A call provision decreases the bond's duration because a call provision introduces prepayment risk that should be factored in the calculation.

For the investor, one of the most significant risks of  callable (or prepayable) bonds is that they can be called/retired prematurely. Because bonds are nearly always called for prepayment after interest rates have decreased significantly, the investor will find it nearly impossible to find comparable investment vehicles. Thus, investors have to replace their high-yielding bonds with much lower-yielding issues. From the bondholder’s perspective, a called bond means not only a disruption in cash flow but also a sharply reduced rate of return.

Generally speaking, the following conditions apply to callable bonds:

• The cash flows associated with callable bonds become unpredictable, since the life of the bond could be much shorter than its term to maturity, due to the call provision.
• The bondholder is exposed to the risk of investing the proceeds of the bond at lower interest rates after the bond is called. This is known as reinvestment risk.
• The potential for price appreciation is reduced, because the possibility of a call limits or caps the price of the bond near the call price if interest rates fall (also known as price compression).

This question is asking: given a change in yield, which of the bonds will exhibit the least price change? Of the four choices, Cavilero is most likely to buy the bond with the shortest maturity and highest coupon because it will have the least price volatility. Price volatility is directly related to maturity and inversely related to the coupon rate.

All else equal, the bond with the shorter term to maturity is least sensitive to changes in interest rates. Cash flows that are further into the future are discounted more than near-term cash flows, so the nearer to maturity the cash flows are received, the higher the present value. Here, this means that one of the 10-year bonds will have the least volatility. Similar reasoning applies to the coupon rate. A higher coupon bond delivers more of its total cash flow earlier than a lower coupon bond. All else equal, a bond with a higher coupon will exhibit less price volatility than a lower-coupon bond. Here, this means that of the 10-year bonds, the one with the 8.50% coupon rate will exhibit less price volatility than the bond with the 6.50% coupon.

The inverse relationship between interest rates and bond prices means that when interest rates increase, fixed-coupon bond prices decrease. In other words, the inverse relationship means that interest rates and bond prices move in opposite directions, it does not infer anything about the magnitude of the change.

The relationship between the coupon rate and price volatility (all else equal) is inverse – a greater coupon results in less price volatility. Remember, if you have a problem with this on the examination, keep in mind that a zero-coupon bond has the highest interest rate risk because it delivers all its cash flows at maturity. Since a zero-coupon bond has a 0.00% coupon, a low coupon equates to high price volatility.

If two bonds are identical in all respects except their term to maturity, the longer term bond will be more sensitive to changes in interest rates. All else the same, if a bond has a lower coupon rate when compared with another, it will have greater interest rate risk. Therefore, for the option-free bonds, the 10 year 4% coupon is the longest term and has the lowest coupon rate. The call feature does not make a bond more sensitive to changes in interest rates, because it places a ceiling on the maximum price investors will be willing to pay. If interest rates decrease enough the bonds will be called.

The duration of a zero-coupon bond is equal to its time to maturity. Its price is greatly affected by changes in interest rates because its only cash-flow is at maturity and is discounted from the time at maturity until the present.