# RDP 2017-03: Financialisation and the Term Structure of Commodity Risk Premiums Appendix C: Calculation of Holding Period Returns

To calculate the holding period returns, a database of futures contracts was constructed for 26 commodities. These contracts were then used to construct a times series of the commodity futures curves. Specifically, a futures curve was constructed for each commodity, each month, with the date based on the expiry date of the futures contract. The price of the expiring contract was considered to be the spot price, while the price of the contract maturing in one month's time was considered to be the price of a contract with a maturity of one month, and so on. These futures curves could then be used to look at the return of holding a futures contract (with a particular maturity) to maturity, the excess holding period return, and therefore the ex post risk premium (the average of these returns).

It is important to note that futures curves with futures prices at each maturity were not available for most commodities, as most commodities do not have contracts expiring in each calendar month. For example, consider Table C1 which shows a commodity that has futures contracts expiring every second month. At time t, we would calculate returns for maturities 2, 4, 6, 8 etc, but then at time t + 1 we would have returns for maturities 1, 3, 5, 7 etc. As we move through time, we calculate returns for every month where an observation is available. We then take the arithmetic average of the returns across maturities.

Table C1: Example Commodity Expiration Schedule
Maturity in months
Spot 1 2 3 4 5 6 7 8
t Y Y Y Y Y
t + 1 Y Y Y Y
t + 2 Y Y Y Y Y
t + 3 Y Y Y Y

Note: Y denotes an observation

Further, the availability (and/or liquidity) of futures contracts out to 24 months varied across commodities and therefore futures curves could not be constructed for the same maturity profile across all commodities.