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Mortgage-Backed Securities: Products, Structuring, and Analytical Techniques by WILLIAM S. BERLINER, ANAND K. BHATTACHARYA, FRANK J. FABOZZI

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DURATION

The risk measure most commonly utilized by fixed income traders and investors is duration. In its basic form, duration calculated in any fashion estimates the percentage change in the price of a fixed income security, given a 100 basis point change in the yield curve. Basic duration measures make the following assumptions:
• The spread of the security relative to its pricing benchmarks remains unchanged.
• The yield curve shifts in a parallel fashion.
• The spread of current coupon mortgages to Treasuries remains unchanged.
• The level of volatility remains constant.
(In some instances, duration is defined by a change in the security’s yield. However, the constant-spread assumption means that these definitions are identical.)
Exhibit 11.1 shows an interpretation of duration in an economic context. Duration measures the rate of change in a bond’s price, given a change in yield. As such, it is a first-order rate of change (akin to speed when measuring movement), and can therefore be conceptualized as the first derivative of the bond’s price/yield function, if such a function existed in reality. As illustrated in Exhibit 11.1, it can be graphically represented as the slope of the tangent line at a single point in a line representing the bond’s price/ yield function. (If the bond’s profile were linear, duration would be the line’s slope; in actuality, the price/yield function for virtually all bonds, even those with no embedded options has some degree of curvature.) ...

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