Convenience Yield Research Articles

Crude oil: Commodity or financial asset?

We examine the relation among daily returns to crude oil prices, equity prices, and commodity markets by modifying previous efforts in two important ways; expanding the model to include the equity price for an oil-producing firm, ConocoPhillips, which ameliorates omitted variable bias and estimating the expanded model using the Kalman Filter, which reduces uncertainty associated with OLS estimates from rolling windows. Consistent with the notion of a commodity price beta for oil industry stocks, there is a positive correlation between returns to the spot price of WTI and ConocoPhillips. This correlation indicates not all price changes in crude oil are expected to persist; indeed, some of the price reductions associated with the Asian Financial crisis and the price increase associated with the 2008 price spike are not included in our estimate for long-run prices. In 2008:Q4, the correlations between daily returns to crude oil and equities flip from negative to positive. We hypothesize that this flip is triggered by a large reduction in interest rates in the fourth quarter of 2008, which is associated with a reduction in convenience yields and a change from backwardation to contango in futures markets. These changes increase the returns to holding crude oil as a financial asset relative to holding oil as a commodity.

A Convenience Yield Approximation Model for Mean‐Reverting Commodities

AbstractStandard option‐based approximations for convenience yields make use of the assumption that commodity spot prices follow a geometric Brownian motion. While there is some empirical support for this assumption, prices of a wide variety of (agricultural) commodities mean revert. Using a mean‐reverting spot price process we derive a novel convenience yield approximation analytically. It corresponds to the difference between the present values of two floating‐strike Asian options written on the spot and the futures prices, respectively. Using natural gas spot and futures price data from four different trading locations, we compare convenience yield estimates derived from existing approximations to those of our new measure. We find that convenience yield estimates vary substantially across approximation methods and that differences can be attributed to the cost of carry and the moneyness of the options. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:625–654, 2015

Convenience yield in commodity price modeling: A regime switching approach

This paper attempts to model the futures term structures of crude oil and natural gas using the notion of convenience yield in a regime switching framework. Unlike the existing studies, which assume the convenience yield to have either a constant value or to have a stochastic behavior with mean reversion to one equilibrium level, the model of this paper extends the Gibson and Schwartz (1990) model to allow for regime switching in the convenience yield along with the other parameters. A closed form solution for the futures price is derived and the model parameters are estimated using the maximum likelihood method. The results show that the estimated regimes are very close to the contango and backwardation regimes commonly seen in futures markets. The results also show that the transitional probabilities play an important role in shaping the futures term structure implied by the model.

Convenience Yield Value of International Emission Allowance Based on Call Options

Convenience yield is call options; spot holders attain excess investment revenues through holding spot assets instituted futures assets. Based on the hypothesis of convenience yields, our empirical results show that monthly convenience yield of emission allowance has significant options feature; convenience yield has strong correlation with price spread between spot and futures and their price volatility. The market information set is helpful to adjust portfolio policy and improve portfolio investment revenues of emission allowances.

Revisiting the relationship between spot and futures prices in the Nord Pool electricity market

This work discusses potential pitfalls of applying linear regression models for explaining the relationship between spot and futures prices in electricity markets, in particular, the bias coming from the simultaneity problem, the effect of correlated measurement errors and the impact of seasonality on the regression results. Studying a 13-year long (1998–2010) price series of spot and futures prices at Nord Pool and employing regression models with GARCH residuals, we show that the impact of the water reservoir level on the risk premium is positive, which is to be expected, but contradicts the results of Botterud et al. (2010). We also show that after taking into account the seasonality of the water level, the storage cost theory proposed by Botterud et al. (2010) to explain the behavior of convenience yield has only limited support in the data.

Hoarding the Herd: The Convenience of Productive Stocks

This paper investigates the convenience yield that emerges in markets with productive stocks. We isolate the economic fundamentals giving rise to the yield, and show how these map to the empirical convenience yield measure. A model for price dynamics is derived from an economic model for optimal stock levels. We show how the price process reduces to a simple non‐linear first‐order Markov process. The model is estimated for the Norwegian market for farmed salmon by Generalized Methods of Moments, where stock growth is approximated by sea‐water temperature. Our estimation result supports the theorized role of stock growth as a convenience yield component. Our results are relevant for the functioning of futures markets for commodities such as fish and other animal production where systematic stock growth affects the term structure. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:679–694, 2015

Using Multivariate Densities to Assign Lattice Probabilities When There Are Jumps

