Suppose you have a perfect model of contingent mortgage prepayments, like the one built in the previous lecture. You are willing to bet on your prepayment forecasts, but not on which way interest rates will move. Hedging lets you mitigate the extra risk, so that you only have to rely on being right about what you know. The trouble with hedging is that there are so many things that can happen over the 30 year life of a mortgage. Even if interest rates can do only two things each year, in 30 years there are over a billion interest rate scenarios. It would seem impossible to hedge against so many contingencies. The principle of dynamic hedging shows that it is enough to hedge yourself against the two things that can happen next year (which is far less onerous), provided that each following year you adjust the hedge to protect against what might occur one year after that. To illustrate the issue we reconsider the World Series problem from a previous lecture. Suppose you know the Yankees have a 60% chance of beating the Dodgers in each game and that you can bet any amount at 60:40 odds on individual games with other bookies. A naive fan is willing to bet on the Dodgers winning the whole Series at even odds. You have a 71% chance of winning a bet against the fan, but bad luck can cause you to lose anyway. What bets on individual games should you make with the bookies to lock in your expected profit from betting against the fan on the whole Series?
Source: Open Yale Courses
- Why Finance?
- Utilities, Endowments, and Equilibrium
- Computing Equilibrium
- Efficiency, Assets, and Time
- Present Value Prices and the Real Rate of Interest
- Irving Fisher's Impatience Theory of Interest
- Shakespeare's Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance
- How a Long-Lived Institution Figures an Annual Budget Yield
- Yield Curve Arbitrage
- Dynamic Present Value
- Financial Implications of US Social Security System
- Overlapping Generations Models of the Economy
- Will the Stock Market Decline when the Baby Boomers Retire?
- Quantifying Uncertainty and Risk
- Uncertainty and the Rational Expectations Hypothesis
- Backward Induction and Optimal Stopping Times
- Callable Bonds and the Mortgage Prepayment Option
- Modeling Mortgage Prepayments and Valuing Mortgages
- Dynamic Hedging
- Dynamic Hedging and Average Life
- Risk Aversion and CAPM
- The Mutual Fund Theorem and Covariance Pricing Theorems
- Risk, Return, and Social Security
- Leverage Cycle and the Subprime Mortgage Crisis
- Shadow Banking: Parallel and Growing?