Question 1 (30 points)

1. Using all the daily data for the S&P 500 in theExam spreadsheet, please measure the (1) annualized volatility of the S&P 500, (2) expected return of the S&P 500, and (3) expected excess return of the S&P 500 assuming:
   • The Sharpe Ratio for the S&P 500 equals .3
   • There are 252 trading days in a year
   • The one-year risk-free rate equals 4.79%
2. Now, let's assume you manage an S&P 500 index fund and are ONLY willing to consider additional strategies that increase expected return without increasing overall portfolio risk. A hedge fund manager proposes you allocate 25% of your assets to her fund which has the following risk characteristics:

Beta to the S&P 500 = 0.4

Volatility = 15%

Expected Alpha = 5%

Correlation with the S&P 500 = .40

Taxes are not a consideration. Would you make the investment? Why or why not?

1. What would the alpha on the hedge fund have to be for you to change your decision in part b?
2. Using the daily data for the S&P 500 and Proctor and Gamble (PG) in the Exam spreadsheet, please measure the following for PG, assuming an Alpha of zero:

• Annualized volatility
• Correlation with the S&P 500
• Beta
• Expected Return

1. If you were to follow the same criteria for the 25% allocation to PG as a 25% allocation to the Hedge Fund referenced in 1b, what minimum Alpha for PG would you need to consider the decision.

Question 2(36 points)

1. You recently received a $500,000 inheritance. You do not plan to use the money for 4 years, at that time, you expect it will be for a down payment for a house/apartment. You want to invest the money in the Capital Markets but want to be certain that you won't lose money on your investments over the four-year period.Let's define certain as having only a 2.28% probability of realizing a loss over the four-year period.

Using the Expected Returns, Volatilities and Covariance's from the Exam spreadsheet, please create an Asset Allocation portfolio that satisfies your risk management requirement and has an Expected Return of at least 9.50%.

Please consider real-world, sound constraints in constructing the portfolio that we discussed in class as well as during the Yale case review. Please provide the following information on the portfolio you created:

• Annual expected return and standard deviation
• Probability of loss over the next 4 years.

On a qualitative basis, please describe the rationale for the portfolio you created. If you used Solver, please explain in detail what instructions you gave and why you gave them. If you made an unusually large or small allocation to a particular asset class, please explain why.

1. Based on the Asset mix you arrive at, please describe exactly how you would invest the $500,000 inheritance, including the number of shares you would purchase in each investment. For each Fund you recommend, please describe your reason for selection in a sentence or two.

For the Equity Asset classes (including REIT's), please choose between Passive, Fundamental Active or Factor/Small Beta exposure, then choose a Mutual Fund or ETF that fulfills your objectives and describe exactly how many shares to purchase.

For Fixed Income, it is probably best to use a Fund you are familiar with given we haven't discussed Fixed Income but feel free to be creative. OK to use the AGG ETF since that is what I used to measure the returns of the Investment Grade Bond Asset Class in the Asset Allocation spreadsheet.

For Risk-Free, it is OK to choose a Money Market Fund or ETF.

For Commodities, please choose any Mutual Fund or ETF that invests in Commodities. For Hedge Funds, I would recommend researching Liquid Alternatives to identify Hedge Fund strategies that can be purchased in Mutual Fund or ETF form. For each Fund you select, please measure the expected annual cost of investing using the Expense Ratio of the Fund, then measure the annual cost of assembling the entire portfolio.