The yield curve movement, Forward Curve and Active Bond Portfolio Management

CFA Level II Fixed Income
#1

Hi all,

Why does the forward contract price increase when the future spot rate is higher than the current predicted forward rates? I’m struggling to link my understanding to current bond price.

Does my summary of understanding regarding future expected spot rate make sense? When future expected spot rate is higher than the current forward rate (or future expected yield curve being greater than the current forward curve):

  • expected bond price would be lower and current bond price is overvalued

  • expected return of bond is less than current YTM

the reason for this is due to the fact that the expected future spot rate is the geometric mean of the current one year spot rate and a series of forward rates.

Thanks!

#2

The point of estimating future price is to eliminate arbitrage opportunities. If the expected spot rate is lower than the future rate, expected price will be greater than the future price. So there is an undervaluation issue going on. In order to eliminate arbitrage, the force of market supplies and demands will make the future price (future rate) to increase (decrease) in order to match the expected spot price (spot rate).

Hope this helps.

#3

Hi phutuongsy,

Just to be clear, are you comparing expected future spot rate to actual future spot rate? I thought we are trying to compare expected future spot rate against current FORWARD rates.

Is it such that when the expected future spot rate is greater than current forward rates, the expected bond price is undervalued and forward contract prices through supply and demand pushes it upwards to eliminate the difference in pricing between bonds priced at spot and forward rates?

Thanks!

#4

The forward market is a derivative of the bond market, not the other way round. Meaning that forward contracts converge towards the expected spot rate implied from the current bond price through time.

The no arbitrage theory tells you that the value (not price) of a forward contract should be derived from the shape of the yield curve, when the forward contract is mispriced, then an arbitrage opportunity exists by shorting the higher priced asset, and longing the other. Transactions exploiting arbitrage will keep occuring until the forward rates converge on the current forward curve implied by no arbitrage. Simillarly, a bond is undervalued if the future expected spot rates are higher than the ones implied by the current spot curve, but in this case, the current spot curve is in fact a function of future expected spot rates (according to expectations framework).

So in a nutshell. The mispricings of bonds depends on the shape of the yield curve through time (whether it will follow through the expected future spot rates derived from the implied forward curve), and the forward contracts prices are derived from that implied forward curve. If an investor values the contract based on future spot rates different than the ones implied by no arbitrage, then it is said to be undervalued or overvalued, but that does not mean that he will make a profit, it all depends on whether the future spot rates follow his prediction, and not the ones implied by the market.

#5

Think of it this way: In order to prevent arbitrage opportunity, the expected spot rate must be equal to forward rate implied by the yield curve. If the expected spot rate is different from the implied forward rate, there must be a convergence of the forward rate to the expected spot rate. And this process is achieved by the interactions between supply and demand.

That’s why we say:

  • When expected spot price > implied forward rate => forward rate must increase

  • When expected sport price < implied forward rate => forward rate must decrease

Hope this helps.

#6
#7

This isn’t true: arbitrage is determined by rates (prices) that are available today, not by expectations. To have an arbitrage opportunity, you have to be able to lock in all prices simultaneously (otherwise there is risk); you cannot lock in an expected rate (price).

#8

This isn’t true: arbitrage deals with prices, not values.

The no arbitrage condition says that the price of a forward contract is determined by the shape of the yield curve; the value doesn’t matter. You make money by buying and selling the same value at different prices, not by buying and selling different values at the same price.

#9

The way CFA has drilled me to understand arbitrage is by the comparison of an asset/derivative price to its synthetic version assuming the ability to borrow or lend risk-free.