Suppose you have a choice between four bond portfolios: Portfolio A is composed of five 10-year...

Suppose you have a choice between four bond portfolios: Portfolio A is composed of five 10-year bonds with a $1000 face value and annual coupons paying 9%, and five 5-year bonds with a $1000 face value and annual coupons paying 10%. Portfolio B is composed of ten 10-year coupon bonds with a $1000 face value with annual coupons paying 9%. Portfolio C is composed of five 10-year bonds with a face value of $1000 and coupons paying 9%, and a 10-year bond with a face value of $5000 and coupon paying 10%. Portfolio D is composed of a one 10-year $10,000 bond paying 9.25%. Which portfolio has the highest duration?

Expert Solution

Portfolio A: 5 numbers of 10-year bonds @ 9% coupon + 5 numbers of 5-year bonds @ 10% coupon

Portfolio B: 10 numbers of 10-year bonds @ 9% coupon

Portfolio C: 5 numbers of 10-year bonds @ 9% coupon + 1 number of 10-year bond @10% coupon

Portfolio D: 1 number of 10-year bonds @ 9.25% coupon

Recall:

All else being same, higher the coupon rate, lower is the duration.
All else being same, lower the term to maturity, lower will be the duration.
Duration of a portfolio of bonds = Weighted average duration of the individual bonds in the portfolio

Portfolio A has 5 years bond in it. These bonds will lower the weighted average duration. Hence, A will have the least duration.

B, C & D all have 10 years maturity bonds. D has bonds @ 9.25% coupon. Higher coupon bonds will have lower duration. Hence, D's duration is lower than that of B & C.

B has all the bonds of 9% coupon while C has one bond of higher coupon (10%). The presence of this bond will lower the weighted average of the duration and hence C will have lower duration than B.

Hence, portfolio B has the highest duration.

jeff jeffy answered 2 years ago

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