Chapter 5.4, Problem 29E

J.P. Morgan Asset Management publishes information about financial investments. Over the past 10 years, the expected return for the S&P 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a core bonds fund was 5.78% with a standard deviation of 2.13% (J.P. Morgan Asset Management, Guide to the Markets, 1st Quarter, 2012). The publication also reported that the correlation between the S&P 500 and core bonds is −.32. You are considering portfolio investments that are composed of an S&P 500 index fund and a core bonds fund.

1. a. Using the information provided, determine the covariance between the S&P 500 and core bonds.
2. b. Construct a portfolio that is 50% invested in an S&P 500 index fund and 50% in a core bonds fund. In percentage terms, what are the expected return and standard deviation for such a portfolio?
3. c. Construct a portfolio that is 20% invested in an S&P 500 index fund and 80% invested in a core bonds fund. In percentage terms, what are the expected return and standard deviation for such a portfolio?
4. d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a core bonds fund. In percentage terms, what are the expected return and standard deviation for such a portfolio?
5. e. which of the portfolios in parts (b), (c), and (d) has the largest expected return? which has the smallest standard deviation? which of these portfolios is the best investment alternative?
6. f. Discuss the advantages and disadvantages of investing in the three portfolios in parts (b), (c), and (d). would you prefer investing all your money in the S&P 500 index, the core bonds fund, or one of the three portfolios? why?