Let's now look at an important difference between FRAs and your rival futures. The convexity adjustment. At first glance, it's tempting to think that the FRA rate and the futures implied rate that is 100 minus the futures price for the same period should be identical, but they're not. And there's a good reason why. The key difference comes down to DV01 or how much a contracts value changes when rates move. Stir futures have a constant DV01 set by the exchange, for example, 25 Euros in the case of EURIBOR futures. But FRAs have a variable DV01, which depends on prevailing discount rates. So FRAs behave a bit like bonds. Their rate sensitivity changes as rates change. If you short an FRA, your DV01 increases in absolute terms when rates move in your favor, that is down. And decreases when rates move against you. With futures, none of that happens. The DV01 is fixed and does not change regardless of the rate level. That means an FRA versus futures position does not have static rate exposure. It has convexity. And that convexity creates a need to rebalance as rates move. So who benefits if you sell an FRA and go short a futures contract? In other words, your long convexity, those rebalancing trades generate a profit. It's a bit like being long gamma in options terms.

Let's look at how that plays out visually. Here's a chart showing the P&L from being short, both an FRA and a EURIBOR future. Assuming both start at the same implied rate. The green line shows the net P&L, and you can see it curves upward. That's convexity in action.

Since both contracts settle against the same rate at expiry. Pricing them the same today gives the trader a convexity free position. But of course, the market does not allow free lunches for long. Once traders spot the opportunity, they respond. FRA rates get pushed down or futures prices get pushed down, meaning implied futures rates go up, or both. This introduces a pricing gap that compensates for the convexity benefit. In other words, the market introduces a negative carry to offset the convexity gain over the holding period. That's why FRA rates almost always trade below the future's implied rate for the same period.

Now, what does this mean in practice? It means that if we use futures prices to infer forward rates, for example, to build a swap curve, we need to apply a convexity adjustment. The size of this adjustment depends mainly on volatility and time to expiry higher volatility and longer time horizons increase the convexity benefit and therefore the size of the adjustment. The overall level of interest rates also plays a smaller role. That said, while the theory is elegant, the practical impact is often minor, especially for front month futures, where the adjustment is typically just a fraction of a basis point. And for longer dated futures while the adjustment can grow to a few basis points, trading interest is often limited by low liquidity and wider bid office spreads. Still, the idea of futures FRA convexity is more than a pricing detail. It's a great introduction to gamma and non-linear risk key concepts in the world of options and dynamic hedging.