Investing in commodity futures markets: can pricing models help?

Abstract

This article empirically investigates whether continuous time pricing models are able to help reveal mispriced commodity futures contracts. Mispricings are identified based on the difference between model and observed prices, using four different pricing models for four different commodity markets, namely crude oil, copper, silver, and gold. Pricing errors are found to carry informational content for future price movements in excess of the overall market. Investment strategies based on these pricing errors yield significant excess returns, particularly for the relatively small copper and silver markets.

Keywords:

• commodity investment
• informational content
• futures

JEL classification :

• G13
• G14
• G11

Acknowledgements

We thank Alexander Kurov, two anonymous referees and participants of the Meeting of the Swiss Society for Financial Market Research 2009, Geneva, the Financial Management Association European Meeting 2009, Turin, the INFINITI Conference on International Finance 2009, Dublin, and the Southern Finance Association Meeting, 2009, Captiva Island, for valuable comments.

Notes

For a recent broad empirical study on commodity investments, see e.g. Gorton and Rouwenhorst (2006). For a rigorous treatment of commodity markets, see Geman (2005).

These inefficiencies might be caused by ill-informed traders, purely liquidity-driven investors, institutinal issues due to fixed roll-over procedures of major indices, regulation, etc.

As pointed out by Sercu and Wu (1997) testing the successfulness of a pricing error-based investment strategy can also be viewed as an efficiency test of the considered markets.

See also Table 1 for the respective formulae.

We have also implemented three-factor models in the spirit of Cortazar and Naranjo (2006), however, due to the increased number of parameters, these models over-fitted the data and did not yield reasonable results.

Contracts with longer maturities than 24 months are also traded at NYMEX. However, as liquidity decreases significantly with maturity of the contracts, contracts with maturities greater than 24 months were not considered for crude oil and copper.

The following trading months are available for silver and gold: the current calendar month; the next two calendar months; any January, March, May, and September falling within a 23-month period; and any July and December falling within a 60-month period beginning with the current month – see www.nymex.com.

The details on the last trading days are available on www.nymex.com: For crude oil, trading terminates at the close of business on the third business day prior to the 25th calendar day of the month preceding the delivery month. If the 25th calendar day of the month is a non-business day, trading shall cease on the third business day prior to the business day preceding the 25th calendar day. For copper, silver, and gold, trading terminates at the close of business on the third to last business day of the maturing delivery month.

We call a term structure to be in bachwardation (contago) if it is decreasing (increasing) with maturity.

This procedure is not entirely consistent, as the models’ parameters are theoretically constant over time. However, as it is the ultimate goal to detect current and not past mispricings, past observations are not used, as they would distort the current price relationships.

In the context of interest rate term structure fitting, these issues are also discussed by Brown and Dybvig (1985), de Munnik and Schotman (1994) and Ioannides (2003).

Note that for presentational reasons, all values in Table 5 (Silver) are scaled by 102.

Before fixing the time period to estimate γ _{i, t} to be 100 days we tried alternatives from 80 to 200 days. The results were very similar. One should keep in mind that, in contrast to a stock market application, the returns of futures with different maturities are highly correlated. Thus, γ _{i, t} is much more stable in the case of futures written on the same underlying compared to the case of securities that are only weakly correlated.

Theoretically, this procedure is not entirely correct. As the time to maturity of a futures contract changes, its sensitivity may also change. However, as a rolling time series is used throughout the study, the differences in sensitivities should be very small, since the dispersion of time to maturity is not large; see Table 2.

The regression constants α _i are not reported, as they are very close to zero and insignificant.

One might argue that the bid-ask spread provides a reasonable approximation of transaction costs. However, due to the market structure of the considered futures exchanges it is not as straight forward as it might appear. This is the case, as there do not exist real market makers in the NYMEX futures trading. Therefore, it often occurs that two customers trade with each other directly. In this case, it is far from obvious which party has actually to pay the ‘bid-ask spread’. Intuitively, it makes sense that the party with the higher execution pressure will trade more aggressively and thus is willing to pay the spread. Market participants who act less aggressively will actually earn the spread and thus experience negative transaction costs. This intuitive argument has been documented in the empirical market microstructure literature on futures markets. Kurov (2005) shows that ‘effective spreads for customer limit orders tend to be negative, suggesting that limit-order traders earn the liquidity premium’. Therefore, transaction costs are directly linked to the time pressure of execution. The longer the trader is willing to wait, the more likely he will experience zero or even negative transaction costs. Clearly, the results presented for a lag of zero, cannot be achieved after transaction costs and therefore provide an upper boundary. The results for a lag of one day are, in our opinion, quite conservative as a trader who accepts to wait for one day until execution cannot be considered an ‘aggressive’ trader.

The number of 50% is to some extend arbitrarily, but we believe that the median is a natural choice.