You are given the following information about Stocks A and B: Rate of Return if

Question

You are given the following information about Stocks A and B:

                                                            Rate of Return if State Occurs

State of Economy

Probability of State of Economy

Stock A

Stock B

Boom

0.20

20%

25%

Normal

0.60

10%

12%

Recession

0.20

-5%

-6%

Stock A has a beta of 0.9, and Stock B has a beta of 1.4. Assume that the CAPM holds, and that neither of these stocks is over or undervalued.

a) What is the risk-free rate and expected return on the market portfolio?

b) What would be the beta of a portfolio consisting of 25% of Stock A and 75% of Stock B?

c) What would be the expected return of the portfolio under b)?

Can someone please help me answer all parts of this question? Struggling... Thanks in advance. **show all the equations/formulas used just so i know how to approach this problem... thank you kindly.

You are given the following information about Stocks A and B:

                                                            Rate of Return if State Occurs

State of Economy

Probability of State of Economy

Stock A

Stock B

Boom

0.20

20%

25%

Normal

0.60

10%

12%

Recession

0.20

-5%

-6%

Explanation / Answer

Expected return on stock A = (20 *.2 ) +(10*.6 ) + (-5 *.20)

                                                = 4 + 6 - 1

                                                  = 9%

Expected return on stock B = (25*.20)+(12*.60)+(-6*.20)

                                               = 5 + 7.2 - 1.2

                                              = 11%

Under CAPM model ,Expected return on stock = Rf+ [Beta* (Rm-Rf)]

        Stock A = 9 = Rf + [.9 *(Rm-Rf)]

                          9- Rf = .9 (Rm-Rf)

                          Rm-Rf = (9 -Rf) / .90                            Equation 1

Stock B, 11 = Rf + [1.4 (Rm-Rf)]

Putting the value of equation 1 in this that is value of Rm-Rf = (9-Rf)/.9

              11 = Rf + [1.4 * (9-Rf) /.9]

              11 =Rf + [1.5556 (9 -Rf)]

              11 = Rf + 14 - 1.5556Rf

             11 = 14 - .5556Rf

            .5556Rf = 14-11

          Rf = 3/ .5556

                = 5.40 % .

Putting the value of Rf in equation 1 :   Rm-Rf = (9 -Rf) / .90    

                     Rm - 5.40 = ( 9 -5.40) / .90

                     Rm - 5.40 = 3.6 /.9

                    Rm- 5.40 = 4

                       Rm = 4+ 5.40

                               = 9.40%

b) Beta of portfolio = (.9 * .25 ) +(1.4 *.75)

                               = .225+ 1.05

                            = 1.275

c)Expected return on portfolio = (9 *.25) +(11*.75)

                                                     = 2.25+ 8.25

                                                      =10.50%

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