InvestorQ : What is the process and logic of calculating duration?

# What is the process and logic of calculating duration?

3 years ago
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Let us consider the base case scenario below to understand the process for calculation of duration using the present value of the cash flows.

 Inputs Rate Convention: 1 = EAR, 0 = APR 0 Annual Coupon Rate (CR) 8.0% Yield to Maturity (Annualized) (y) 9.0% Number of Payments / Year (NOP) 2 Number of Periods to Maturity (T) 8 Face Value (FV) ? 1,000 Outputs Discount Rate / Period (RATE) 4.5% Coupon Payment (PMT) ? 40 Calculate Bond Duration using the Cash Flows Period 0 1 2 3 4 5 6 7 8 Time (Years) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Total Cash Flows ? 40.00 ? 40.00 ? 40.00 ? 40.00 ? 40.00 ? 40.00 ? 40.00 ? 1,040.00 Present Value of Cash Flow ? 38.28 ? 36.63 ? 35.05 ? 33.54 ? 32.10 ? 30.72 ? 29.39 ? 731.31 ? 967.02 Weight 4.0% 3.8% 3.6% 3.5% 3.3% 3.2% 3.0% 75.6% 100.0% Weight * Time 0.02 0.04 0.05 0.07 0.08 0.10 0.11 3.03 3.49 Duration 3.49 Modified Duration 3.34

What we can infer from the above calculation is that the calculation of duration has the following steps…

Firstly, the future cash flows are projected which include the coupon payments on the bond and the redemption value.

Secondly, the flows are all reduced to present value and the sum of all these present values discounted at the yield represents the current price of the bond.

Thirdly, the discounted cash flows are weighted with reference to each cash flow vis-à-vis the price of the bond (PV of cash flows).

Once the weighs are calculated, the time periods (based on the frequency of compounding are multiplied by these weights to get the weighted average values.

The sum of these weighted average values represents the duration of the bond.

Lastly, when the duration of the bond is divided by (1+r) you get the modified duration.
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