I’m getting confused with roll down return and roll yield. When long (and assuming upward sloping yield curve) why does roll down return gain value, while roll yield has negative value? - Roll down return (upward sloping yield curve) Say we purchase a 5 year bond, 5% coupon and 5% yield. After 2 years we own a 3 year bond and if rates have not changed, market yield should be lower, meaning higher market value. So we have gained value as we have rolled down the yield. - Roll yield (upward sloping yield curve) If we are long the forward, we have a negative roll yield.
Well I don’t know where did you get the roll down return. Never heard of it. For the roll yield you must distinguish between interest future contracts and the underlying is the interest it self or the underlying is bond. If the underlying is interest rate then in upward sloping the roll yield is negative as you have to buy another contract at higher rate assuming your current future is expired. If the underlying is bond then maybe the roll yield should be positive in upward yield slop but dunno if that applicable.
You are correct regarding the bond, as you ‘roll down’ the treasury yield curve you are getting the coupon of a 5yr bond but the maturity of a 3yr bond, giving you a positive roll return.
In the other scenario, you buy a futures at a premium (due to upward sloping forward curve). This has to converge with spot upon maturity otherwise there’s an arbitrage opportunity. That means the premium you paid is diminishing in value every day, hence a negative roll return.
The difference is that bonds are negatively correlation with their yields, so as you roll down the yield curve the value of the bond increases. Futures are (obviously) positively correlated with the futures curve, so as it rolls down the value of the futures decreases.
I can only remember the roll yield portion and it makes sense if you visualize it:
The idea of F (forward price) and S (spot price) is that as the contract approaches maturity F converges towards S. Keep this in your mind.
If the curve is upward sloping (CONTANGO), it means that F is greater than S. It also means that for F to eventually converge to S by expiration, it has to move DOWN towards S. = negative return
If the curve is downward sloping, (BACKWARDATION), it means that F is less than S. It also means that for F to eventually coverge to S by expiration, it has to move UP towards S. =positive return.
Roll yield in Ch 19 discusses movement of forward prices to spot. Why do we have to make the distinction between futures and bonds here, as mentioned by mattmania and glue85?
futures price is positively correlated with the interest rate. (when rate increases - futures price increases)
bond price is negatively correlated with the yield on the bond. (interest rate goes up, bond price goes down).
I understand this relationship, but why are we talking about futures and bond price, when roll yield in chapter 19 is regarding forwards?