Jun 05

Eurodollar future convexity adjustment

by David Harper, CFA, FRM, CIPM

FRM |

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  • 2008 FRM Learning Objective: Compute the Eurodollar futures contract convexity adjustment 

In the FRM assigned reading (Hull Chapter 6), a forward rate is estimated given a futures contract price. The relevant difference is the same forward/futures distinction that applies to other commodities: one is exchange-traded, the other is OTC. The key trade-off is: an exchange gives liquidity but since contracts are standardized, basis risk is likely higher; an OTC contract can be tailored, but at the price of less liquidity and counterparty risk.

  • Eurodollar futures  (CME overview): a futures contract on the 90-day (3 month) Eurodollar interest rate.
  • Forward rate agreement (FRA): the LIBOR-based equivalent but instead an over the counter (OTC) agreement between counterparties.

Since the Eurodollar futures contract applied to a three-month rate, the corresponding FRA is a three month rate also; e.g., FRA 3 x 6, FRA 9 x 12, FRA 12 x 15.

At this point, no-arbitrage suggests the future rate in one year should be the same as an FRA 12 x 15 (the three month rate in one year). However, the key difference is that futures are settled daily. If you are long a FRA, you do not suffer daily volatility. But if you have a futures position, and rates go high, you have excess margin (cash inflow). If rates go low, you have margin calls (cash outflow). So, at the margin (pun intended), you experience more volatility with the futures contract: the futures rate should be slightly higher to compensate.

The difference is the convexity adjustment, which can be estimated various ways. Hull employs "Ho & Lee" method:

eurodollar_adjustment

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