The negative convexity of pass-throughs is directly reflected in their market prices such that prices increase more slowly for each 50 basis point step in coupon above par. This is shown in Exhibit 3-8 using the 30-year Fannie Mae coupon stack.
Analyses using a constant prepayment assumption are called static. As the term implies, they are limited in usefulness; many scenarios need be compared to arrive at an understanding of the potential variability of pass-through cash flows
15. Yield-to-maturity calculations assume that cash flow is reinvested at the same rate.
EXHIBIT 3-8
Negative Convexity as Coupon Price Compression
110 108 106 104 102 m 100 98 96 94 92 90
over, for instance, an interest-rate cycle. For this reason, market participants prefer to use option-adjusted spread (OAS) or price models that take into account a large sample of potential interest-rate paths over the remaining term of the security. This OAS methodology, which is discussed in Chapter 31, incorporates realistic short-term prepayment projections from sophisticated econometric prepayment models. These models extract a mean cost of call and extension risk over the full term of the security in generating yield, spread, and price sensitivity measures. They also can be used to estimate the price sensitivity of pass-throughs to small changes in interest ratesâ€”effective durationsâ€”or to project price changes and rates of return given interest-rate shifts, changes in the shape of the curve, or both.
Exhibit 3-9 illustrates prices of 30-year Fannie Mae 5.5s over a range of parallel shocks to the yield curve using an OAS methodology. Notice how this price curve captures the same sort of negative convexity actually priced into the Fannie Mae coupon stack.
Exhibit 3-10 tracks the effective, or option-adjusted, duration of 30-year Fannie Mae 5.5s from January 2003. For reference, the 10-year swap rate ($US) is included. Notice that the duration ranged from one to five years over the period shown. Market participants (broker-dealers, GSEs, hedge funds, and servicers in particular) use durations from OAS models to size their mortgage hedges. It should be clear that in rapidly moving markets, pass-through durations and hedge ratios can shorten or lengthen explosively; the sheer size of the market can generate hectic buying or selling of hedges as pass-through investors attempt to stay hedged. These flows can add to the speed and extent of both rallies and sell-offs.
EXHIBIT 3-9
Negative Convexity: Theoretical Price Sensitivity of a Conventional 30-Year 5.5, Start Price 101-7+
Negative Convexity: Theoretical Price Sensitivity of a Conventional 30-Year 5.5, Start Price 101-7+
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If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.