You are evaluating various investment opportunities currently available and you

Question

You are evaluating various investment opportunities currently available and you have calculated expected returns and standard deviations for five different well-diversified portfolios of risky assets: Portfolio Expected Return Standard Deviation Q 7.8% 10.5% R 10.0 14.0 S 4.6 5.0 T 11.7 18.5 U 6.2 7.5 a. For each portfolio, calculate the risk premium per unit of risk that you expect to receive ([E(R) ? RFR]/?). Assume that the risk-free rate is 3.0 percent. b. Using your computations in Part a, explain which of these five portfolios is most likely to be the market portfolio. Use your calculations to draw the capital market line (CML). c. If you are only willing to make an investment with ? = 7.0%, is it possible for you to earn a return of 7.0 percent? d. What is the minimum level of risk that would be necessary for an investment to earn 7.0 percent? What is the composition of the portfolio along the CML that will generate that expected return? e. Suppose you are now willing to make an investment with ? = 18.2%. What would be the investment proportions in the riskless asset and the market portfolio for this portfolio? What is the expected return for this portfolio?

Explanation / Answer

Solution:

A)

Q= (Expected Return – Assumption Risk free rate) / Standard Deviation

    = (7.8% – 3%) / 10.5%

    = 4.8% / 10.5%

    = 0.4571

    = (10% – 3%) / 14%

    = 7% / 14%

    = 0.5000

= (4.6% – 3%) / 5%

   = 1.6% / 5%

= 0.3200

    = (11.7% – 3%) / 18.5%

    = 8.7% / 18.5%

    = 0.4703

    = (6.2% – 3%) /7.5%

    = 3.2% / 7.5%

   = 0.427

B) Among the 5 portfolios, portfolio R is the most likely market portfolio with the highest ratio of 0.5000. Thus, CML slope is 0.5000 and the intercept is 3%.

C) The CML equation is E(Rportfolio) = 3% + (0.50)portfolio.

The desired standard deviation = 7.0%

E (Rportfolio) = 3% + (0.50) (7%)

                    = 0.03 + 0.035

                    = 0.065 or 6.5%.

No, it is not possible to earn an expected return of 7%.

D) By using CML equation, the expected portfolio return = 7%

    E(Rportfolio) 7% = 3% + (0.50) portfolio

                       ( 7% - 3%) = (0.50) portfolio  

                   4% = (0.50) portfolio  

         portfolio = 4% / 0.50

                     =8%.

Therefore, 8% is the composition of the portfolio along with the CML that will generate the expected return.

E) portfolio= 18.2%

so wMKT = 18.2% / 14.0%

              =1.30

wrisk-free asset= 1 – (1.3) = -0.30.

Weighted average of the risk-free and market portfolio returns = 1.30 (10%) + (-0.30) (3%)

                                                                                                    = 12.1%.

Using CML equation to find the expected return

E(R portfolio) = 3% + (0.50) portfolio

                        = 3% + (0.50)(18.2%)

                       = 12.1%.

Therefore, both the methods agree the expected portfolio return

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