# Duration and Convexity for ABS/MBS

Effective Duration and Convexity for ABS/MBS are calculated with the same formulas as those used for bonds valued with a binomial interest rate tree model (see the notes at the beginning of the module).

Different ABS/MBS security dealers may calculate different effective durations because:

• Different dealers may use different interest rate changes in the calculation (i.e. not all dealers may use the standard 100 basis points/1%).
• Different dealers may use different prepayment assumptions in valuing the ABS/MBS.
• Different dealers may use different interest rate paths and interest rate volatility.

Various Duration Measures for MBS

• Cash Flow Duration: This is the same as effective duration. The problem with this measure is that the effect of changes in prepayment rates is not fully captured, which may change due to changes in cash flow yield. It assumes one prepayment rate throughout the life of the MBS.
• Modified Duration: Modified duration indicates the percentage change in the price of a bond for a given change in yield. It is a more adjusted measure of Macaulay duration that produces a more accurate estimate of bond price sensitivity. This less accurate than cash flow duration because modified duration does not consider how prepayments may change. Cash flow duration, on the other hand, does recognize prepayments, even though with a very simple assumption. Duration is obtained by rolling up and rolling down the coupon, as the price changes.
• Coupon Curve Duration: In this method, the market prices are used to calculate the duration of the MBS. The coupon curve is the curve of various MBS with different coupons and prices. You will generally take different MBS from an issuer with different coupon rates.
• Empirical Duration: It does not use any theoretical formula, rather uses historical pricing data for calculating duration.

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