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If you are long a FRA and short a ED future with the same fixing dates, do you have positive convexity or negative convexity?

The answer is positive convexity, because a Eurodollar future has no convexity and the FRA has positive convexity. What are the implications of this from a trading perspective? Specifically, under what conditions does this lead to an opportunity for arbitrage?


hypothetically if we assume that $R_{fra}=R_{fut}-\frac{1}{2} \cdot \sigma^2\cdot T^2$ holds (convexity adjustment) and you are able to observe $R_{fra}$, $R_{fut}$ and $T$ then you can extract implied volatility of reference interest rate. If your view on volatility is different then you can make a bet: long convexity position (if you expect volatility should be higher); or short convexity position (if you expect volatility should be lower).

  • $\begingroup$ is the following an accurate non-quantitative interpretation of this? As yields rise, Eurodollars will decrease in value linearly, whereas a short FRA will increase in value, but at an increasing rate This would suggest that this long-FRA/short-ED is a good position if yields are expected to decline; Is that not true? Is that actually a bet on increasing convexity? How does this position profit when yields rise? $\endgroup$ – hedgedandlevered Dec 17 '15 at 16:45
  • $\begingroup$ ED future is quoted as 100 less yield (i.e. price 98.5 implies 1.5% yield); which means long position in ED future is effectively a bet on a decrease of underlying rate (and vice versa short ED future - on an increase of rate). Long FRA (pay fixed; receive float) benefits from an increase of underlying rate. So in your example "long-FRA/short-ED" is actually a magnified position on an increase of rates. $\endgroup$ – Nicholas Dec 21 '15 at 10:24
  • $\begingroup$ To construct a bet on increasing convexity, you can decompose sensitivity [to change in rates] of each instrument (ED, FRA) into linear (duration) and non-linear (convexity) components; then you compute weights of FRA, ED in your constructed position so that your position is duration hedged (linear component becomes zero); in the end you are left only with non-linear component aka convexity $\endgroup$ – Nicholas Dec 21 '15 at 10:39

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