# Market Invariant for Commodity Futures

In the same sense that Meucci describes "compounded returns" as the invariant for equities and "changes in yield-to-maturity" as the invariant for fixed-income, what is the invariant for a commodity future like a corn future?

What have I tried?

Take the commodity forward pricing formula from Hull (and ignore the convexity correction for a future vs. forward, which is probably immaterial for short-term futures like corn futures):

$$F_0=S_0e^{(r+u-y)T}$$

where:

• $$F_0$$ = forward price
• $$S_0$$ = spot price
• $$r$$ = risk-free interest rate
• $$u$$ = storage costs [as a constant proportion of $$S_0$$]
• $$y$$ = convenience yield [as a constant proportion of $$S_0$$]

I observe $$S_0$$ from the market for spot corn (e.g. on USDA) and $$F_0$$ from the market for futures. I'm already estimating $$r$$ via interest rate derivatives (e.g. Fed Funds Futures, Eurodollar Futures and Options). That leaves physical cost-of-carry $$u-y$$ as the remaining unknown. I would think that measuring the change in a constant-maturity physical cost-of-carry $$u-y$$ would be the market invariant.