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 no roll, the pnl is simply $P^k_{i+1} - P^k_i$.
• if there is a roll, the "on the run" price difference shown is a difference 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 cost (or roll impact) term $P^k_i - P^{k+1}_i$

We show the naive on the run price time series below in green as well as the series with roll impact. For strongly uptrending assets such as SP500 or Nasdaq, the downdrift of roll impact is not very high, for oil, or many rates futures, it is a game changer, and rolling 1d before or 5d before contract change, or buying longer expiry future can significantly alter pnl.

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