The lattice approximation to a continuous time process is an especially useful way to value American and real options. We choose lattice probabilities by extending density matching for diffusions to density matching for jump diffusions. Technically, this requires that diffusion and jump components be cast as independent state variables. In this setup, the diffusion probabilities are locally normal and the jump probabilities are locally a mixture of distributions. The lattice is structurally uniform and density matching ensures that all probabilities are legitimate without requiring jumps to non‐adjacent nodes. The approach generalizes easily to several state variables, does not require node adjustments, and does not appear to be dominated by more specialized numerical algorithms. We demonstrate the model for scenarios where the option may depend on a jump diffusion with possible stochastic interest rates and convenience yields. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:385–398, 2015

On the Performance of the Comonotonicity Approach for Pricing Asian Option in Some Benchmark Models from Equities and Commodities

In this paper we investigate the applicability of the Albrecher et. al. (2005) comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Levy models as in Albrecher et. al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz' 1997 stochastic convenience yield model. We show that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by product delivers super-hedging strategies which can be easily implemented.

Booms and Busts in Commodity Markets: Bubbles or Fundamentals?

This paper considers whether there were periodically collapsing rational speculative bubbles in commodity prices over a forty year period from the late 1960s. We apply a switching regression approach to a broad range of commodities using two different measures of fundamental values – estimated from convenience yields and from a set of macroeconomic factors believed to affect commodity demand. We find reliable evidence for bubbles only among crude oil and feeder cattle, showing the popular belief that the extreme price movements observed in commodity markets were caused by pure speculation to be unsustainable.

Maximal Gaussian Affine Models for Multiple Commodities: A Note

AbstractThis study extends the maximal affine models of single assets to a multi‐commodity setup. We show that the correlated version of maximal affine models for a single commodity is no longer maximal for multiple commodities. In the maximal model, the convenience yield of a certain commodity could depend on the prices of other commodities, which is consistent with the structural model in our companion study Casassus, Liu, and Tang [Review of Financial Studies, 26, 1324–1362, 2013]. This cross‐commodity relationship is a feedback effect that may generate substantial co‐movement among long‐run commodity prices, a fact that is consistent with many empirical studies. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:75–86, 2015

On the lease rate, convenience yield and speculative effects in the gold futures market

By examining data on the Gold Forward Offered Rate (GOFO) and lease rates, we conclude that the convenience yield of gold is better approximated by the lease rate than the interest adjusted spread. Using the former quantity, we study the relationship between gold leasing and the level of COMEX discretionary inventory and show that lease rates are negatively related to inventories. We also show that futures prices have increasingly exceeded forward prices over the period, and this effect increases with the speculative pressure and the maturity of the contracts.

Exchange Rates and UIP Violations at Short and Long Horizons

The much-studied Uncovered Interest Rate Parity (UIP) puzzle, the observation that exchange rates do not adjust sufficiently to offset interest rate differentials, is more complicated than commonly understood. It changes nature with the horizon. I conrm existing short-run evidence that high interest rate currencies depreciate less than predicted by the interest rate differential. But, building on Engel ( 2015 ), at longer horizons (4 to 7 years) Ind a reverse puzzle: high interest rate currencies depreciate too much. Interestingly, the long-horizon excess depreciation leads exchange rates to converge to the UIP benchmark over the long-run. I propose a novel model, based on the mechanism of bond convenience yields, that can explain both the short and the long horizon UIP violations. The model presents interesting new links between ex- change rates and monetary-�scal interaction. I also provide direct empirical evidence that supports the mechanism.

Commodities as Collateral

We propose and test a theory of using commodities as collateral for financing. Under capital control and collateral constraint, investors import commodities and pledge them as collateral to earn higher expected returns. Higher collateral demands increase commodity prices and make the inventory -- convenience yield relation less negative. Our model illustrates these equilibrium effects and suggests that the violation of covered interest-rate parity is a proxy for collateral demands. Evidence from eight commodities in China and developed markets supports the theoretical predictions. Our findings complement the theory of storage and provide new insights into the financialization of commodity markets.

The Tourinho model: neglected nugget or a receding relic?

This article evaluates Tourinho's (1979b) work as one of the earliest contributors to the real options literature. His model pioneered the application of risk neutrality to uncertain investments, but his originality of introducing an option-holding cost albeit to overcome the extraction paradox is rarely imitated. We claim that the combination of a convenience yield and an option-holding cost produces a more satisfying representation. Moreover, variations in the holding cost give rise to a host of investment decisions ranging from the standard real option solution for a zero-holding cost to a net present value solution for an infinite-holding cost. Not only does the holding cost mediate between these two poles, but it provides the option seller (usually a landowner or a government) with a policy instrument for influencing the extraction timing and thus the extraction profit of the option buyer. We derive the holding cost that optimizes the landowner's combined value of the option premium, holding costs and eventual royalties.

