Which of the following bonds is exposed to the greatest interest rate (price) risk?

Introduction / Context:
Interest rate risk, or bond price risk, is a central concept in fixed income investing. When market interest rates change, the prices of existing bonds move in the opposite direction. Some bonds are more sensitive to interest rate changes than others. This question tests whether you know which combination of maturity and coupon rate creates the highest interest rate price risk for a bond investor.

Given Data / Assumptions:

• All bonds listed are assumed to be otherwise similar (same credit quality, same payment frequency, etc.).
• We are comparing only the effects of maturity (5 years vs 10 years) and coupon rate (5 percent vs 10 percent).
• Interest rate price risk refers to the sensitivity of the bond's price to changes in market interest rates.
• We are not focusing on reinvestment risk or default risk in this question.

Concept / Approach:
Interest rate price risk is higher for bonds with longer maturities and lower coupon rates, because a larger portion of the bond's value is tied up in distant cash flows. Duration, a measure of interest rate sensitivity, increases with longer maturity and decreases with higher coupons, all else equal. Therefore, the bond with the longest maturity and the lowest coupon will generally have the highest duration and hence the greatest price sensitivity to changes in interest rates.

Step-by-Step Solution:
Step 1: Compare maturities. A 10 year bond has a longer maturity than a 5 year bond, so, other things equal, the 10 year bond will have greater interest rate risk than the 5 year bond. Step 2: Compare coupons. A 5 percent coupon is lower than a 10 percent coupon. Lower coupon bonds pay smaller periodic cash flows and rely more on the final principal payment, increasing duration and price sensitivity. Step 3: Evaluate each option: option a (10 year, 5 percent) combines long maturity with a low coupon; option b (5 year, 5 percent) has a shorter maturity; option c (5 year, 10 percent) has both shorter maturity and higher coupon; option d (10 year, 10 percent) has long maturity but a higher coupon. Step 4: Recognise that among these, the 10 year, 5 percent coupon bond will have the highest duration and therefore the greatest interest rate price risk. Step 5: Conclude that option a is correct.

Verification / Alternative check:
To visualise the difference, imagine a sudden increase in market interest rates by 1 percent. The prices of all existing bonds will fall, but the price drop will be larger for bonds with higher duration. If you calculate approximate durations (without detailed formulas), you will find that the 10 year, 5 percent bond has a duration noticeably longer than the 10 year, 10 percent bond and much longer than any 5 year bond. This means a larger percentage change in price for the same change in interest rates, confirming that option a has the greatest interest rate price risk.

Why Other Options Are Wrong:
Option b has a lower coupon but only a 5 year maturity, so its duration and price sensitivity are lower than those of the 10 year, 5 percent bond. Option c has both a shorter maturity and a higher coupon, so its price is less sensitive to interest rate changes. Option d has the same 10 year maturity as option a but a higher 10 percent coupon, which increases the weight of earlier cash flows and reduces duration compared to the 10 year, 5 percent bond.

Common Pitfalls:
A common mistake is to look only at maturity and ignore the coupon rate, assuming that the longest maturity always has the highest risk. While maturity is a major factor, coupon size also matters significantly. Another pitfall is confusing interest rate price risk with reinvestment risk; higher coupon bonds have lower price risk but higher reinvestment risk. In this question, focus strictly on price sensitivity to interest rate changes and remember that lower coupon plus longer maturity means higher price risk.

Final Answer:
The bond with the greatest interest rate price risk is a 10 year bond with a 5 percent annual coupon rate.