AIMs: Calculate the effective duration and convexity of a portfolio of fixed income securities.
Questions:
18.1. A $100 face value bond with 20 years to maturity pays a semi-annual coupon with a 4.0% coupon rate. If we compute effective duration and effective convexity, at a yield of 6.0%, with a shock of ten basis points (i.e., we re-price the bond at 5.90% and 6.10%), what is the estimate given by duration and convexity in PERCENTAGE terms if the yield DROPS by 100 basis points (1.0%)?
a. + 6.488%
b. + 9.717%
c. + 12.025%
d. + 13.670%
18.2. A fixed income manager owns a barbell portfolio with equal weights in two zero-coupon bonds: 50% of its value in a two-year zero-coupon bond and 50% in a 12-year zero-coupon bond. The manager is considered shifting the investment to a bullet portfolio with the same value but instead 100% invested in a zero-coupon bond with seven years to maturity. Each of the following is true about the portfolios EXCEPT (please assume semi-annual compounding):
a. At a yield of 4.0%, the bullet portfolio's Macaulay duration is 7.0 years
b. At all yields, the barbell's Macaulay duration is similar to bullet's Macaulay duration
c. At a yield of 4.0%, the barbell portfolio's convexity approximately 50 years^2
d. At a yield of 4.0%, the barbell portfolio's convexity is higher than the bullet's convexity
18.3. A portfolio is invested in three zero-coupon bonds (please assume annual compounding): 40% in a two-year bond, 30% in a 10-year bond, and 30% in a 25-year bond. At a yield of 4.0%, which is nearest to the portfolio convexity?
a. 99
b. 213
c. 525
d. 916
Answer:
Questions:
18.1. A $100 face value bond with 20 years to maturity pays a semi-annual coupon with a 4.0% coupon rate. If we compute effective duration and effective convexity, at a yield of 6.0%, with a shock of ten basis points (i.e., we re-price the bond at 5.90% and 6.10%), what is the estimate given by duration and convexity in PERCENTAGE terms if the yield DROPS by 100 basis points (1.0%)?
a. + 6.488%
b. + 9.717%
c. + 12.025%
d. + 13.670%
18.2. A fixed income manager owns a barbell portfolio with equal weights in two zero-coupon bonds: 50% of its value in a two-year zero-coupon bond and 50% in a 12-year zero-coupon bond. The manager is considered shifting the investment to a bullet portfolio with the same value but instead 100% invested in a zero-coupon bond with seven years to maturity. Each of the following is true about the portfolios EXCEPT (please assume semi-annual compounding):
a. At a yield of 4.0%, the bullet portfolio's Macaulay duration is 7.0 years
b. At all yields, the barbell's Macaulay duration is similar to bullet's Macaulay duration
c. At a yield of 4.0%, the barbell portfolio's convexity approximately 50 years^2
d. At a yield of 4.0%, the barbell portfolio's convexity is higher than the bullet's convexity
18.3. A portfolio is invested in three zero-coupon bonds (please assume annual compounding): 40% in a two-year bond, 30% in a 10-year bond, and 30% in a 25-year bond. At a yield of 4.0%, which is nearest to the portfolio convexity?
a. 99
b. 213
c. 525
d. 916
Answer:
