Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

Hedging with Two Futures Contracts: Simplicity Pays

We propose to use two futures contracts in hedging an agricultural commodity commitment to solve either the standard delta hedge or the roll‐over issue. Most current literature on dual‐hedge strategies is based on a structured model to reduce roll‐over risk and is somehow difficult to apply for agricultural futures contracts. Instead, we propose to apply a regression based model and a naive rules of thumb for dual‐hedges which are applicable for agricultural commodities. The naive dual strategy stems from the fact that in a large sample of agricultural commodities, De Ville, Dhaene and Sercu (2008) find that GARCH‐based hedges do not perform as well as OLS‐based ones and that we can avoid estimation error with such a simple rule. Our semi‐naive hedge ratios are driven from two conditions: omitting exposure to spot price and minimising the variance of the unexpected basis effects on the portfolio values. We find that, generally, (i) rebalancing helps; (ii) the two‐contract hedging rules do better than the one‐contract counterparts, even for standard delta hedges without rolling‐over; (iii) simplicity pays: the naive rules are the best one–for corn and wheat within the two‐contract group, the semi‐naive rule systematically beats the others and GARCH performs worse than OLS for either one‐contract or two‐contract hedges and for soybeans the traditional naive rule performs nearly as well as OLS. These conclusions are based on the tests on unconditional variance ( Diebold and Mariano, 1995 ) and those on conditional risk ( Giacomini and White, 2006 ).     

中国大宗商品期货市场定价机制研究

大宗商品期货市场是我国资本市场的重要组成部分,其定价有效性关系到投资者套期保值和价格发现等功能的实现。本文对国际前沿研究中常用的定价因子进行全面系统梳理,并对这些因子对我国商品期货合约收益率的解释和预测能力进行检验。在此基础上,本文构建了适用于我国大宗商品期货市场的包含市场、基差以及基差动量的三因子定价模型。进一步研究表明,基于大宗商品存储理论和现货存货数据构建的投资组合收益率可以被本文三因子模型有效解释,验证了经典的存储理论在我国的适用性。此外,本文对基差与基差动量两个重要因子的经济学意义进行了阐释。本文研究为进一步厘清大宗商品期货市场定价机制提供了一定参考。     

Financialization and speculators risk premia in commodity futures markets

J.M. Keynes coined the term normal backwardation, a situation where a futures price for a particular expiry month is less than the expected spot price for that month. He argued hedgers pay speculators a risk premium, giving rise to normal backwardation. We study the behavior of commodity futures before and since financialization of the markets, which started about 20 years ago. We find the poor returns to managed futures in recent years are likely due to the impact of financialization and the associated outside money suppressing the futures risk premium.     

Hedging Equity-Linked Life Insurance Contracts

Abstract

This paper examines a portfolio of equity-linked life insurance contracts and determines risk-minimizing hedging strategies within a discrete-time setup. As a principal example, I consider the Cox-Ross-Rubinstein model and an equity-linked pure endowment contract under which the policyholder receives max(S_T , K) at time T if he or she is then alive, where S_T is the value of a stock index at the term T of the contract and K is a guarantee stipulated by the contract. In contrast to most of the existing literature, I view the contracts as contingent claims in an incomplete model and discuss the problem of choosing an optimality criterion for hedging strategies. The subsequent analysis leads to a comparison of the risk (measured by the variance of the insurer’s loss) inherent in equity-linked contracts in the two situations where the insurer applies the risk-minimizing strategy and the insurer does not hedge. The paper includes numerical results that can be used to quantify the effect of hedging and describe how this effect varies with the size of the insurance portfolio and assumptions concerning the mortality.     

Portfolio selection with commodities under conditional copulas and skew preferences

This article investigates the portfolio selection problem of an investor with three-moment preferences taking positions in commodity futures. To model the asset returns, we propose a conditional asymmetric t copula with skewed and fat-tailed marginal distributions, such that we can capture the impact on optimal portfolios of time-varying moments, state-dependent correlations, and tail and asymmetric dependence. In the empirical application with oil, gold and equity data from 1990 to 2010, the conditional t copulas portfolios achieve better performance than those based on more conventional strategies. The specification of higher moments in the marginal distributions and the type of tail dependence in the copula has significant implications for the out-of-sample portfolio performance.     

