In addition to the information in exercise 29 on the S&P 500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts (REITs) during the same time period was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Management, Guide to the Markets). The correlation between the S&P 500 and REITs is .74 and the correlation between core bonds and REITs is −.04. You are considering portfolio investments that are composed of an S&P 500 index fund and REITs as well as portfolio investments composed of a core bonds fund and REITs.

a. Using the information provided here and in exercise 29, determine the covariance between the S&P 500 and REITs and between core bonds and REITs.

b. Construct a portfolio that is 50% invested in an S&P 500 fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

c. Construct a portfolio that is 50% invested in a core bonds fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

d. Construct a portfolio that is 80% invested in a core bonds fund and 20% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio?

e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an aggressive investor? Which would you recommend to a conservative investor? Why?