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Fixed-Income Sensitivities
The toolbox includes SIA-compliant functions to perform sensitivity analysis such as convexity and the Macaulay and modified durations for fixed-income securities. The Macaulay duration of an income stream, such as a coupon bond, measures how long, on average, the owner waits before receiving a payment. It is the weighted average of the times payments are made, with the weights at time T equal to the present value of the money received at time T. The modified duration is the Macaulay duration discounted by the per-period interest rate; i.e., divided by (1+rate/frequency).
To illustrate, the following example computes the annualized Macaulay and modified durations, and the periodic Macaulay duration for a bond with settlement (12-Jan-2000) and maturity (01-Oct-2001) dates as above, a 5% coupon rate, and a 4.5% yield to maturity. For simplicity, any optional input arguments assume default values (i.e., semi-annual coupons, and day-count basis = 0 (actual/actual), coupon payment structure synchronized to the maturity date, and end-of-month payment rule in effect).
CouponRate = 0.05;
Yield = 0.045;
[ModDuration, YearDuration, PerDuration] = bnddury(Yield,...
CouponRate, Settle, Maturity)
The durations are
ModDuration = 1.6107 (years)
YearDuration = 1.6470 (years)
PerDuration = 3.2940 (semi-annual periods)
Note that the semi-annual periodic Macaulay duration (PerDuration) is twice the annualized Macaulay duration (YearDuration).
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