Pricing a class of exotic commodity options in a multi-factor jump-diffusion model

In a recent paper, Crosby introduced a multi-factor jump-diffusion model which would allow futures (or forward) commodity prices to be modelled in a way which captured empirically observed features of the commodity and commodity options markets. However, the model focused on modelling a single individual underlying commodity. In this paper, we investigate an extension of this model which would allow the prices of multiple commodities to be modelled simultaneously in a simple but realistic fashion. We then price a class of simple exotic options whose payoff depends on the difference (or ratio) between the prices of two different commodities (for example, spread options), or between the prices of two different (i.e. with different tenors) futures contracts on the same underlying commodity, or between the prices of a single futures contract as observed at two different calendar times (for example, forward start or cliquet options). We show that it is possible, using a Fourier transform-based algorithm, to derive a single unifying form for the prices of all these aforementioned exotic options and some of their generalizations. Although we focus on pricing options within the model of Crosby, most of our results would be applicable to other models where the relevant ‘extended’ characteristic function is available in analytical form.     

Investment in Commodities Futures: The Accounting Implications

There are no rules within existing Generally Accepted Accounting Principles that apply to investment in commodities futures. In this paper, the accounting implications of investing in futures are explored. The accounting problems relate to the first record of the contract and to the subsequent recognition of gains and losses. There is no unequivocal answer under GAAP as to how futures contracts should be recorded. As with many other items in conventional accounting practice, the method of recording depends upon managers'intentions. This has obvious, and serious, implications for auditors.     

Using futures contracts for corporate hedging: The problem of expiry and a possible solution

Companies using futures contracts for hedging purposes need to roll over their contracts if the maturity of their exposure exceeds that of the futures contracts. This entails basis risk that can reduce significantly the effectiveness of the hedge. In this paper an alternative form of futures contract is proposed. the contract never expires and can be used for long-term hedging without the need for rolling-over into a new contract. the contract is shown to be equivalent to a portfolio of conventional futures contracts of differing maturities. Its price is determined by arbitrage against the underlying asset.     

An Anatomy of Commodity Futures Risk Premia

We identify two types of risk premia in commodity futures returns: spot premia related to the risk in the underlying commodity, and term premia related to changes in the basis. Sorting on forecasting variables such as the futures basis, return momentum, volatility, inflation, hedging pressure, and liquidity results in sizable spot premia between 5% and 14% per annum and term premia between 1% and 3% per annum. We show that a single factor, the high‐minus‐low portfolio from basis sorts, explains the cross‐section of spot premia. Two additional basis factors are needed to explain the term premia.     

Does futures exhibit maturity effect? New evidence from an extensive set of US and foreign futures contracts

In a seminal article, Samuelson (1965) [Samuelson, P. A. (1965), “Proof that properly anticipated prices fluctuate randomly,” Industrial Management Review 6, 41-49.] proposes the maturity effect that the volatility of futures prices should increase as futures contract approaches maturity. This study provides new evidence on the maturity effect by examining a more extensive set of futures contracts than previous studies and analyzing each contract separately. Using 6805 futures contracts drawn from 61 commodities, including some data from non-US markets, we find that the maturity effect is absent in the majority of contracts. In addition, the maturity effect tends to be stronger in agricultural and energy commodities than in financial futures. We also examine the hypothesis in Bessembinder et al. (1996) [Bessembinder, H., J. F. Coughenour, P. J. Seguin, & M. M. Smoller (1996), “Is there a term structure of futures volatilities? Reevaluating the Samuelson hypothesis,” Journal of Derivatives 4, 45-58.], which states that negative covariance between the spot price and net carry cost causes the maturity effect in futures. Our results provide very weak evidence in favor of this hypothesis.     

New No-arbitrage Conditions and the Term Structure of Interest Rate Futures

Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts. Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (J Finance 52(1); 409–430, 1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.     

