Two firms, Groening Inc. and Shearer Co., have just completed simultaneous bond issuances. Both issues have a stated coupon rate of 5%, pay interest semiannually, and have a face value of $i,000 per bond. The Groening and Shearer issues both have a maturity of 15 years and their duration is approximately the same. If the Groening bond have a higher convexity measure than the Shearer bonds, which issuance will sell for the higher price?
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A. B. C.A
To determine which bond issuance will sell for a higher price, we need to analyze the relationship between bond prices and interest rates, considering the stated coupon rate, duration, and convexity.
Duration measures the sensitivity of a bond's price to changes in interest rates. Generally, as interest rates increase, bond prices decrease, and vice versa. So, if two bonds have approximately the same duration, we can infer that their prices will change in a similar manner when interest rates fluctuate.
Convexity, on the other hand, provides additional information about how a bond's price changes in response to interest rate movements. It measures the curvature of the price-yield relationship. A higher convexity indicates that the bond's price is more responsive to changes in interest rates, resulting in a greater price increase when rates fall and a smaller price decrease when rates rise.
In this scenario, the Groening bond has a higher convexity measure than the Shearer bond. Therefore, we can deduce that the Groening bond will experience a greater price increase when interest rates fall and a smaller price decrease when interest rates rise compared to the Shearer bond.
Given the options provided, we can eliminate option C because it suggests that Shearer bonds would depreciate less in a period of rising interest rates, which is inconsistent with the higher convexity measure of the Groening bond.
Between options A and B, we need to consider the scenario of rising or falling interest rates. Option A suggests that Groening bonds will depreciate less in a period of rising interest rates. However, since Groening bonds have a higher convexity, they will actually experience a smaller price decrease compared to Shearer bonds in such a scenario. Hence, option A is incorrect.
Option B states that Groening bonds will depreciate less in a period of falling interest rates. Since Groening bonds have higher convexity, they will indeed experience a greater price increase compared to Shearer bonds in this situation. Therefore, option B is correct.
To summarize, the correct answer is:
B. Groening, since the bonds will depreciate less in a period of falling interest rates.