Answer :
Let's analyze each of the given options step-by-step:
1. Option a: If the yield to maturity on each bond decreases to 6%, Bond A will have the largest percentage increase in its price.
- This statement is incorrect because while a decrease in yield to maturity generally increases bond prices, it isn't necessarily true that Bond A will have the largest percentage increase. The increase depends on various factors like coupon rates and duration.
2. Option b: Bond A has the most interest rate risk.
- This statement may not be correct without further context. Bonds with prices significantly above par or below par may have higher or lower interest rate risk, but a bond's interest rate risk is typically evaluated based on its duration. Since detailed duration figures aren't provided, we can't make this determination solely based on provided information.
3. Option c: If the yield to maturity on the three bonds remains constant, the prices of the three bonds will remain the same over the next year.
- This is incorrect. Even if the yield to maturity remains constant, the prices of the bonds will change as they get closer to maturity because the price will converge towards par value.
4. Option d: If the yield to maturity on each bond increases to 8%, the prices of all three bonds will increase.
- This statement is incorrect because increasing the yield to maturity results in a decrease in bond prices. Yield to maturity and bond prices have an inverse relationship.
5. Option e: If the yield to maturity on each bond decreases to 6%, the prices of all three bonds will increase.
- This statement is correct. When the yield to maturity decreases, the prices of bonds increase, as bond prices and yields are inversely related.
Given these analyses, the correct choice is:
e. If the yield to maturity on each bond decreases to 6%, the prices of all three bonds will increase.
1. Option a: If the yield to maturity on each bond decreases to 6%, Bond A will have the largest percentage increase in its price.
- This statement is incorrect because while a decrease in yield to maturity generally increases bond prices, it isn't necessarily true that Bond A will have the largest percentage increase. The increase depends on various factors like coupon rates and duration.
2. Option b: Bond A has the most interest rate risk.
- This statement may not be correct without further context. Bonds with prices significantly above par or below par may have higher or lower interest rate risk, but a bond's interest rate risk is typically evaluated based on its duration. Since detailed duration figures aren't provided, we can't make this determination solely based on provided information.
3. Option c: If the yield to maturity on the three bonds remains constant, the prices of the three bonds will remain the same over the next year.
- This is incorrect. Even if the yield to maturity remains constant, the prices of the bonds will change as they get closer to maturity because the price will converge towards par value.
4. Option d: If the yield to maturity on each bond increases to 8%, the prices of all three bonds will increase.
- This statement is incorrect because increasing the yield to maturity results in a decrease in bond prices. Yield to maturity and bond prices have an inverse relationship.
5. Option e: If the yield to maturity on each bond decreases to 6%, the prices of all three bonds will increase.
- This statement is correct. When the yield to maturity decreases, the prices of bonds increase, as bond prices and yields are inversely related.
Given these analyses, the correct choice is:
e. If the yield to maturity on each bond decreases to 6%, the prices of all three bonds will increase.
