return
  • R_{RF} = Risk free return
  • R_{M} = Market Return

E_{r} = 4+0.75 (11-4)

E_{r} = 9.25 \%

B)

Asset Beta Return
Risk Free (Rf) 0 4.00%
Market Portfolio (Rm) 1 11.00%
C 0.75 9.25%

Market portfolio always has a beta of 1 and the risk free rate is risk free so it has a beta of 0. Using these two points, we can plot the SML and using the expected return calculated for the stock in the previous part, we can calculate where it will lie on the SMP graph:

11.00% Expected return 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% Stock, 0.75, 9.25% 4.00% 0 0.2 0.4 0.8 1 1.2 0.6 Beta SML

C) If the risk free return falls to 3% the expected return will be as follows:

E_{r} = R_{RF}+\beta(R_{M}-R_{RF})

  • E_{r} = Expected return
  • R_{RF} = Risk free return
  • R_{M} = Market Return

E_{r} = 3+0.75 (11-3)

E_{r} = 9.00\%

Following is the SML graph:

phpft6BGO.png

We can see that if risk free return reduces to 3, the SML becomes steeper

D)

E_{r} = R_{RF}+\beta(R_{M}-R_{RF})

  • E_{r} = Expected return
  • R_{RF} = Risk free return
  • R_{M} = Market Return

E_{r} = 4+0.75 (14-4)

E_{r} = 11.50\%

Following is the SML graph:

phpHopAPG.png

Again the SML has become steeper in comparison to how it was in part A

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