Duration and Interest Rate Sensitivity

ALBA GRADUATE BUSINESS SCHOOL |

INVESTMENTS AND PORTFOLIO MANAGEMENT

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FINAL EXAM : TAKE HOME PART |

Ntzathas Sotiris

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Calculate Macaulay’s duration, modified duration, and the convexity of the following bonds (annualize the parameters). Assume all of the bonds pay principal at their maturity.

a. Four-year, 9% coupon bond with a principal of $1000 and annual coupon payments trading at par.

b. Four-year, zero coupon bond with a principal of $1000 and priced at $708.42 to yield 9%.

c. Five-year, 9% coupon bond with a principal of $1000 and annual coupon payments trading at par.

d. Ten-year, 7% coupon bond with a principal of $1000 and semiannual coupon payments (3.5%) and priced at par.

e. Three-year, 7% coupon bond with a principal of $1000 and semiannual coupon payments (3.5%) and priced at par.

f. Three-year zero-coupon bond with a principal of $1000 and priced at $816.30 to yield 7%.

Please answer the following questions (each worth 10 points):

1. Which bond has the greatest price sensitivity to interest rate changes?

2. For an annualized 1% decrease in rates what would be the approximate percentage change in the prices of Bond d and Bond e?

3. Which bond has the greatest non-symmetrical capital gain/ loss feature?

4. If you were a speculator and expected yields to decrease in the near futures by the same amount across all maturities (a parallel downward shift in the yield curve), which bond would you select?

5. If you were a bond portfolio manager and expected yields to increase in the near future by the same amount across all maturities (a parallel upward shift in the yield curve), which bond would you select?

6. Comment on the relation between maturity and a bond’s price sensitivity to interest rate changes.

MAIN TABLE WITH RESULTS

  |   | THE RESULTS ARE PRESENTED IN YEARS-NOT SEMIANNUAL PERIODS |   |   |

BOND | COUPON PAYMENT | PRICE | PAR VALUE | PERIOD YIELD | PERIODS TO MATURITY | PAYMENTS PER YEAR | MACAULAY...