The Handbook of Commodity Investing

CHAPTER 5

The Relationship Between Risk Premium and Convenience Yield Models

Viola Markert, Ph.D.

Managing Director

CYD Research GmBH

Heinz Zimmermann, Ph.D.

Professor of Finance

Wirtschaftswissenschaftliches Zentrum WWZ

University of Basel

The valuation of commodity futures contracts is typically regarded to be more complex than the valuation of financial assets and their derivatives. The reason is the hybrid character of the underlying commodity: On one hand, commodities serve as consumption and processing goods. On the other hand, they also share certain characteristics of financial assets in the sense that they have a unique equilibrium market price, and that they are subject to speculative storage. In short, commodity spot prices are a mixture of prices for consumption goods, reflecting the current scarcity of the good, and of asset prices, reflecting the expectation of future spot prices and an expected risk premium. Depending on either view, commodity futures are:

• Derivatives written on asset-like underlying securities and should be valued using arbitrage-based techniques, or alternatively
• Derivatives written on nontradable state variables or spot commodity prices and should be valued with equilibrium asset pricing techniques

As a result of that hybrid character, two broad classes of valuation models are used for commodity futures: risk premium models (RPM) and convenience yield models (CYM). Risk premium models value commodity futures with respect to the expected commodity ...