1. The purpose of this portion of the project is to calculate the benefits to diversification across broad asset classes. Assume the expected returns, standard deviations, and correlations for well-diversified portfolios of US stocks, US bonds, US real estate and international stocks are given as follows: US Stocks US Bonds US Commercial Real Estate International Stocks Expected Annual Return 9.5% 3.5% 7% 9% Annual Standard Deviation 20% 12% 13% 19% US Stocks US Bonds US Real Estate Annual Correlations US Bonds US Real Estate International Stocks 35% 50% 55% 60% 25% 40% a. Derive the efficient frontier using US equities and bonds. b. Derive the efficient frontier using US bonds, US equities, real estate, and international stocks. (Use solver. In setting the objective function and the constraints, do not permit short-sales, and recall that the goal is to choose the portfolio weights that minimize the level of portfolio risk, given some level of expected return. Start with the level of portfolio expected return equal to that of 9.5%, and then lower this constraint in .5% increments to 3.5%. c. Superimpose this efficient frontier on the efficient frontier graph from(a). d. Comparing the efficient frontiers from (a) and (b)for an expected return of8%, what is the estimated reduction in portfolio risk from international, and real estate diversification? e. What are the portfolio weights for the 4-fund portfolio with an expected return of 8%? f. Determine the optimal risky portfolio if the risk free rate is 0.5%? (The optimal risky portfolio has the highest Sharpe Ratio). 1. The purpose of this portion of the project is to calculate the benefits to diversification across broad asset classes. Assume the expected returns, standard deviations, and correlations for well-diversified portfolios of US stocks, US bonds, US real estate and international stocks are given as follows: US Stocks US Bonds US Commercial Real Estate International Stocks Expected Annual Return 9.5% 3.5% 7% 9% Annual Standard Deviation 20% 12% 13% 19% US Stocks US Bonds US Real Estate Annual Correlations US Bonds US Real Estate International Stocks 35% 50% 55% 60% 25% 40% a. Derive the efficient frontier using US equities and bonds. b. Derive the efficient frontier using US bonds, US equities, real estate, and international stocks. (Use solver. In setting the objective function and the constraints, do not permit short-sales, and recall that the goal is to choose the portfolio weights that minimize the level of portfolio risk, given some level of expected return. Start with the level of portfolio expected return equal to that of 9.5%, and then lower this constraint in .5% increments to 3.5%. c. Superimpose this efficient frontier on the efficient frontier graph from(a). d. Comparing the efficient frontiers from (a) and (b)for an expected return of8%, what is the estimated reduction in portfolio risk from international, and real estate diversification? e. What are the portfolio weights for the 4-fund portfolio with an expected return of 8%? f. Determine the optimal risky portfolio if the risk free rate is 0.5%? (The optimal risky portfolio has the highest Sharpe Ratio)
