in Schweser notes , reading 42 page 145 , it states that if spot rates went lower than what is implies by the forward curve , the forward price increases , can anyone explain why ? and whats the relaton between the two ?
I’m not quite sure what you mean, given that the forward curve is derived from the spot curve.
If you can put that comment in context, I can probably make something of it.
When spot rates turn out to be lower (higher) than implied by forward curve, the forward price will increase (decrease). A trader expecting lower future spot rates (than implied by the current forward rates) would purchase the forward contract to profit from its appreciation.
this is the exact text from Schweser notes under the term structure and interest rate dynamics reading page 145
I don’t get that all either. I would think the trader expecting lower future spot rates would want to sell future contracts. That way, he could deliver oil at price x and buy it at lower than price x on the spot market. Would be curious what others have to say?
I think the intuition behind this is that if an investor expects lower spot rates, this also implies that he expects bonds to be discounted at lower spot rates, which would increase the value of the bond.
So if the expected future spot rates
That’s at least how I made sense out of it
Having looked at the reading, I found the one missing piece of information: these are forwards on (risk-free) bonds. The conclusion doesn’t hold for forwards on other assets whose prices don’t depend exclusively on interest rates.
If future spot rates are lower than those implied by the forward curve, then the price of the underlying bond will be higher than expected, so the value of the forward contract will have increased by more than the risk-free rate.
If future spot rates are higher than those implied by the forward curve, then the price of the underlying bond will be lower than expected, so the value of the forward contract will have increased by less than the risk-free rate.
then the price of the underlying bond will be higher than expected, so the value of the forward contract will have increased by more than the risk-free rate.
Why when bond’s price increase higher the value of forward contract increase more than risk free rate? I cant connect those two elements what did I miss here?
Suppose that you have $1,000 par, annual pay, 6% coupon, 2-year bond, and the spot rates are:
- 1-year: 2%
- 2-year: 4%
Then the implied 1-year forward rate starting 1 year from today is 6.0392%, and the present value of the bond is $1,038.85.
Suppose that 1 year from today the 1-year spot rate is 4% (less than the 6.0392% implied forward rate). Then the value of the bond (plus the coupon payment) will be $1,079.23, an increase of 3.8868%, which is higher than the original 2% 1-year spot rate.
How is this calculated? I see that one year from today we will receive one coupon plus principal, i.e. 1060. How can PV be greater than this?
It’s a 2-year bond.
One year from today we get a $60 coupon payment, plus the present value of $1,060 coming one year after that.
1038.85=60/(1.02)+1060/(1.04)2
1079.23=60+1060/(1.04)
Yup.
so when we are saying we should long the contract because the forward price will be higher in a situation when expected spot in future is lower than the forward
we are really just saying the realized future price based on such expectation (aka the forward price) will be higher?
I think when i think of it i think of forward price as the price of a forward contract
the forward price appreciate in value because the bond is more expensive and your forward contract can lock in a higher rate so you can buy the bond cheaper? or use the forward to lock in a cheaper price
and now thinking about it, how we demonstrate this buy mathmatical equation of higher forward price？
Can you please explain how you worked out the value of 1079.23 ?
I asked krok: