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# Fact that two securities with the same maturity may have different durations reminds

1. Under certain circumstances (small equal changes in interest rates on all maturities) the percentage change in the price of a security with duration Dn, in response to an interest rate change is approximately given by: ï„ï€ V - Dn ï„ I V - Dn = Duration = I1 - I0 1 + I = where ï„ I Consequently, duration is an important concept in fixed interest portfolio management and hedging strategies. 2. The fact that two securities with the same maturity may have different durations reminds us that the pattern of cash flows makes them respond differently to interest rate changes. Compounding periods per annum Interest Rate per annum Debt Security Face value Coupon Rate Contribution Cupon value per period Time to to PV Weight Receipt Duration 1.06 1 1.06 2 1.06 3 1.06 4 1.06 5 1.06 6 Total 95,082.68\$ 100% 5.310 Half Years 5000 5000 2 0.12 100000 10% 5000 105000 5000 5000 5000 5 0.1965 = 74,020.86\$ 77.85% 6 4.6709 3 0.1325 = 3,960.47\$ 4.17% 4 0.1666 1 0.0496 = 4,449.98\$ 4.68% 2 0.0936 = 4,716.98\$ 4.96% = 4,198.10\$ 4.42% = 3,736.29\$ 3.93% Compounding periods per annum Interest Rate per annum Debt Security Face value Coupon Rate Contribution Cupon value per period Time to to PV Weight Receipt Duration 1.06 1 1.06 2 1.06 3 1.06 4 1.06 5 1.06 6 Total 85,248.03\$ 100% 5.538 Half Years 3000 3000 2 0.12 100000 6% 3000 103000 3000 3000 3000 5 0.1315 = 72,610.94\$ 85.18% 6 5.1106 3 0.0886 = 2,376.28\$ 2.79% 4 0.1115 1 0.0332 Using the relationship between duration, security prices and interest rates, calculate the change in the prices of securities A and B predicted by their calculated durations. I1 I0 ï„ï€ V - Dn ï„ I 0.090 0.100 V - Dn = Duration 5.00 ï„ï€ V -5 -0.01 I0 = V 1 + 0.1 0.10 = 4.55% = I1 - I0 1 + I = where ï„ I I1 I0 ï„ï€ V - Dn ï„ I 0.090 0.100 V - Dn = Duration 4.17 ï„ï€ V -4.17 -0.01 I0 = V 1 + 0.1 0.10 = 3.79% = I1 - I0 1 + I = whe