## Wednesday, September 16, 2015

### Pairs trading the commodity futures curve - Antti Nikkanen

Notes on Antti Nikkanen Master's thesis Aug 2012

## Ch1. Introduction

Commodity futures trading strategy, which exploits the roll returns of commodity futures as its main driver of excess return. To minimize the volatility of returns, pairs trading methodology is used to trade the futures curve, with a Sharpe of 3. Liquidity is taken into account with trading cost of 3.3 bps. Commodity is still unknown because of lack of good data, it being a derivative security, short maturity claim on a real asset and have pronounced seasonality in prices levels and volatility.

## Ch2. Literature Review

Hong and Yogo (2012) show that aggregate basis (ratio of futures price to commodity price) is the most important predictor of commodity returns. The main factor behind the fluctuation of the aggregate basis is hedging pressure (how much producers short commodity futures to hedge their long positions in the underlying spot).

Erb and Harvey (2006) show that roll returns explain more than 90% of long-run cross-sectional variation of commodity futures returns over 1982-2004. The time-series variation of future returns is mostly explained by spot price movement. To become spot neutral the author creates spreads.

Fuertes and Miffre (2010) show tactical position of shorting contangoed and long backwarded futures. They also include momentum.

Gorton and Rouwenhorst (2005) state that the commodity futures returns are negatively correlated with those of equity and bond returns. But this low correlation exists only in 'normal' markets. The spread strategy reduces correlation even in 'abnormal' markets.

## Ch3. Theory

Commodity markets do not fit the CAPM (Bodie and Rosansky 1980) because it is difficult to make a distinction between systematic risk/return and unsystematic risk/return. Also, the price is dependent on demand and supply factors, not perceived adequate risk premiums.

Stocks (like Finnish mining company Talvivaara) follow closely the price of underlying commodity (nickel). But many companies, especially the oil companies have hedged away its oil exposure e.g. ExxonMobile. With commodity ETFs there may be large tracking error e.g. USO is an oil ETF but lagged massively the movements in oil prices after the 2008 crash due to rolling the portfolio in times of negative roll returns. GLD on the other hand tracks the spot gold quite closely.

Less than 1% of futures contract result in a delivery of the underlying asset. Commodity futures do not represent direct exposures to actual commodities. They are bets on expected future spot prices (Gourton and Rouwenhorst 2005). The relationship between the futures and spot price is $F=Se^{(r+c-y)(T-t)}$, where $r$ is the risk free rate, $c$ is the storage cost (storage facilities, insurance, inspections, transportation and maintenance, spoilage and financing), $y$ is the convenience yield (ability to profit from local supply demand imbalances, leasing of gold to jewelry manufacturers).

#### Economics of backwardation and contango

Upward sloping (contango) and downward sloping (backwardation) are determined by demand, supply and seasonal changes. For a hedger who is inherently long (petroleum producer long on crude through exposure to oil exploration, developing refining and marketing), speculators are going to take the long risk if the price is sufficiently discounted vs spot price, i.e they are in backwardation. (Anson 2009). Contango occurs for commodities in which the hedger is inherently short to the exposure of commodity (e.g. aircraft manufacturers that does not have aluminum mines, willing to purchase the futures contract of a future aluminum delivery). Hence, profits for the speculator is determined by the amount the hedgers have interest for risk capital, not the long-term price trends of the commodity markets (Anson 2009).

Hicks' rational expectations hypothesis states that the price of an asset for delivery in future must be the market's current forecast of the spot price on the future delivery date (spot does not move in presence of any further information). This has proven not to be useful practically. Storage models have been better at explaining practicality, which states that relationship between the spot and future depends on storage levels and expected storage levels in the future (i.e. inventory). This mean there is an expectation of the spot price to move as well through maturity. A difficult to store commodity (NG) has steep forward curve. When inventories are high relative to demand, the curve will be upward-sloping and when tight downward-sloping (Till, Feldman 2006). These, difficult to store commodities (HO, HG, LC, LH) have the highest average excess returns versus easy to store commodities.

#### Commodity futures returns composition

Commodity returns is the sum of spot return, risk-free rate and roll return. Commodity markets are usually favorable for sudden spot price rises but show mean-reverting tendency over longer periods.

#### CTAs

Generally trend following, in contrast to market timing strategies where statistical techniques are used to predict the trends before they become apparent. Managed futures strategies are either technical or fundamental in either systematic or discretionary manner. Most do technical systematically. Bridgewater, an exception, does fundamental systematically, e.g. in 2008 they spotted the possibility for either an inflationary or a deflationary deleveraging through contraction in private credit growth, declining stock market and a widening credit spread and adjusted their positions based on 1920s Germany, 1980s Latin American inflationary deleveraging and the deflationary deleveraging of Great depression in the 1930s and Japan in 1990s (Schwager 2012).

#### A hedge against inflation

In inflationary periods, usually long commodity future positions benefit and stock and bond returns are negatively impacted, because the purchasing power of the money declines and earning power of the corporation erodes.

Johansen test can check the cointegration of multiple time series at a time. It is a relative strategy and does not care about absolute value of the assets. With stocks, it is more common that just one of the assets is over or under priced (Gatev, Goetzmann, Rouwenhorst 2006). For futures curve, even the underpriced contracts when in contango, usually have a negative expected return.

The main reason to pairs trade the future curve is to hedge price movement risk and only capture the part of the commodity futures roll return. This strategy could be made dynamically adjusting to be more profitable.

For two time series to move together there needs to be something called the error correction, which causes correction of prices and hence mean reversion. Usually the order of integration is first determined with a unit root test before running an actual cointegration test (crucial to check with common sense and graphics). Augmented Dickey-Fuller test takes care of the autocorrelation in the difference variable series. Johansen test is based on the error-correction representation of the VAR equation and testing for reduced rank and then using Granger's representation theorem to get the cointegration vector.

## Ch4. Empirical work

1991 to 2012. Daily frequency of 12 nearest contracts of 20 commodities. Transaction cost of 3.3 bps per leg per trade and contracts with open interest less than 20000 not traded.

#### Methodology

1. Determine the shape (contango vs backwardation) by taking the difference of the first five contracts, and taking an average of them. $$\frac{1}{5}\sum_{i=1}^5(f_i-f_{i+1}).$$
2. If the result is positive (backwardation), go long the 'most' backwarded contract (maximum absolute slope), which is equivalently the most out of its path regarding its cointegration with the other data points in the curve. The position is taken onto the further contract.
3. The short position is determined by taking the smallest value of differenced contracts and going short on the further contract.
4. The pair is chosen only if both have open interest more than 20000.
5. If contango, the process is same but reversed. Take position into the largest difference and a long position into the smallest absolute difference.
6. At the start of each month the portfolio is set up for next 30 days, with equal weights.
All the commodity curves are found to be cointegrated. The information ratio is 3.1 for monthly rebalancing. All assets show positive returns. This can be bifurcated between roll returns (alpha genration) and hedged returns (to reduce volatility). Feeder cattle is invested only 3% of the time period while CL is invested 100%. daily traded strategy is similar with more trading cost, but good returns.

#### Improvements

1. The current strategy is suboptimal in terms of when to trade.
2. Entry should be based on price deviations form the equilibrium level.
3. Best 5 instead of all would produce better results.
4. To choose the 'hedging pair' from the real difference of the futures price and not the absolute price difference. This would capture the, though rare, instances where the futures curve has elements of both backwardation and contango.