5.5 Binomial Probability Distribution 243 29. 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 devia- tion 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, Ist 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. a. Using the information provided, determine the covariance between the S&P 500 and core bonds. 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? 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? d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested omg illcomed saved bell in a core bonds fund. 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) has the largest expected return? Which has the smallest standard deviation? Which of these portfolios is the best investment alternative? alsen work on 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 sidimay molest all rhiw core bonds fund, or one of the three portfolios? Why? Joinsme to ed 30. In addition to the information in exercise 29 on the S&P 500 and core bonds, J.P. Mor- gan Asset Management reported that the expected return for real estate investment trusts (REITs) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Manage- ment, Guide to the Markets, Ist Quarter, 2012). The correlation between the S&P 500 and REITs is . 74 and the correlation between core bonds and REITs is -.04. You are consider- ing 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? 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? 5.5 Binomial Probability Distribution The binomial probability distribution is a discrete probability distribution that has many applications. It is associated with a multiple-step experiment that we call the binomial