689CHAPTER 47THE USE AND MISUSE OF MODELS IN INVESTMENT MANAGEMENT Douglas T. BreedenFinancial models can be extremely helpful in adding disciplined thinking to the investment decision - making process. A failure to recognize some common misuses of models, however, such as overreliance on recent historical experiences and volatilities or a failure to identify nonlinear relationships, makes the use of models less effective than they would be otherwise. Understanding the difficulties and estimation risks associated with modeling complex securities can lead to better investment decisions in the future. A problem with using models is that they are always imperfect descriptions of economic behavior and human decision making. Although they are often very useful, it is also easy to misuse them. Unfortunately, in the last two years it seems that the latter has been more the case. Oftentimes, we are overconfident in the efficacy of our models. Still, models can be very useful as long as investors remember their proper roles and limitations in the decision - making process. WHERE FINANCIAL MODELS ARE USEFUL Having been trained by Bob Merton and Myron Scholes, I became quite familiar with option - pricing models at Massachusetts Institute of Technology (and later at Stanford University with John Cox, Bill Sharpe, and Bob Litzenberger as teachers). When I cofounded Reprinted from CFA Institute Conference Proceedings Quarterly (December 2009):3645. This presen- tation comes from the 2009 CFA Institute Annual Conference held in Orlando, Florida, on 2629 April 2009.CH047.indd 689CH047.indd 6898/28/10 8:50:43 PM8/28/10 8:50:43 PM690 Part III: Managing RiskNonfinancial RiskSmith Breeden in 1982, I brought this type of modeling to mortgage - backed securities (MBS) when we began building prepayment models. Then through the latter part of the 1980s, we built price elasticity and duration models, as well as pricing models for the MBS market. In the 1990s, I focused on studying empirical durations and brokers forecasts of risks and returns and published that applied mortgage research in the Journal of Fixed Income in 1991, 1994, and 1997. One thing that struck me about the models that Fischer Black, Scholes, and Merton gave us was that they were really good about giving us the shapes of the curves but not always so good about the locations . That is, in options pricing, many of the pricing patterns, such as deltas, exhibit S - curve shapes. I checked and noticed that the same pattern emerged in mortgage price data as the theory predicted. It was really helpful to us in risk management to know that mortgage price data were not a straight line. It was a curve, and it was not a curve that went up forever. It was a curve that flattened out at some point. Figure 47.1 illustrates what I mean. The figure plots the price of a U.S. Treasury note versus the price of a Ginnie Mae mortgage - backed security as interest rates decline. As shown, the price increase of the Ginnie Mae loan flattens out as interest rates decrease because mort-gages have an embedded prepayment option. As interest rates drop, homeowners refinance their mortgages, and the refinancing holds down the price growth of the mortgage security. The price of the Treasury security, however, which does not have a prepayment option, keeps going up. This figure illustrates the negative convexity of MBS as opposed to the positive convexity of noncallable Treasuries, which is very important. Figure 47.2 shows the 10 - year Treasury rate (right axis) against the duration of a Fannie Mae 6 percent fixed - rate mortgage (left axis) from the first quarter of 1997 to the first quarter Price ($)T reasury NoteGinnie Mae Fixed-Rate Mortgage12412212011811611411211010810610410210098961171098 Yield (%)FIGURE 47.1 Price of a 10-Year Treasury Note Compared with a Ginnie Mae MBS as Yield DecreasesSource: Merrill Lynch.CH047.indd 690CH047.indd 6908/28/10 8:50:44 PM8/28/10 8:50:44 PMChapter 47 The Use and Misuse of Models in Investment Management 691of 2009. The Fannie Mae mortgage has a beginning duration of about 5.5 years, which means that if rates go up 1 percent, the mortgage will lose about 5.5 percent of its value. If rates go down 1 percent, however, the Fannie Mae mortgage will gain about 5.5 percent. Notice that as interest rates declined in 2003, duration came down as well. During this period, duration declined from about five years to about two years. This decline means that price volatility decreased by half as interest rates came down. Conversely, higher yields mean lower prepayments, a longer duration, and thus greater price volatility. If you are managing risk, then you need to be able to model this risk. Theory predicted this relationship, and we found it in the data. Another way of demonstrating the S - curve nature of the relationship between mortgage prepayments and duration is shown in Figure 4