# Effective Durations of Callable, Putable, and Straight Bonds

## Callable Bonds

The effective duration of a callable bond cannot be greater than that of a straight bond.

As interest rates rise above the coupon rate, the call option becomes out of money. Therefore, straight and callable bonds will have the same effective durations.

On the other hand, when interest rates fall, the call option moves into the money, and the bond is most likely called. Thus, the call option reduces the effective duration of the callable bond relative to that of a straight bond. In other words, call options have limited upside potential.

## Putable Bonds

The effective duration of a putable bond cannot exceed that of a straight bond.

When interest rates fall below the bond’s coupon rate, the put option will be out of money. In this case, the effective duration of a putable bond will be identical to that of a straight bond.

When interest rates rise, the put option moves into the money. The bond is more likely to be put, meaning that its downward potential is limited. Therefore, the bond’s effective duration is lower than that of a straight bond.

## Question

When interest rates rise, the effective duration of a putable bond most likely:

1. Shortens.
2. Lengthens.
3. Equals that of a straight bond.

#### Solution

When interest rates rise, the put option moves into the money. This limits price depreciation as the investor is more likely to put the bond and reinvest the bond’s proceeds at a higher yield. Thus, the put option reduces the effective duration of the putable bond relative to that of a straight bond.

B and C are incorrect. When interest rates fall below the coupon rate, the put option will be out of money. Therefore, the option will not be exercised. In this case, the effective duration of a putable bond will be identical to that of a straight bond.

Reading 30: Valuation and Analysis of Bonds with Embedded Options

LOS 30 (j) Compare effective durations of callable, putable, and straight bonds.

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