Future Total Return: Price Change and Roll

Future contract Price Time Series vs Roll

Yahoo shows the on-the-run future price time series, on the day of a contract roll, the price changes suddenly from one contract to the next. If the trader wishes to maintain his position through a roll, he needs to sell the old contract and buy the next one.

• For a contract $k$ if there is not roll, the pnl is simply $P^k_{i+1} - P^k_i$.
• if there is a roll, the on the run price differemce is between two contracts: $P^{k+1}_{i+1} - P^k_i$ to rewrite it as price changes of contract k and $k+1$, we add the roll impact term $P^k_i - P^{k+1}_i$

Interest Rate

The impact of roll is bigger when contango rate is larger, we see a larger impact for long term bonds, which implies the contango is larger for longer maturity bonds. It appears that $contango=y_{bond}-r_{shortterm}$

Currency

Currency future contango is given by the interest rate differential between the 2 currencies. A currency such as AUD has positive carry due to higher rates than USD, whereas JPY has negative carry due to lower rates than USD.

Equity

Precious Metal and Copper

Energy