Forwards and futures price

[Peter van Vliet]

David,
Risking that this question is already somewhere is the forum. But..

Which is worth more i.e price higher; a forward or a future. I seem to read contradicting explanations (not particularly with your program).

It seems this is structurally different because of mtm on futures but does is change if there is an option for delivery (t bonds futures).

How does correlation between future price and interest rate tie into that?
Thanks

 

[David Harper CFA FRM]

Hi Peter,

Question does exist in several places but I am happy to try and summarize:

With respect to Hull's consumption/investment commodities, Hull says: If correlation between spot price, S, and interest rate (r) is positive, price (futures) > price (forward).
Why? the expected return on your excess margin cash is asymmetric, skewed in your favor. When spot price and rates both go up (+ correlation), your forward goes ITM, and you can withdraw excess margin cash, to be deposited at higher rates; but your downside, spot and rates go down, has your forward OTM, with margin calls but at lower borrowed rates. On the margin (pun intended), you invest at higher rates but borrow at lower rates.

In this *general* case, you can see it depends on correlation ... however, in FRM, the only reference to convexity bias is really in the context of the Eurodollar futures contract (on LIBOR) vs FRA. The way that I view this, FWIW, is that it is simply the special case of the above where we can assume, by definition, that the underlying (LIBOR) is highly correlated with interest rates (!), so here we have Hull 6.3: FRA forward rate = Eurodollar futures rate - (Ho & Lee's) convexity adjustment; i.e., futures rate > forward rate, consistent with "positive correlation between underlying spot (LIBOR) and the rate.

Now, one of my favored interest rate texts (http://www.amazon.com/Interest-Rate-Risk-Modeling-Valuation/dp/0471427241 ; their website http://www.fixedincomerisk.com/index.html ) puts this in different terms:

"The futures interest rate is different from forward interest rate. The difference arises because futures contracts are marked-to-market every day, which makes these contracts more volatile than the corresponding forward contracts. Though the exact relationship between the futures rates and forward rates is dependent on the assumptions of a specific term structure model, the following approximation based on Ho and Lee (1986) [i.e., same as Hull's version] ...
Due to marking-to-market, futures contracts are riskier investments than forward contracts and, hence, it is natural that the futures rate is higher than the forward rate." Interest Rate Risk Modeling, Nawalkha et al pp 146-7

Hope that helps, David

 

[Peter van Vliet]

David,
That helps a lot... Fully understand the reasoning (did not before).

Then, what about this;
Interest rate futures are designed to move like bonds,that is, to lose value when interest rates increase...relative to forward contracts this mtm is disadvantageous to long futures positions, this has to be offset by a lower futures contract value.

 

[David Harper CFA FRM]

Peter, great! I agree the futures price, unlike the FRA, moves (like a bond) in the opposite direction of rates/LIBOR as P = 100 - LIBOR. The only "add/edit" i would make to your final sentence is: it's not (IMO) the marking-to-market (or the inverse relationship between price and rates) that is the crux of the difference.

The difference emerges due to, in a word, liquidity. Or, the daily settlement enabled by M2M (we can't settle daily without M2M, but we can imagine M2M with daily settlement). Hull gives two reasons for the convexity difference (and one is technical, concerning the fact that FRA effectively automatically "tail") but both are about settlement, which amounts to the futures position experiencing, if you will, "interim cash flow volatility" whereas the forward "waits for cash". So, as far as summary narrative, IMO, settlement/liquidity are more to the point than inverse pricing or M2M per se ... not that what i am saying contradicts your statement, i don't think it does! thanks, David