MBS
- Thread starter rickm123
- Start date
Hi Rick,
Right, that is due to the different authors (Fabozzi versus Veronesi) but it's the same effective duration, as you'll note Veronesi negates with a negative ("-") to produce a final positive duration, whereas Fabozzi reverses with (V- - V+) to ensure a positive duration. It's the same (computing the slope of a secant line near the tangent). Veronesi's is more technically appealing as it directly matches D = -1/P*d^2P/dy^2 = -1/P*slope, where slope is dollar duration (rise/run) and the slope is negative.
BTW, our convexity does have an error (p 53), it should be 1/P*[P(+) + P(-) - 2*P]/y^2 not 1/P*[P(+) - P(-) - 2*P]/y^2
Thanks,
Right, that is due to the different authors (Fabozzi versus Veronesi) but it's the same effective duration, as you'll note Veronesi negates with a negative ("-") to produce a final positive duration, whereas Fabozzi reverses with (V- - V+) to ensure a positive duration. It's the same (computing the slope of a secant line near the tangent). Veronesi's is more technically appealing as it directly matches D = -1/P*d^2P/dy^2 = -1/P*slope, where slope is dollar duration (rise/run) and the slope is negative.
BTW, our convexity does have an error (p 53), it should be 1/P*[P(+) + P(-) - 2*P]/y^2 not 1/P*[P(+) - P(-) - 2*P]/y^2
Thanks,
But the calculation startes with the price of V if interest rates be drop on the numerator - the V if interest rates rise correct?
Um, it really doesn't matter, esp for convexity which adds. But Veronesi is given by P(+ x bps) - P(- x bps) where P(+ x bps) is the lower price implied by a higher rate (yield), so the numerator and the slope (rise/run) will be negative, which is negated to a positive by the "-" out front. Fabozzi reverses and so he doesn't need the "-" out front. Best is to realize this as a slope such that both are okay, thanks,
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