Question

1. Assume the spot curve is negatively sloped. How does the yield on a coupon bond compare to the yield on a zero coupon bond with the same time to maturity?

2. Assume you buy a zero coupon bond with maturing at time t + 1 with price P_t+1. You sell the bond next period. The rate y'_t at that time is lower than the current forward rate ₁f_t. How does the rate of return on your investment compare to y₁? Where y'_t is expected rate at time t. ₁f_t is the forward rate starting in period 1 going forward t years. y₁ is the actual yield in period 1.

Answer 1

The spot rate is the rate of return earned by a bond when it is bought and sold on the secondary market without collecting interest payments. The spot interest rate for a zero-coupon bond is the same as the YTM for a zero-coupon bond. The YTM is the annual rate of return (IRR) calculated as if the investor will hold the asset until maturity.

a)With a negative spot curve, YTM for a zero-coupon bond will be lower as compared to a bond with coupons payments as YTM of a coupon paying bond.

b) y1 is the actual yield

y't is the expected rate

1ft is the forward rate

SInce y't is lower than 1ft and zero-coupon bond is being sold before the maturity the actual yield would be lower than the rate of return. Here price and selling price won't be a factor since its a zero-coupon bond.