Is the convenience yield a good indicator of a commodity's supply risk?

A strong increase in the demand for some commodities over the last decade will have a major impact on their future supply situation. Of increasing importance, therefore, is an assessment of a commodity's criticality, and especially its supply risk, by appropriate indicators. The literature has proposed numerous indicators of the supply risk. Here, we use the convenience yield of commodity futures as a supply risk indicator to address some of the major shortcomings of existing indicators, especially regarding their predictive power. This paper aims to test the applicability of the convenience yield as an indicator of a commodity's future supply risk. Therefore, we calculate historical convenience yields for 3-, 15-, and 27-month futures contracts for five major industrial metals (aluminum, copper, lead, nickel, and zinc) during the period 1999 to 2011. We compare the convenience yields at the beginning of the contract period to known indicators at maturity to find that the convenience yield has generally predictive power for the static stock lifetime (i.e., inventory volume/turnover) and future spot prices. Furthermore, we find that, with some restrictions, the convenience yield is an applicable indicator of a commodity's supply risk.

The stochastic seasonal behavior of energy commodity convenience yields

This paper contributes to the commodity pricing literature by consistently modeling the convenience yield with its empirically observed properties. Specifically, in this paper, we show how a four-factor model for the stochastic behavior of commodity prices, with two long- and short-term factors and two additional seasonal factors, may accommodate some of the most important empirically observed characteristics of commodity convenience yields, such as the mean reversion and stochastic seasonality. Based on this evidence, a theoretical model is presented and estimated to characterize the commodity convenience yield dynamics that are consistent with previous findings. We also show that commodity price seasonality is better estimated through convenience yields than through futures prices.

Commodity futures price volatility, convenience yield and economic fundamentals

Commodity price volatility increased during 2006 to 2011 first with the commodity bull cycle of 2006 to 2008 and then with the credit freeze crisis and Great Recession. This letter uses both high- and low-frequency data over 1990 to 2011 to examine the link between economic fundamentals and measures of realized volatility and convenience yield computed from estimated futures price forward curves. The possible influence of institutional investors (index traders) is also examined. Affine term structure models are estimated using Intercontinental Exchange (ICE) futures prices on cotton, a commodity for which economic fundamentals can be readily identified and measured. The results, robust across specifications, suggest that the determinants of volatility, but not convenience yield, changed during the period 2006 to 2011. There is no evidence that index traders are responsible for increased volatility or changes in convenience yield.

Scarcity, Risk Premiums, and the Pricingof Commodity Futures:The Case of Crude Oil Contracts

In this article, risk premiums of commodity futures are directly related to the physical scarcity of commodities. For this purpose the authors propose a simple decomposition of spot prices into a pure asset price plus a scarcity related price component. This replaces the traditional convenience yield that results from an imperfect no-arbitrage relationship of the term structure of commodity futures prices. The empirical tests confirm that two separate commodity-specific risk premiums affect the pricing of crude oil futures contracts: a net hedging pressure premium and a scarcity premium. The two premiums show different cyclical characteristics. The authors also find that asset market risk factors such as exchange rates or stock market shocks affect the term structure of oil futures prices in a much more homogeneous way than commodity-specific hedging pressure or scarcity shocks do.

The Simple Economics of Commodity Price Speculation

The price of crude oil never exceeded $40 per barrel until mid-2004. By July 2008 it peaked at $145 and by late 2008 it fell to $30 before increasing to $110 in 2011. Are speculators partly to blame for these price changes? Using a simple model of supply and demand in the cash and storage markets, we determine whether speculation is consistent with data on production, inventory changes, and convenience yields. We focus on crude oil, but our approach can be applied to other commodities. We show speculation had little, if any, effect on oil prices. (JEL G13, G18, G23, G31, Q35, Q38)

Commodity Prices, Convenience Yields, and Inflation

This paper provides evidence that the two leading principal components in a panel of 23 commodity convenience yields have statistically and quantitatively important predictive power for inflation even after controlling for unemployment gap and oil prices. The results hold up in out-of-sample forecasts, across forecast horizons, and across G7 countries. The convenience yields also explain commodity prices and can be seen as informational variables about future economic conditions as conveyed by the futures markets. A bootstrap procedure for conducting inference when the principal components are used as regressors is also proposed.