Macaulay Duration Formula Macaulay Duration = T ∑ t=1 t × PVCFt k× p PVCFt = present value of cash flow discounted by the yield to maturity t = time period k = number of payments per year p = bond priceExample 1: Calculating Macaulay Duration A 3-year bond has a par value ...
Duration of a bond is the measure of the bond price volatility, usually defined as the weighted average term of maturity of a security bond's cash flows. It is calculated using four ways that includes the Macaulay duration, modified duration and effective duration formula. Duration allows an ...
the Macaulay Duration, which is measured in years, will always be between 0 and the maturity length of the bond. Macaulay Duration is calculated according to this formula:
Following is the formula for Macaulay duration:Macaulay DurationintiPViPWhere ti is the time till cash flows I, PVi is the present value at time 0 of cash flow I and P is the bond price which equals the sum of all the present values....
Once you are done entering the values, click on the 'Calculate Bond Duration' button and you'll get the Macaulay Duration of1.912and the Modified Duration of1.839: Formulas to Calculate the Bond Duration You can use the following formula to calculate theMacaulay Duration (MacD): ...
The calculation of Bond Duration brings all these factors together in one number, allowing us to have a measurement of a bond’s price sensitivity to changes in market interest rates.Derivation of Macaulay's Duration Factor We can represent the present value, or current market price, of ...
Modified Duration Formula The modified duration formula is: MacaulayDuration1+YTMAnnualPayments\frac{Macaulay\ Duration}{1+\frac{YTM}{Annual\ Payments}}1+AnnualPaymentsYTMMacaulayDuration Where: Macaulay Duration:The duration of the bond as measured in years (see how to compute it above) ...
P(2) = the price of the bond if the yield were to increase by Y percent. Y = the estimated change in yield used to calculate P(1) and P(2). The complete formula for effective duration is: Effective duration = (P(1) - P(2)) / (2 x P(0) x Y) ...
Frederick Robertson Macaulay dubbed the effective-maturity concept the “duration” of the bond.1In doing so, he suggested that this duration becomputed as the weighted average of the times to maturity of each coupon, or principal payment, made by the bond.Macaulay's durationformula is as ...
Macaulay Duration=(∑t=1nt∗C(1+y)t+n∗M(1+y)n)Current bond pricewhere:C=periodic coupon paymenty=periodic yieldM=the bond’s maturity valuen=duration of bond in periodsMacaulay Duration=Current bond price(∑t=1n(1+y)tt∗C+(1+y)nn∗M)where:C=pe...