This is a nice question -- roughly "What does the futures curve look like for quarterly futures that settle into quarterly GDP % growth estimates"?https://twitter.com/bennpeifert/status/1378192287352557571 …
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So the curve you end up with, based on expectations only, will be basically anchored to short term expectations for the first three expiries, tend to the long-term average for distant expectations, and have a regular annual seasonality.
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Then we need to talk about risk premium. GDP numbers are correlated with things that you can trade, e.g. stocks, interest rates, the dollar, implied volatility. Generally +ve GDP surprises are good for stocks and the dollar, bad for interest rates and implied vol.
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Just consider stocks. A +ve GDP surprise is good for stocks, so you expect GDP futures to be somewhat correlated with stocks. That means that GDP futures need to trade at a discount to expectations.
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To see why, note that if they traded in line with expectations, you could buy stocks and short GDP futures. In general you expect to make money from stocks and since GDP futs are in line with expectations, you expect to neither make nor lose money on your futures.
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If GDP surprises to the upside your stocks will be up and you will lose on your futs. If GDP surprises to the downside your stocks will be down but you will win on your futs. So you have hedged your stock position (reduced the volatility) without a decrease in expected return.
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That's a free lunch and the market doesn't allow it for long. Eventually the GDP futs will trade at a discount to expectations, so that shorting them is a -ve expected value trade -- the convergence to spot as the futs mature is what pays for your hedge.
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So the final answer is -- the front end of the curve is anchored to short term expectations, has seasonality, and for long expiries it tends toward long-term expectations minus a discount to account for the risk premium. The size of the discount depends on ...
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... the beta of GDP surprises to stocks, interest rates, the dollar, implied volatility, and anything else you can trade which has a risk premium embedded in it.
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Final note -- nothing here is specific to GDP except the particular values for expectations, seasonality, betas etc. Take a look at this thread I did on VIX futures - it's saying exactly the same thing with different words.https://twitter.com/macrocephalopod/status/1366517635433783302?s=20 …
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