You are a portfolio manager at Richardson GMP, a well-known wealth management firm in Montreal. Your objective is to customize your clients' portfolios so that they achieve high growth and low volatility each year, taking both their financial capital and human capital into account. In other words, your mandate is threefold:.
1) you view a client's total wealth as one big portfolio, 2) you run a mean-variance optimization on this total wealth portfolio, and 3) you can only adjust the shares of the client's financial wealth invested in stocks and bonds.
a. Your first client today is Martin Tremblay, a 40-year old individual working at the Societe de Transport de Montreal (STM) as treasurer. His job is100% safe. When you take the present value of his future earnings you estimate a human capital of $1M. He has already accumulated $200K of savings, all of which are currently being invested in one-year GIC bonds. For the purpose of this exercise assume no other assets and liabilities. After having interviewed him, you believe that Martin's current portfolio allocation isn't optimal. He should invest in stocks. Richardson has three external funds to offer, and here is the table of your forecasts for the upcoming year: Fund µ s ba R2RBC Global Balanced Fund 12% 17% .8 0.1% 95% Desjardins Canadian Equity Growth Fund 10% 20% 1.5 -1% 60% Investors Dividend Equity Fund 09% 15% .85 2% 50% where the a, b, and R2 statistics come from first-pass CAPM regressions for each fund. The µ, s, and a statistics are all annualized.
Assuming that Martin can 1) only pick one fund among the three candidates, and 2) borrow/save any amount in the chosen fund and the risk-free GIC bond, which
one of the three funds above is optimal? GIC 1-yr bonds yield 1%
b. Building on your answer to part a., if you convince Martin to accept a standard deviation of 3% per year on his total wealth portfolio, how much of his financial wealth should be invested in the fund you selected in part a? As a result, what would be the expected return on his financial wealth portfolio (If you're unsure about your answer to part a. then assume the RBC fund as the selected fund). Explain.
c. Assume that 1) Martin follows your investment advice from part b., 2) the chosen fund performs well this year (e.g. it generates 15%), 3) he comes back to you next year for a follow-up appointment, 4) he has the exact same job and salary, and 5) you have the same forecasts moving forward one year. Should he buy more shares of the fund? Should he sell shares? Comment intuitively on how you would advise him to proceed and why. (This is a qualitative question).
d. This is a side-question. Martin wanted to know more about the nature of the risks he is taking. Which of the three funds is most exposed to risks not related to market-wide fluctuations?
e. Let's go back to part b. If instead Martin isn't comfortable with the idea of borrowing, is there an alternate solution that would also generate a standard deviation of 3% per year on his total wealth portfolio? If so, what would be the expected return on his financial wealth? Explain the difference with part b. (If you're unsure about your answer to part b. then you can assume an expected return of 14%).
f. Your next client is Louise Gagnon. Like Martin, she also has accumulated savings of $200K and she is not comfortable with the idea of borrowing. She works as a real time market strategist at Vigilant Global, a R&D firm based in Montreal that builds financial software. Her annual salary is higher than Martin's but it is also riskier so you also come up with $1M in present value.
The human capital risk can be decomposed as follows: 90% of it is risk-free, and the remaining 10% looks like the RBC Global Balanced Fund. This 10% risky\component comes from bonuses that are paid out when the company's sales are up, which is typically when the stock market does well. Assume that Louise goes for the RBC fund. If you also target a standard deviation of 3% per year on her total wealth portfolio, how should she allocate her savings? That is, how much in the RBC fund and how much in the GIC bonds? Explain why her allocation is different from Martin's from part e. (If you're unsure about your answer to part e. then assume that the RBC fund should be 100% of Martin's financial wealth). Explain.
Question II: Financial Engines Inc. [30pt]You are a research associate for Financial Engines Inc., a firm specialized in providing research and consultancy on asset allocation to pension funds and foundations. The firm was founded in 1996 by Bill Sharpe who is well-known for his pioneering work on the CAPM.
a. Your current client, Ford Motors, needs from you a precise estimation of the CAPM beta of an equally-weighted portfolio of the two other big car industry companies: Chrysler and GM. However, this report is due today and your intern lost the regression output of the portfolio. You quickly go back over the regression output for each stock (on the next page). The dots correspond to the ten past annual nominal excess returns. The black line corresponds to the first-pass regression equation. Based on this information, what should be the beta and alpha of the portfolio?