macrocephalopod

Quarterly GDP numbers are not tradable which means there is no cash and carry arbitrage. If you can't trade spot then futures will be priced on three things -- 1. Expectations 2. Seasonality 3. Risk premium

1. and 2. are kind of the same thing, basically "what is your best guess of GDP prints for the next three years?" This depends on long term expectations, seasonal fluctuations, and other factors.

Long term expectations means the futures curve should tend toward whatever the long-run expected growth rate for distant maturities -- we have less information to predict the distant future so we rely more on long-term averages.

There is also strong seasonality in quarterly GDP due to stuff like weather, holidays, seasonal production (e.g. in agriculture) so for example 3rd quarter tends to be less than 4th quarter as people are saving for the holidays in Q3 and spending in Q4.

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.