Duration

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DURATION

BOND A BOND BCoupon 6.50% Coupon 9.00%Face value 100 Face value 100Frequency 2 Frequency 2Maturity 4 Maturity 5Yield 6.00% Yield 9.00%

Price 101.755 Price 100.000Difference, A&B 1.755

Macaulay Dur 3.590 Macaulay Dur 4.134Modified Dur 3.486 Modified Dur 3.956Dollar Dur 3.547 Dollar Dur 3.956

Ian Giddy

Duration - The Long Way

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DURATION, THE LONG WAY

MACAULAY DURATION

Yield 0.08

Bond A Time (year) 0.5 1 1.5 2 2.5 3 3.5Cash-Flows 4 4 4 104PV of CFs 3.84615 3.6982 3.556 88.9 0 0 0Price 100Weighted CFs 4 8 12 416 0 0 0PV of weighted CFs 3.84615 7.3964 10.668 355.6 0 0 0Sum of weight. CFs 377.509Semiannual duration 3.77509Macaulay duration 1.88755

Bond B Time (year) 0.5 1 1.5 2 2.5 3 3.5Cash-Flows 4.5 4.5 4.5 4.5 4.5 4.5 4.5PV of CFs 4.32692 4.1605 4.0005 3.8466 3.6987 3.5564 3.4196Price 104.055Weighted CFs 4.5 9 13.5 18 22.5 27 31.5PV of weighted CFs 4.32692 8.321 12.001 15.386 18.493 21.338 23.937Sum of weight. CFs 864.529Semiannual duration 8.30835

With a yield of 8.00%Bond A's Macaulay duration is 1.88755Bond B's Macaulay duration is 4.15418

With a yield of 8.00%Bond A's Modified duration is 1.81495Bond B's Modified duration is 3.9944

With a yield of 8.00%Bond A's Dollar duration is 181.495Bond B's Dollar duration is 415.639

MODIFIED DURATION (Same inputs as Macaulay's).

DOLLAR DURATION (Same inputs as Macaulay's)

Duration - The Long Way

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4 4.5 5

0 0 0

0 0 00 0 0

4 4.5 54.5 4.5 104.5

3.2881 3.1616 70.596

36 40.5 104526.305 28.455 705.96