Assume that the risk-free zero rates are increasing with maturity (That is, the 6-months zero rate is lower than the one-year zero rate, which is lower than the two-year zero rate, etc). It must be that:
A) The yield-to-maturity curve for coupon bonds lies below the yield-to-maturity curve for zeros
B) The yield-to-maturity curve for coupon bonds equals the yield-to-maturity curve for zeros
C) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros
D) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros for maturities less than one year, but lies below the yield-to-maturity curve for zeros for maturities greater than one year.

Question

Assume that the risk-free zero rates are increasing with maturity (That is, the 6-months zero rate is lower than the one-year zero rate, which is lower than the two-year zero rate, etc). It must be that: 
A) The yield-to-maturity curve for coupon bonds lies below the yield-to-maturity curve for zeros
B) The yield-to-maturity curve for coupon bonds equals the yield-to-maturity curve for zeros
C) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros
D) The yield-to-maturity curve for coupon bonds lies above the yield-to-maturity curve for zeros for maturities less than one year, but lies below the yield-to-maturity curve for zeros for maturities greater than one year.

Quizplus · Accepted Answer

When the risk-free zero rates are increasing with maturity, the yield-to-maturity curve for coupon bonds will lie below the yield-to-maturity curve for zeros. This is because the price of a coupon bond is equal to the present value of its future cash flows, which are discounted at the appropriate zero rates. When the zero rates are increasing with maturity, the present value of the future cash flows will be lower, which will result in a lower price for the coupon bond. This will, in turn, lead to a higher yield-to-maturity for the coupon bond.

Assume That the Risk-Free Zero Rates Are Increasing with Maturity