Futures returns

• Typical strategy: buy contracts 2 or 3 months out
• When the contract becomes the front month contract, sell it and buy new contracts 2 or 3 months out.
• Return = % change in futures price 2 or 3 months \(\rightarrow\) 1 month
• \(\neq\) % change in front month price

Futures roll

• Consider a forward curve with months to maturity on the x axis.
• Consider a contract with expiration at a certain date.
• As time passes, the location of this contract on the curve moves to the left (months to maturity become less).
• If the forward curve doesn’t move, then
  • The futures price of the contract falls if the market is in contango
  • And rises if the market is in backwardation

• Consider buying a contract 2 months out at date \(t\) and hold it for 2 months (date \(t+2\)). At \(t+2\), its price is the spot price.
• Gain is \(\text{spot}_{t+2} - \text{futures}_t\).
• This equals

Gold example

History of USO

History of spot crude prices

Normalized histories

Forward Curves

• Examples: SPXL, SPXS (L=Long, S=Short) are 3x levered
• Each day hold futures contracts (long or short) with

Daily SPXL returns versus daily SPY returns

Daily SPXS returns versus daily SPY returns

SPY, SPXL, and SPXS returns

Principles about levered etfs

• In an up-and-down market, both levered long and levered short ETFs lose money.
• In trending markets, levered ETFs do better than leverage ratios indicate.
• In an upward (downward) trending market, a levered long ETF outperforms by more (underperforms by less) than the leverage ratio.
• Due to daily rebalancing. For a levered long ETF, $ at risk rise on positive returns and fall on down returns.