3. Suppose bond A has 20 years left to maturity, an 8% coupon rate, pays interes

Question

3. Suppose bond A has 20 years left to maturity, an 8% coupon rate, pays interest semi-annually, and has a 6% yield to maturity and bond B has 25 years left to maturity, a 5% coupon rate, pays interest semi-annually, and has a 7% yield to maturity. What is the duration of each bond? What is the convexity of each bond? What are the optimal weights for bond A and bond B if the duration of your portfolio is 10 years? Supposed interest rate increases by 1%, estimate of the percent price change in each bond due to both duration and convexity. Which bond is preferred for a portfolio inclusion?

Explanation / Answer

Let Investment amount be $100

Calculation of Duration of Bond A:

Duration of Bond A = Aggregate of Weighted PV of Cash Flows / Aggregate of PV of Cash Flows

= 1996.914 / 130.093

= 15.35 half years

= 7.675 years

Alternatively,

Duration of Bond A = 7.675 years

Calculation of Duration of Bond B:

Duration of Bond A = Aggregate of Weighted PV of Cash Flows / Aggregate of PV of Cash Flows

= 1103.268 / 72.399

= 15.24 half years

= 7.62 years

Alternatively,

Duration of Bond B = 7.619 = 7.62 years

Calculation of weights of bonds:

Let Weight of Bond A = x

then weight of bond B = 1-x

Duration of Portfolio = (x * 7.675) + ((1-x)*7.62)

7.675x + 7.62 - 7.62x = 10 years

0.055x + 7.62 = 10

0.055x = 2.38

x = 43.27%

Therefore weight of bond A = 43.27%

Weight of Bond B = 100 - 43.27 = 56.73%

Time doesnt permit me to answer the remaining answers

Year Cash Flow PVF (6%) PV of cash flow Weighted PV 1 8 0.943 7.547 7.547 2 8 0.890 7.120 14.240 3 8 0.840 6.717 20.151 4 8 0.792 6.337 25.347 5 8 0.747 5.978 29.890 6 8 0.705 5.640 33.838 7 8 0.665 5.320 37.243 8 8 0.627 5.019 40.154 9 8 0.592 4.735 42.617 10 8 0.558 4.467 44.672 11 8 0.527 4.214 46.357 12 8 0.497 3.976 47.709 13 8 0.469 3.751 48.759 14 8 0.442 3.538 49.538 15 8 0.417 3.338 50.072 16 8 0.394 3.149 50.387 17 8 0.371 2.971 50.506 18 8 0.350 2.803 50.450 19 8 0.331 2.644 50.238 20 8 0.312 2.494 49.889 21 8 0.294 2.353 49.418 22 8 0.278 2.220 48.841 23 8 0.262 2.094 48.171 24 8 0.247 1.976 47.420 25 8 0.233 1.864 46.600 26 8 0.220 1.758 45.720 27 8 0.207 1.659 44.791 28 8 0.196 1.565 43.821 29 8 0.185 1.476 42.817 30 8 0.174 1.393 41.786 31 8 0.164 1.314 40.735 32 8 0.155 1.240 39.669 33 8 0.146 1.169 38.593 34 8 0.138 1.103 37.512 35 8 0.130 1.041 36.429 36 8 0.123 0.982 35.349 37 8 0.116 0.926 34.275 38 8 0.109 0.874 33.209 39 8 0.103 0.824 32.153 40 108 0.097 10.500 420.000 130.093 1996.914

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