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 4.73% with a standard deviation of 18.24%, and an investment-grade bond fund offered by Vanguard has an expected return of 5.32% with a standard deviation of 2.25%.

Based on the information provided, what is the covariance between this stock index fund and the investment-grade bond fund? (Keep the means and standard deviations as percents when finding the covariance. Round your answer to four decimal places.)

(b)

What is the expected return (as a percent) for a portfolio composed of 60% invested in the stock index fund and 40% invested in the investment-grade bond fund?

%

What is the standard deviation (as a percent) for a portfolio composed of 60% invested in the stock index fund and 40% invested in the investment-grade bond fund? (Round your answer to four decimal places.)

%

(c)

What is the expected return (as a percent) for a portfolio composed of 40% invested in the stock index fund and 60% invested in the investment-grade bond fund?

%

What is the standard deviation (as a percent) for a portfolio composed of 40% invested in the stock index fund and 60% invested in the investment-grade bond fund? (Round your answer to four decimal places.)

%

(d)

Which of the portfolios in part (b) or (c) has the highest expected return?

Invest 40% in the stock index fund and 60% in the investment-grade bond fund.Invest 60% in the stock index fund and 40% in the investment-grade bond fund.

Which portfolio has the lowest standard deviation?

Invest 40% in the stock index fund and 60% in the investment-grade bond fund.Invest 60% in the stock index fund and 40% in the investment-grade bond fund.

(e)

Which portfolio would should be preferred?

Invest 40% in the stock index fund and 60% in the investment-grade bond fund.Invest 60% in the stock index fund and 40% in the investment-grade bond fund.

Is the portfolio you chose guaranteed to perform better than the other portfolio in any given year?

YesNo