Asset Class Expected Return Std. Deviation Gold Large Stocks Small Stocks Value Stocks Growth Stocks 1.01% 4.30% 1.00 0.65 0.75 0.93 -0.01 Large Stocks Small Stocks 1.35% 6.10% 1.00 0.75 0.07 0.69 0.65 Value Stocks 1.51% 5.94% 0.75 0.01 0.65 0.75 0.93 -0.01 1.00 0.65 Growth Stocks 0.95% 5.13% 0.69 0.00 1.00 0.00 Gold 0.54% 5.66% 0.07 0.01 1.00 For the questions below, assume a risk-free rate of 0.4% per month 1. Suppose you are currently invested 100% in LARGE stocks, and you CANNOT short (i.e., portfolio weights cannot be negative): a. Find the portfolio that maximizes expected return if you want the same risk of LARGE stocks. b. What is the expected return of this portfolio and what are the portfolio weights in this case? c. How much are expected returns increased on a monthly basis by switching from 100% LARGE stocks to this new portfolio? 2. Suppose you CAN short assets at no extra cost (so weights can be negative). a. Find the portfolio that maximizes expected return if you want the same risk of LARGE stocks. What are the portfolio weights? b. Which asset do you SHORT in this portfolio? What asset has the biggest increase in portfolio weight from the CANNOT short to CAN short examples? Why? c. Consider the portfolios you found that maximize expected returns subject to having the same risk as LARGE stocks. What is the benefit in terms of expected returns, in being able to SHORT assets vs. not being able to SHORT assets? Given this benefit, is allowing the investor to SHORT important in this example? 3. Suppose you CANNOT short: a. What is the expected return and portfolio standard deviation of the tangency portfolio? What are the portfolio weights? b. Does GOLD have any part in this portfolio? If yes, why is GOLD a useful part of the portfolio? If not, why is GOLD not part of it? Asset Class Expected Return Std. Deviation Gold Large Stocks Small Stocks Value Stocks Growth Stocks 1.01% 4.30% 1.00 0.65 0.75 0.93 -0.01 Large Stocks Small Stocks 1.35% 6.10% 1.00 0.75 0.07 0.69 0.65 Value Stocks 1.51% 5.94% 0.75 0.01 0.65 0.75 0.93 -0.01 1.00 0.65 Growth Stocks 0.95% 5.13% 0.69 0.00 1.00 0.00 Gold 0.54% 5.66% 0.07 0.01 1.00 For the questions below, assume a risk-free rate of 0.4% per month 1. Suppose you are currently invested 100% in LARGE stocks, and you CANNOT short (i.e., portfolio weights cannot be negative): a. Find the portfolio that maximizes expected return if you want the same risk of LARGE stocks. b. What is the expected return of this portfolio and what are the portfolio weights in this case? c. How much are expected returns increased on a monthly basis by switching from 100% LARGE stocks to this new portfolio? 2. Suppose you CAN short assets at no extra cost (so weights can be negative). a. Find the portfolio that maximizes expected return if you want the same risk of LARGE stocks. What are the portfolio weights? b. Which asset do you SHORT in this portfolio? What asset has the biggest increase in portfolio weight from the CANNOT short to CAN short examples? Why? c. Consider the portfolios you found that maximize expected returns subject to having the same risk as LARGE stocks. What is the benefit in terms of expected returns, in being able to SHORT assets vs. not being able to SHORT assets? Given this benefit, is allowing the investor to SHORT important in this example? 3. Suppose you CANNOT short: a. What is the expected return and portfolio standard deviation of the tangency portfolio? What are the portfolio weights? b. Does GOLD have any part in this portfolio? If yes, why is GOLD a useful part of the portfolio? If not, why is GOLD not part of it