The Vanguard Group is one of the largest investment firms in the world with approximately $7 trillion in assets in 2021. Vanguard offers investment funds in stocks, bonds, annuities, and many other forms. Vanguard estimates the average correlation between the returns offered by stocks and bonds to be -0.32. Suppose that a particular stock index fund offered by Vanguard has an expected return of 4.78% with a standard deviation of 18.04%, and an investment-grade bond fund offered by Vanguard has an expected return of 5.33% with a standard deviation of 2.65%. Suppose that in addition to the stock index fund and investment-grade bond fund, that Vanguard also offers the ability to invest in a real-estate fund. The real-estate fund has an expected return of 11.99% and a standard deviation of 25.65%. The correlation between the stock index fund and the real-estate fund is 0.64, and the correlation between the investment-grade bond fund and the real-estate fund is -0.19. (a) Based on the information provided, what is the covariance between the stock index fund and the real-estate fund? (Round your answer to four decimal places.) What is the covariance between the investment-grade bond fund and the real-estate fund? (Round your answer to four decimal places.) (b) What is the expected return (as a percent) for a portfolio composed of 50% invested in the stock index fund and 50% invested in the real-estate fund? % What is the standard deviation (as a percent) for a portfolio composed of 50% invested in the stock index fund and 50% invested in the real-estate fund? (Round your answer to four decimal places.) % (c) What is the expected return (as a percent) for a portfolio composed of 50% invested in the investment-grade bond fund and 50% invested in the real-estate fund? % What is the standard deviation (as a percent) for a portfolio composed of 50% invested in the investment-grade bond fund and 50% invested in the real-estate fund? (Round your answer to four decimal places.) % (d) Consider a portfolio composed of 60% invested in the stock index fund and 40% invested in the investment-grade bond fund, a portfolio composed of 40% invested in the stock index fund and 60% invested in the investment-grade bond fund, as well as the portfolios from parts (b) and (c) of this problem. The expected returns and standard deviations of the two portfolios consisting of the stock index and the investment grade bond fund are given in the table below. Portfolio Expected Return (%) Standard Deviation 60% stock index and 40% investment-grade bond 5% 10.5328 40% stock index and 60% investment-grade bond 5.11% 6.8743 Which portfolio would be most appropriate for a conservative investor? O portfolio that invests 50% in the investment-grade bond fund and 50% in the real-estate fund O portfolio that invests 60% in the stock index fund and 40% in the investment-grade bond fund O portfolio that invests 40% in the stock index fund and 60% in the investment-grade bond fund portfolio that invests 50% in the stock index fund and 50% in the real-estate fund Which portfolio would be most appropriate for an aggressive investor who wants the highest possible returns? O portfolio that invests 50% in the investment-grade bond fund and 50% in the real-estate fund O portfolio that invests 60% in the stock index fund and 40% in the investment-grade bond fund O portfolio that invests 40% in the stock index fund and 60% in the investment-grade bond fund O portfolio that invests 50% in the stock index fund and 50% in the real-estate fund