# Eurodollar future vs Eurodollar forward contracts

You are considering two contracts: a Eurodollar futures contract with six months to maturity, selling at 5%, settled on three-month LIBOR, marked to market every day; and a Eurodollar forward contract with six months to maturity, selling at 5%, settled on three-month LIBOR

Which contract do you prefer?

I don't understand the answer given in Crack's Book Heard on the Street.

Could anyone else explain this to me please.

• I guess I would select the future because it would be easier to trade (standardized contract). Jun 26 '20 at 18:33

I guess the author's argument is that, because of the frequent settlements, one needs to invest the mark-to-market gains and fund the losses. As the exchange traded futures contract is negatively correlated to interest rates, the mark-to-market gain happens when interest rates are low, so not a great time to invest, while the loss happens when interest rates are high, so not a great time to look for funding.

Over-the-counter (OTC) forward contract does not have to go through this pressure (even though these days some forms of initial margins, variation margins and collateralization - all of them needing to account for some funding/investing - are accompanying most OTC contracts).

Edit: In general, theoretically, there is an expectation that futures price is less than forward price, if the uknown amount (at expiry) is positively correlated to the (stochastic) discount factor.

Given $$T$$ expiry date and $$S$$ payment date and unknown $${\cal F}_T$$-measurable amount $$X$$, $$\beta_t = \exp (-\int_0^t r_udu)$$ stochastic discount factor (its inverse, bank account value, being the standard numeraire here) and (zero-coupon) bond price $$B(t,T)=\beta_t^{-1}\mathbf{E}[\beta_T | \cal{F}_t]$$, we have:

$${\rm Fwd}_t^X = B(t,S)^{-1}\beta_t^{-1}\mathbf{E}_t[\beta_S X]$$

and, due to (continuous) resettlement (and other technical assumptions),

$${\rm Fut}_t^X = \mathbf{E}_t[X]$$

(making futures prices a martingale).

It can then be proved that the futures convexity correction is:

$${\rm Fut}_t^X = {\rm Fwd}_t^X - \beta_t^{-1} B(t,S)^{-1} \mathrm{Cov}_t(X, \beta_S).$$ Time $$0$$ relation is: $${\rm Fut}_0^X = {\rm Fwd}_0^X - B(0,S)^{-1} \mathrm{Cov}(X, \beta_S).$$

In the Libor futures/forward price context above (long futures contract), the covariance is positive.

(Proofs are available in Hunt and Kennedy's book, Financial derivatives in Theory and Practice.)

• ".. as exchange-traded futures contract is negatively correlated to interest rates.. " what does this mean? which contract is that exactly? IR swap? how does that compare to forwards? how does low IR environment translate into "bad time to invest"?
– John
Jun 28 '20 at 1:18
• @Jonat You long \$10000*(100 - 90/360*r), where r tends toward 3m Libor at maturity. Contract value is negatively correlated to r which in turn is positively correlated to the environment rates at which you can invest or raise cash.
– ir7
Jun 28 '20 at 1:32
• @ir7: pls see my answer below. I believe your argument is only valid for being long the futures contract. When you are short the futures, you benefit when rates go up: so you should receive positive MtM in a higher rates environment and you need to post collateral in a lower rates environment. Jun 28 '20 at 7:20

I have written a response here:

Why are FRA/futures convexity adjustments necessary?

The credit risk is eliminated in either case since, these days the future will trade on the exchange and the FRA contract will be settled with the clearing house.

There might actually be some value created dependent upon which futures exchange you trade: LCH versus EUREX can (at time) have significant value differentials solely due to the positioning of dealers looking to reduce concentrated exposure. This effect can outweigh convexity and can be in either direction. However, if you traded a future and a FRA across different exchanges you would want to ensure the carry charge on the required margin at each institution was smaller than the gain - if the two were traded at the same settlement venue then the margin would be much more reduced.

didn't read the book, but I would guess the future contract all else being equal.

the point being credit risk.

as mentioned the future contract is settled daily by the exchange. forwards are traded over the counter and settled at expiration, by that time, the party owing to the other could default on the payment.