Can someone explain how/why bond prices have not changed at t=1. I would expect that even though the curve is not changing, the price at t=1 would not be same at it was at t=0? Shouldn’t new prices at t=1 be calculated by using forward rates, which can be backed out from the spot rates?
The following text is from Page 234 (Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies):
8.1.1 Timing Bets on No Change in the Yield Curve or ‘‘Riding the Yield Curve’’
When an investor invests in a fixed-income security with a maturity different from his desired holding period, he is exposed to either reinvestment risk or capital risk. Consider, for example, a portfolio manager who has a given amount to invest over 9 months. If he buys a 6-month T-bill, he incurs a reinvestment risk because the 3-month rate at which he will invest his funds in 6 months is not known today. And if he buys a 1-year T-bill, he incurs a risk of capital loss because the price at which he can sell it in 9 months is not known today. Riding the yield curve is a technique that fixed-income portfolio managers traditionally use in order to enhance returns. When the yield curve is upward sloping and is supposed to remain unchanged, it enables an investor to earn a higher rate of return by purchasing fixed-income securities with maturities longer than the desired holding period, and selling them to profit from falling bond yields as maturities decrease over time.
We consider at time t = 0 the following zero-coupon curve and five bonds with the same $1,000,000 nominal value and a 6% annual coupon rate. The prices of these bonds are given at time t = 0 and 1 year later at time t = 1, assuming that the zero-coupon yield curve has remained stable (see table below).
Maturity (Years) Zero-coupon rate (%) Bond price at t = 0 Bond price at t = 1
1 3.90 102.021 102.021
2 4.50 102.842 102.842
3 4.90 103.098 103.098
4 5.25 102.848 102.848
5 5.60 102.077 —
A portfolio manager who has $1,020,770 cash at disposal for 1 year buys 1 unit of the 5-year bond at a market price of 102.077%, and sells it 1 year later at a price of 102.848%. The total return, denoted by TR , of the buy-and-sell strategy is given by the following formula:
TR = (102. 848 + 6) / 102. 077 − 1 = 6. 633%
Over the same period, a 1-year investment would have just returned 3.90%. The portfolio manager has made 2.733% surplus profit out of his ride. Of course, the calculation is based on the assumption that future interest rates are unchanged. If rates had risen, then the investment would have returned less than 6.633% and might even have returned less than the 1-year rate. Reciprocally, the steeper the curve’s slope at the outset, the lower the interest rates when the position is liquidated, and the higher the return on the strategy.