rates move or are expected to move in either direction. In other words, a portfolio that is positively exposed to volatility benefits by large swings in interest rates and a portfolio that is negatively exposed (i.e., short volatility) benefits when interest rates are more stable than expected. Volatility exposure arises when the portfolio has instruments with asymmetric payoffs: An interest rate movement in one direction generates a larger gain than the loss associated with the equal but opposite interest rate move. Volatility exposure is typically achieved either by using instruments that have explicit exposure to volatility such as options on fixed income securities or by using securities that exhibit sensitivity to volatility due to imbedded options such as callable and putable bonds. A good example of a sector that creates volatility exposure is the MBS market. Because the home mortgage borrowers backing a standard residential mortgage-backed security can refinance their mortgages if mortgage rates decline, the holder of the MBS is effectively short a call option. Therefore, holders of most MBSs have a short exposure to volatility. There are two different risk exposures that generally arise when investing in options or securities with embedded options: gamma and vega (the names come from the Black-Scholes option pricing model). Gamma exposure is the market value impact from experiencing a change in interest rates. If you are long volatility, you experience a gain when the market moves, because in an interest rate rally the instrument will increase more than is suggested by its duration, and in a sell-off the instrument will decline less than is suggested by its duration. The measure that is often used to quantify gamma exposure in a fixed income portfolio is convexity. The units of the convexity measure for bonds are actually years2 because it is effectively the second derivative of the bond's price with respect to a change in interest rates. However, convexity is typically thought of as a percentage measure where the approximate price return impact due to convexity exposure given a change in interest rates is determined by the formula: Price gain from convexity = \ X Convexity X Change in interest rates2 The other exposure that is created by investing in fixed income instruments that exhibit volatility risk is vega risk. The price change in an instrument that results from vega exposure is due to a change in the market expectation of future volatility of interest rates. The market price of a fixed income option will increase if the market expects interest rates to be more volatile over the remaining life of the option. In the fixed income world, the measure frequently used to quantify vega risk is volatility duration, which is defined to be the percentage change in the price of the instrument due to a 1 percent change in expected future (or implied) volatility. Prepayment Risk Prepayment risk is a risk that is somewhat unique to the residential MBS market. As described in the preceding section, the borrowers underlying a mortgage-backed security can prepay their mortgages at face value and replace them with other mortgages at a lower rate. Therefore, an investor in an MBS security is short the option