 # Forward Rates in relation to Spot Rates

Suppose you are given the following table of zero-coupon Treasury rates Maturity Spot (years) Rate 1.0 4.00 2.0 4.80 3.0 5.50 4.0 6.10 5.0 6.60 Using the no-arbitrage condition to derive the yield curve, you find that the one-year forward rates implied by the spot rate curve: a. Continually rise with the forward start date, but increase at a slower rate than the spot rate increases with maturity. b. Continually rise with the forward start date, but increase at a faster rate than the spot rate increases with maturity. c. Initially rise with the forward start date, but then begins to fall because the rate of increase in spot rates with respect to maturity slows down. d. Continually rise with the forward start date, but increase at the same rate of increase as the spot rate increases with maturity.

This one shoud be B. Under the assumption that interest rates are rising: In the graph: Y-axis= Interest X-axis= Years We will have: Forward above Spot rate above Par Therefore, the one-year forward rates implied by the spot rate curve continually rise with the forward start date, but increase at a faster rate than the spot rate increases with maturity to bring the average up. Having said that, I think the answer is B.

Can we know the solution?

Strange, My is B too. Forward rates with rise with an increasing rate than spot rates. The reason I say this a) take a look at graph FR > SP > YTM (if yield curve is upward sloping) If someone can explain conceptually why this is true, i’d appreciate it. Joey!!

If the YTM average is rising the spot rates must also be rising, and rising faster to pull the average up, and the forward rates too must be rising faster than the spot rates if the spot “average”, is getting pulled up. Note: Bear in mind the formula you use to calculate FR from spot rates