Can anyone help me understand this answer below from Schweser? The forward rate associated with a forward rate agreement (FRA) is: A)less than that implied by the Eurodollar futures rate especially when the maturity of the contracts is longer. The forward (FRA) rate = implied futures rate – convexity bias. The convexity bias is considered negligible for contracts of less than one or two years. It is generally viewed as a consideration for contracts with a maturity of longer than two years.
The convexity bias goes with the ED futures contract not the FRA. Imagine trying to hedge an FRA with a ED futures contract. The FRA has convexity which means that if you are on the lending side of a $1,000,000 3 month FRA (i.e., committed to making a fixed interest rate loan) and rates go up you do not lose as much as the duration of the loan would suggest. This is because the rate at which you PV the loss back increases as well. The ED contract has no convexity. If you go short an ED contract, you will gain exactly $25/tick with no convexity at all when interest rates rise. That means you will gain more on the ED contract than you will lose on the FRA. That means that the futures rate should be higher than the forward rate it is meant to hedge (i.e., as interest rates rise the futures rate should not rise as much as the futures rate converges with the spot rate). The difference between the futures price and the forward price is the convexity bias.