Final answer:
The effective duration of a callable bond decreases when interest rates rise because the likelihood of the issuer calling the bond increases. As a result, the bond's price becomes less sensitive to rate changes, leading to a lower effective duration.
Step-by-step explanation:
When interest rates rise and are high relative to the bond's coupon rate, the effective duration of a callable bond typically decreases. This is due to the nature of callable bonds, as they give issuers the right to redeem the bond before its maturity.
The likelihood of the issuer calling the bond increases when existing interest rates are higher than the bond's coupon rate, as they can refinance the debt at a lower cost. The bond's price also becomes less sensitive to changes in interest rates (since it is likely to be called), which results in a lower effective duration.
If interest rates rise from 8% to 11%, for instance, the present value of the bond's payments, discounted at the higher rate, will be lower. The bond's value decreases because the future dollar payments remain unchanged and are now worth less in today's dollars.
This effect is explained through present value calculations that show the inverse relationship between bond prices and interest rates. In the case of callable bonds, the investment value falls because the investor is locked into a coupon payment that is lower than the prevailing market rates.
Since the investor cannot benefit from the higher interest rates as much as they would with a non-callable bond, the effective duration shortens to reflect that decreased interest rate risk.