Yield Curve Movement and the Forward Curve


In the Fixed Income section 2.3 in the CFA Institute book it says:

“Thus, if a trader expects that the future spot rate will be lower than what is predicted by the prevailing forward rate, the forward rate contract value is expected to increase.”

I’m having trouble understanding this concept. Can anyone help explain? Thanks!

Just look at it as the present value of cash flows.

How bonds are valued? Discounting cash flows using spot rates and forward rates.

Suppose a flat forward curve of 5%. The cupons and the face value are discounted at the forward rate of 5% and give a price of 100. Remember that forward curve is derived from the spot curve. If the future spot rates get lower (4%), the bond price will increase in value because the the remainning cash flows are discounted at a lower rate.

This is much simplier than it looks. It is saying that if you buy a bond today and rates get lower in the future, then bond price will increase.

Glad to further discuss this :slight_smile:

1 Like

Like Peru suggested, don’t over-think it. The principle is basic.

Let’s say that you take out your crystal ball and you think that mortgage rates are going to drop by more than forward pricing implies (like the trader in your quote). Here is your trade: Agree to buy a 30-year FNMA 2.5% coupon in 90 days at today’s market price of x. And wait. And cross your fingers.

If you are right, and rates drop next month, then your locked in price of x is looking pretty sweet. That 2.5% bond increased in value, but you are still only going to pay what you agreed - x. Thus the value of your position increased. You could trade out of your position at a profit, or take delivery of the bond at an old/stale/cheap price at the end of the contract.

allow me to simplify this reading. even if after so many years someone stumbles on this topic which is difficult to understand as explained in cfa books

pls feel free to correct me if my understanding is wrong or incomplete but this is what i can comprehend:-

there are 3 things to notice here:-

  1. current spot rates
  2. forward rates (which are a derivation of spot rates)
  3. future spot rates (which is an analyst estimation/assumption)

now, remember the relationship between price of the bond and interest rate which is an inverse relationship

now, assume current spot rates to be 5% , a derivation of forward rate from this spot rate can be lets say 5.2%.
now analyst expects the future spot rate to be 4%.

he has entered into a forward rate contract of 5.2% , so if he expects the future spot rate to be at 4%, then the value of his current contract increases, taking cue from the logic of inverse relationship between interest rate and price of the bond

so far, this is how I have understood this topic and have fared well. i don’t know if my understanding is flawed or not but breaking it down like this has certainly help.