In preparation for our class on Decision Making (Session 10), I want you to experience the thrills and joys of "real-life" decision making that prior ISB graduates confronted! You all have had a class in investments/portfolio theory either as an undergraduate or at the ISB. So, this should be a very straightforward problem. It should take no more than 30 minutes - really! (Excel Solver will help you speed this up - but feel free to use any other tools at your disposal.) There are no surprises here; no hidden strategies; etc. Background (Imagine the time is June 2007): Congratulations, given the success of your business strategies, your corporation has generated lots of idle USD cash. The CEO wants to invest this money with a relatively short time horizon (say, about a year). The CEO assigns the task to you, a recent distinguished ISB graduate. Although you are the company's Chief Strategist, the CIO knows you took some classes in investments/portfolio theory As this money may be needed for future capital investments or acquisitions, the CEO is very worried about risk. She tells you, "No surprises!" However, the CEO wants to earn more than riskless, short-term Treasury (AAA-rated) yields on this money, so investing in 3-month/6-month Treasury bills is out of the question. After all, it doesn't take an ISB grad to invest in T-bills. Since you are a highlypaid member of the Executive Team, the CEO expects better performance. "How hard can it be to outperform risk-free, short-term Treasuries?" After some research, you decide to invest only in very highly-rated (i.e., BBB-rated or better) assets that offer a spread (i.e., additional yield) over Treasuries. You have identified the following three suitable asset classes that have good liquidity (i.e., easy to sell on short notice) and a long track record: a. AAA-rated mortgage-backed securities (MBS); b. AAA-rated commercial mortgage-backed securities (CMBS); and c. Investment-grade-rated (i.e., BBB-rated, or better) corporate bonds (Credit). Assume you can invest in a diversified pool of individual securities for each of the asset classes. So, there is negligible idiosyncratic risk. Unfortunately, all three asset classes have longer durations (maturities) than the CEO's horizon. This allows you to pick up some additional yield by "moving out along the spread curve." Fortunately, since all the assets have good liquidity, you are confident you will be able to sell them at the 1y horizon which is before their stated maturity. However, to avoid too much interest rate sensitivity (i.e., duration risk), you decide to hedge out this duration risk using Treasury futures. In other words, you "short" Treasury futures to offset the duration risk of each of the three asset classes under consideration. Consequently, for this analysis use "excess returns over Treasuries" rather than "total returns." Excess returns are returns net of Treasury duration exposure. For example, suppose the AAA-rated MBS, with a duration of 5, generated a 1.4% return last month. At the same time, a Treasury note also with a duration of 5 generated a 1.25% return. So, the excess return for the MBS in the month was 1.4% - 1.25% = +0.15%, or 15bp. You call your friendly investment banker (probably another ISB grad!) for time series data of monthly returns for the three asset classes. You are given monthly data for August 1999 - May 2007. These data are in the attached spreadsheet. Tasks: 1. Make a case for why these three asset classes may or may not be suitable for your optimal portfolio. To bolster your case in #1, you may want to consult the Moody's Default Study 1920 - 2007 that provides long-term credit losses for various credit ratings. (Note: The rating agencies often like to say "an AAA is an AAA no matter the underlying credit instrument." In other words, you can reasonably assume that the expected credit losses for a AAA-rated credit bond should be similar to the expected losses for a AAA-rated MBS.) 2. Construct an "efficient frontier" containing these asset classes subject to the constraint that the portfolio weights for each asset must be between [0%, 100%]. The weights for all three asset classes must sum to 100%. a. To get started, compute and report the monthly mean and standard deviation of the monthly excess returns for each of the three asset classes. Then compute and report the variance-covariance matrix for these monthly excess returns. b. For the efficient frontier consider overall portfolio volatilities of 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, and 0.7%. (Note: you may not have solutions for all these values.) In other words, for each portfolio volatility value, calculate the optimal portfolio weights for the three asset classes that will maximize the portfolio's expected return. c. Put these results in a simple bar chart: overall portfolio volatility value on the horizontal axis and portfolio weights for the three asset classes on the vertical axis. So, for each volatility value, you will have three vertical bars. 3. Suppose your company can borrow 1y funds at Treasuries + 40bp/y. What might you, as an aggressive "can-do" ISB graduate, be tempted to propose to the CEO?