macrocephalopod

The same seasonality needs to show up in the futures curve too, otherwise you could easily make money by always shorting Q3 (Dec expiry) and buying Q4 (Mar expiry).

The short end of the curve (first 1-3 expiries) will be strongly affected by "other factors" e.g. everyone knew that Q1 2020 (Jun) was going to be negative and Q2 2020 (Sep) would be *really* negative but that Q3 2020 (Dec) would be really positive.

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.

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.

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.

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.

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.

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.