David Garcia, CFA, is analyzing two bonds. Bond X is an option tree corporate security with a 7% annual coupon and ten years to maturity. Bond Y is a mortgage backed security that also matures in ten years. Garcia is considering two possible interest rate scenarios""one in which rates are flat over the entire 10-year horizon, and one in which the yield curve is sloped steeply upwards. For each bond, Garcia has calculated the nominal spread over the 10-year U.S. Treasury issue as well as the zero-volatility spread. The zero-volatility spread would differ the most from the nominal spread:
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A. B. C.Explanation
The zero-volatility spread (Z-spread) measures the spread over the risk-free Treasury yield curve that makes the present value of a bond's cash flows equal to its market price. It is used to evaluate the relative value of a bond compared to the risk-free Treasury securities. The nominal spread, on the other hand, is simply the difference between a bond's yield and the Treasury yield.
In this question, David Garcia is analyzing two bonds: Bond X and Bond Y. Bond X is an option tree corporate security with a 7% annual coupon and ten years to maturity, while Bond Y is a mortgage-backed security that also matures in ten years.
Garcia is considering two interest rate scenarios: one in which rates are flat over the entire 10-year horizon and another in which the yield curve is sloped steeply upwards.
To determine which bond's Z-spread would differ the most from its nominal spread, we need to understand how the yield curve slope affects each bond.
When the yield curve is sloped steeply upwards, it means that interest rates increase significantly as the maturity of the bonds extends. This has an impact on the pricing of bonds, especially those with longer maturities.
For Bond X, the option tree corporate security, the Z-spread would differ the most from the nominal spread when the yield curve is sloped steeply upwards. This is because the option tree security has embedded options, such as call or put options, which are sensitive to changes in interest rates. When interest rates rise, the value of the embedded options tends to decrease, affecting the overall pricing of the bond. As a result, the Z-spread, which considers the risk-free Treasury yield curve, would differ more from the nominal spread.
For Bond Y, the mortgage-backed security, the Z-spread would be less affected by the steep slope of the yield curve compared to Bond X. Mortgage-backed securities are typically backed by a pool of mortgage loans, and their cash flows are influenced by factors such as prepayments and refinancing. While the steep upward slope of the yield curve may impact mortgage rates, it does not directly affect the Z-spread as much as it does for option tree securities like Bond X. Therefore, the Z-spread for Bond Y would differ less from its nominal spread when the yield curve is sloped steeply upwards.
Based on this analysis, the correct answer is:
A. For Bond X, when the yield curve is sloped steeply upwards.
This choice reflects the fact that the Z-spread for Bond X would differ the most from its nominal spread when the yield curve has a steep upward slope.