国外著名商品指数编制比较及其对我国的启示

商品期货指数,是商品期货的金融化,是期货市场发展到一定阶段的必然产物。为了更好编制和开发我国商品指数及其衍生品,本文对国外著名商品指数的编制方法从编制目的和原则、品种选择、权重设计、合约选择、指数计算等五个方面进行全方位比较研究,进而提出编制我国相关商品指数的总体思路。     

FINANCIAL FUTURES AND IMMUNIZATION

This paper investigates the ability of any portfolio that contains both bonds and financial futures contracts to immunize a lump sum liability having the same initial duration and value as the portfolio itself. An analysis of second order conditions shows that immunization against a local change in interest rates is possible only if the number of futures contracts lies within a critical interval; the endpoints depend on cash flow characteristics of the specific bonds and contract being combined. Immunization against any large change in rates is impossible if the portfolio contains any long position in futures but is achieved by some portfolios that contain short positions in futures.     

The effectiveness of incorporating higher moments in portfolio strategies: evidence from the Chinese commodity futures markets

This paper examines portfolio strategies that incorporate individual and systematic higher-order moments, within a stochastic optimization framework with uncertain mean and covariance. Using weekly, daily, and 30-minute interval data on Chinese commodity futures, we show that incorporating higher moments into portfolio strategies generally leads to better performance. The systematic fourth-order moment, among all systematic moments considered, can lead to the most robust, and a relatively large, improvement in investment performance, while the contribution of individual moments to the improved performance depends on the data horizon. We also find that adding higher moments brings superior performance in more cases for 30-minute-interval data than for other low-frequency data, suggesting that our strategy most likely performs best in 30-minute-rebalancing investments.     

Trend following,risk parity and momentum in commodity futures

We show that combining momentum and trend following strategies for individual commodity futures can lead to portfolios which offer attractive risk adjusted returns which are superior to simple momentum strategies; when we expose these returns to a wide array of sources of systematic risk we find that robust alpha survives. Experimenting with risk parity portfolio weightings has limited impact on our results though in particular is beneficial to long–short strategies; the marginal impact of applying trend following methods far outweighs momentum and risk parity adjustments in terms of risk-adjusted returns and limiting downside risk. Overall this leads to an attractive strategy for investing in commodity futures and emphasises the importance of trend following as an investment strategy in the commodity futures context.     

Currency futures-spot basis and risk premium

This paper explores the usefulness of currency futures-spot basis in predicting spot rate changes and currency futures returns. We conjecture that the currency risk premium may be an important component of the basis for long-maturity futures contracts, but may not be so for short-maturities. Thus, the basis of long-maturity contracts cannot predict the spot rate changes between now and maturity, rejecting uncovered interest rate parity (UIP), but can predict currency futures returns, which are solely determined by the risk premium. Conversely, the basis of the short-maturity contracts can predict the spot rate changes between now and maturity, validating the UIP, but cannot predict currency futures returns. Empirical tests support these conjectures for the Japanese, British, Swiss, and German currencies over the last two decades. The results are also consistent with Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the Expectation Hypothesis. Journal of Financial Economics 58, 397–415], who shows that the Expectations Hypothesis holds at the very short end of the term structure of interest rates.     

Long term spread option valuation and hedging

This paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium (i.e., cointegrated). The spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly. This approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model. In this paper, we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads. Two examples of spreads in energy markets – the crack spread between heating oil and WTI crude oil and the location spread between Brent blend and WTI crude oil – are analyzed to illustrate the results.     

Basis‐Momentum

We introduce a return predictor related to the slope and curvature of the futures term structure: basis‐momentum. Basis‐momentum strongly outperforms benchmark characteristics in predicting commodity spot and term premiums in both the time series and the cross section. Exposure to basis‐momentum is priced among commodity‐sorted portfolios and individual commodities. We argue that basis‐momentum captures imbalances in the supply and demand of futures contracts that materialize when the market‐clearing ability of speculators and intermediaries is impaired, and that it represents compensation for priced risk. Our findings are inconsistent with alternative explanations based on storage, inventory, and hedging pressure.     

Markov models for commodity futures: theory and practice

The objective of this paper is to develop a generic, yet practical, framework for the construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results concerning the low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switching models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their ‘smile’, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed form and of the same complexity as the Black–Scholes formula.