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Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is .8 while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S and P 500 index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%.

a. If currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.

b. If instead you could invest only in bills and one of these portfolios, which would you choose?

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Retselisitsoe Pokothoane
Retselisitsoe PokothoaneLv10
28 Sep 2019

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Related questions

Two investment advisers are comparing performance. One averaged a 19% return and the other a 16% return. However, the beta of the first adviser was 1.5, while that of the second was 1.

a. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)?

b. If the T-bill rate were 6% and the market return during the period were 14% which adviser would be the superior stock selector?

c. What if the T-bill rate were 3% and the market return 15%?

Consider a pension fund at 01/01/2018 that requires a payout of $100, 000, 000 at the end on 31/12/2020. The fund would like to invest into a portfolio that delivers this payout for sure. The yield curve is flat at y = 10% across maturities, so that the net present value of the liability is given by $68, 301, 345.54. The fund considers two bonds. Bond A is a one year pure discount bond, while Bond B is a 5 year bond with coupons paid annually at the rate of 5%. All payouts and investment decisions take place at the start of each year.

(a) Construct a portfolio using the two bonds that immunizes the investment to market movements when funds need to be reinvested on 01/01/2019.

(b) Show that if any cash flow received at the end of 2018 and 2019 can be invested for two years at a yield of 8%, the pension fund will receive $100, 000, 000 at the on 31/12/2020.

(c) Suppose now that the pension fund can invest in Bond B again and Bond C which is a one year pure discount bond on 01/01/2019. Find the investments in Bond B and Bond C that immunize the portfolio against market movements when funds need to be reinvested on 01/01/2020.

(d) Show that the new portfolio yields $100,000,000 at the end of 2019 given that yields in 2019 increase to 9%.

(e) How would your reinvestment strategy change on 01/01/2019 if there was a Bond D available which is a two year pure discount bond maturing on 31/12/2020?

3. Consider three alternative bonds that you might invest in, each of which matures in one year. The following table shows the probability that you will receive each possible return. For example, if you buy bond A, the probability is 90 percent that your return will be 20 percent and the probability is 10 percent that your return will be 100 percent.

Bond Probability Return Bond A 90% 20% 10% -100% Bond B 75% 40% 25% -40% Bond C 60% 10% 40% -10%

a. Calculate the expected return for all three bonds in percentage terms.

b. Calculate the standard deviations of the returns on these bonds. If you are extremely risk-averse, which of the three bonds would you buy? Why?

c. Would a risk-averse investor ever buy Bond A instead of one of the other bonds? Why or why not?

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