Todd Kelley is a representative for Hermes Investors, a money management firm based in New York, with a portfolio of $350 million, invested by a client base composed principally of pension managers. Kelley is not a money manager per se, but instead is a product designer. His role over the past five years has been to meet with clients, to listen to their requests and to make strategic recommendations to top management. Occasionally he had an opportunity to create a new investment product for the firm.
The New Jersey State Metal Workers Pension Fund (NJSMWPF or hereafter, "The Fund") has always considered itself a conservative organization. It has long had a policy of investing 100 % of its assets in bonds, because bonds offer a guarantee of a minimum target return. Howard Boyle, director of the fund has noticed that their performance has consistently lagged the stock market over the past 10 years, and he is considering a switch to a more aggressive position in stock. At the same time, he realizes that the board of directors will never allow him to deviate from the policy of a guaranteed minimum return.
Kelley suggests an experiment to Boyle. Hermes will manage $ 1 million with the following objective. After three years, Hermes will guarantee at least the $ 1 million that the fund started with. In addition, they will match 75 % of the increase in the S&P 500 (with dividends re-invested). That is, if the S&P 500 is down at the end of three years, the fund will get their $ 1 million back. If it is up by 20%, the fund will get $1.15 million, if it is up by 40 %, the fund will get $1.3 million and so on.
Boyle likes this idea, but has heard about the dangers of portfolio insurance. He wants an actual guarantee rather than the promise of best efforts to try and achieve the "tailored" payoff. He asks how much the contract will cost the fund.
Tod Kelley believes there is a large market for such "guaranteed floors." He knows, however, that he must realistically assess the costs as well as the exposure of the fund to risk. Prepare Todd Kelley's report in two stages. In the first stage, make some simplifying assumptions about the behavior of the stock market and interest rates.
Stage I. The simple model:
1) The S%P 500 will either double or halve in value each period with equal probability. The interest rate is currently 0% and will remain so for at least the next 3 years.
2) There are no transactions costs to rebalancing, and rebalancing is done at the end of each year only.
1) What is the minimum Hermes should charge to manage this contract?
2) What must they do in order to ensure that the goals of the contract will be met, i.e. at each stage of the contract over the next three years, how will they mix the S&P 500 with T-Bills to meet their target?
3) What is the average return that the fund will realize on its investment with Hermes? I.e., on average, how much will it have at the end of three years compared to the initial investment of $1 million?
Stage II. The real-life model:
1) What additional factors must be considered in order for Hermes to apply this idealized model to the guaranteed floor contract?
2) How would you hedge Hermes' position over three years? What kind of instruments exist in the financial markets to allow Hermes to offer this contract?
3) How would you fit transactions costs into the model?
4) What could go wrong, and cause Hermes to lose a large amount on this contract?
5) Make a conservative estimate of the value the Hermes contract using current interest rates, and any assumption you wish to make about the frequency of rebalancing, about transactions costs and about the current (and future) volatility of the stock market. Explain the reasoning behind your estimate (binomial model, Black-Scholes, simulation, related instruments etc.)
Stage III. A Programming Challenge!
Take every ten-year period in U.S. capital market history, and simulate the return that would be achieved under the following scenarios:
1) The investor held 100% in the stock market
2) The investor followed the portfolio insurance strategy detailed above, neglecting transactions costs for simplicity.
3) The investor pursued a fixed-weight portfolio strategy of a mixture of t-bills and stocks eqaul to 70% stocks, 30% Bills.