# Futures returns and P&L

### Abstract

Exchange-listed futures play an important part in many active strategies; they offer leverage, efficient access to illiquid physical markets, and risk management tools. In this paper, we illustrate the issues and procedures related to incorporating futures in our strategy (e.g. contract specifications, margin requirements, contract size, leverage, mark-to-market (MTM) etc.). Finally, we define returns on margin and compute strategy's P&L and max P&L draw throughout the holding period.

### Overview

From our perspective, a futures contract for a given delivery month is similar to any other security with the exception of limited lifetime (i.e. expiry). Furthermore, at any given time, the exchange lists several contracts for different delivery months of the same underlying. The returns series for these contracts are strongly correlated and usually the liquidity is highest at front-contract. As time approaches expiry date of the front contract, the trading volume switches to the next nearest expiry contract (i.e. rollover); futures participants primarily seek exposure and are unwilling to take delivery so they rollover their position.. The actual mechanism for rolling forward can vary significantly from a simple switch (i.e. price jump) on a given day before or on expiry date, to a more gradual rollover (i.e. continuous price) before expiry.

### Raw Data

For our analysis, we will use the front-month contract with simple rollover mechanism. Our series may experience price jump on rollover days, but for daily returns, we are only concerned with prices at market open-close and do not hold a position overnight, thus the analysis of this data set is immune from day to day price jumps.

We will use S&P E-mini future contract listed on Chicago Mercantile Exchange (CME) under (ES). The futures are traded in two trading sessions: day-session on trading floor (pit), and after-hours electronic trading session. In this paper, we will assume the following strategy:

• Underlying asset – S&P 500 E-minis.
• Entry decision - we buy (go long) the futures contract on market open using a Market-on-open order (MOO).
• Exit decision – we close the futures position by taking an offsetting position (unwind) in the same future market at market close (MOC)

### Underlying future

• Exchange - CME
• Contract Months - Quarterly cycle (March, June, September and December)
• Contract Size – 50
• Expiry – 3rd Friday of the contract month

### Data Analysis

The descriptive statistics above suggest a mixture of ARMA model (serial correlation) for the mean and with GARCH/EGARCH (ARCH effect) process for volatility.

For the sake of our discussion here, we will use a plain EGARCH model, but with GED leptokurtic innovations. The model does not capture the serial correlation, but does represent the volatility to some extent[FN].

### Other Considerations

In our earlier discussion, we ignored the transaction costs and we assumed we invested all our capital in the strategy, which implies we can buy/sell fractional shares.

1. Transaction cost The transaction cost refers to brokerage fees to work the buy/sell order on our behalf. The fee structure varies significantly across brokers, traded asset, order type (market versus limit order), order size, and any special agreement your firm has with their primary broker. For future contract, brokerage fees are higher than simple equity shares. Check your broker fees schedule.

2. Non-fractional shares Aside from mutual fund accounts, a trader can only buy whole number of contracts. Why do we care? The initial margin requirement for a future contract can be large. You will need to round down the number of contracts when we compute the P&L and computed weighted returns.

### Conclusion

Prior to any analysis, we should understand the structure of the underlying contract. Define the strategy, compute returns and P&L. In our discussion, we assumed a daily holding period, ES front contract as trading instrument, and specified when we long/short the underlying security. Finally, we compute the P&L at close, minimum and maximum value within holding period and compare it with our risk limits.

Our proposed strategy loses 2.1% of our capital daily and has a volatility of 19.8%. The large returns and volatility are due primarily to the leveraged-nature of futures contracts.

This is not a great strategy, so we’ll try to improve it in following white papers.