Question

Other things equal, which of the following bonds has the highest interest rate risk? (Hint: you do not need to do any calculation; just do pair-wise comparisons to determine which one is more sensitive to interest rate changes.)

1. A 10-year, 10% coupon bond issued by the US Department of the Treasury.
2. A 10-year, 20% coupon bond issued by the US Department of the Treasury.
3. A 10-year, 20% coupon bond issued by Microsoft.
4. A 15-year, 10% coupon bond issued by Santander.
5. A 15-year zero-coupon bond issued by the Massachusetts State Government.

Answer 1

The interest rate risk of a bond is measured by a parameter known as duration. The higher the bond's duration the higher is its interest rate risk.

Now the duration of a bond is directly proportional to the tenure of the bond as longer the tenure greater is the uncertainty of interest rates and greater is the risk generated by interest rates. Hence, the three 10-Year Bonds (A, B and C) will have lower interest rate risk as compared to the two 15-Year bonds (D and E).

Further, the bond duration is inversely related to the magnitude of the bond's coupon. The higher the bond's coupon (high magnitude of initial cash flows) the lower is its duration or risk owing to changes in interest rates. This happens because in a coupon bond a major part of the bond's price is recovered earlier in the bond's tenure by means of these coupons.However, in a zero coupon bond no portion of the bond's price is recovered earlier and consequently this bond has a greater exposure to interest rate risk as compared to a coupon bond.

Therefore, between the bonds D and E, the latter has a higher interest rate risk as quantified by its higher duration.