PART 1
Theory
Chapter 1
Commodity Prices and the Option Value of Storage
Lewis Evans* and Graeme Guthrie†
School of Economics and Finance, Victoria University of Wellington,
PO Box 600, Wellington, New Zealand
Commodities are physical, not financial assets. We investigate the effects on equilibrium spot-price behavior of frictions in the storage process, which introduce an element of irreversibility to storage decisions and lead to periods when storage operators do not trade in the spot market. We value the real option to delay selling a stored commodity, which comes bundled with the stored commodity itself and generates a convenience yield. The latter arises if the spot price is incorrectly used to measure the market value of the stored commodity, ignoring the embedded real option. It can be interpreted as the expected excess return on the real option to delay selling the stored commodity. Rather than equaling a flow of benefits received during the period over which the return from storage is being calculated, it actually represents changes in the present value of benefits that will be received only some time after the measurement period, when the commodity is released from storage. Storage frictions also generate heteroskedastic spot prices, with volatility being much higher when storage operators decide not to trade in the spot market.
1.1.Introduction
Commodities are physical, not financial assets, and transporting them between spot markets and storage facilities is costly. In this chapter, we investigate the implications for spot prices and storage policies of frictions in the storage process. In the presence of such frictions, there are actually two distinct goods: the commodity being traded in the spot market and the commodity being held in storage. The market value of the stored commodity is determined in the market for ownership of storage operators. This ensures that the expected growth rate in the market value of the stored commodity, adjusted for ongoing costs of holding the commodity in storage, equals the appropriate risk-adjusted discount rate.a The spot price inherits this property as long as storage operators are trading in the spot market. However, whenever they do not participate in the spot market, the items traded there are created and consumed instantaneously, so that there are no intertemporal restrictions on the spot price. In this situation, the expected growth rate in the spot price, adjusted for ongoing storage costs, deviates from the risk-adjusted discount rate, giving the appearance of a convenience yield. Spot price volatility also varies according to whether or not storage operators are trading in the spot market. If they are trading, they will help dampen shocks. However, when storage operators withdraw, the spot price will bear the full impact of shocks. This results in periods of relatively low price volatility while storage operators are trading in the spot market, interrupted by relatively brief periods of much higher volatility when they do not participate.
The convenience yield and spot-price heteroskedasticity stem from a small cost that is incurred each time a unit of the commodity is moved into storage. This friction introduces an element of irreversibility into storage decisions; it is costly to move the commodity into and then immediately out of storage (and also to empty and then immediately refill a storage facility). As a result, the real option to delay selling the stored commodity can be valuable, and this option drives a wedge between the spot price and the market value of the stored commodity.b A storage operator that wishes to increase its inventory by one unit must buy that unit in the spot market, as well as incur the cost of moving it into storage. In return, the operator receives one unit of the commodity ready for immediate sale, as well as the real option to wait and sell it at some future date. It is optimal for the operator to buy the commodity in the spot market only when the value of this delay option is at least as great as the cost of moving the commodity into storage. In contrast, a storage operator that wishes to reduce its inventory by one unit must sell that unit in the spot market. Because such a sale destroys the real option to wait and sell at a later date, it is optimal for the operator to sell the commodity in the spot market only when this delay option is worthless. Thus, storage operators will be buyers in the spot market when the delay option’s value reaches some strictly positive threshold, and they will be sellers when its value is zero. When the value of the delay option lies anywhere between zero and the positive threshold, storage operators do not trade in the spot market.c
In our model, the owner of the stored commodity receives no benefits, pecuniary or otherwise, other than the capital gain. The expected rate of return from storage equals the risk-adjusted discount rate, provided the rate of return is calculated using the market value of the stored commodity. However, if the...