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Commodity futures value at risk

A difference between financial markets and physical commodities markets is the fungibility of what is traded. Japanese yen, Eurodollar futures, and shares of IBM are fungible. Coffee, oil, and electricity are not. Because of transmission costs, electricity in Quebec is worth a different price than electricity in Massachusetts. Because of marketing and perceived quality differences, coffee grown in Nicaragua commands a different price than coffee grown in Colombia. A value-at-risk measure for a commodities portfolio may need to address different qualities, origins, or delivery locations.

In many commodities markets, futures contracts are used as a benchmark for pricing spot or forward contracts. A future is for a specific quality, origin, and/or point of delivery. Spot or forward transactions for other qualities, origins, and/or points of delivery trade at spreads to the future.

Assume cash valuation and measure value-at-risk as 1-day 90% USD VaR. An international coffee wholesaler trades arabica coffee from its US headquarters as well as local offices around the world. Although coffee transacts in various currencies, each office hedges foreign exchange risk locally. Accordingly, our firm-wide value-at-risk measure does not consider foreign exchange risk. All prices are in USD, and all transactions mature within a year. We shall construct a primary mapping 1 = θ(1R) of the form


Exhibit 8.19 indicates the specific arabicas traded by our firm. Although the value-at-risk measure distinguishes between growths of coffee, it does not distinguish between delivery points. This is because the cost of shipping coffee is small compared to its value. This does not mean that coffee at one location is fungible with that at another—you can’t deliver coffee at Rotterdam while it is afloat off the Horn of Africa. A value-at-risk measure can only address market risk. Liquidity issues must be addressed with alternative means, such as careful scheduling of deliveries.

Because of the vagaries of shipping, forward contracts typically specify a delivery month, with delivery acceptable on any day during that month. For this reason, the precise day counts and discounting of our earlier examples will not be evident in this example.

Our selection of key factors 1Ri is driven as much by practical issues of data availability as by pricing theory. We model futures’ settlement prices, spreads for individual growths, and interest rates. Futures prices for various nearbys define a term structure. Conceivably, spreads for each growth might also vary by maturity. As a practical matter, individual growths do not trade in sufficient volume for such spread term structures to be discernable. Market participants track cash spreads—spreads between cash prices and the first nearby future. Spreads for other maturities are treated as equal to these. This practice is common in a number of commodities markets.
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Popular Q&A

How is Risk Premium for commodity futures contract computed?

Risk Premium is the difference between commodity's futures contract price and its expected spot price at maturity.

The expected spot price at maturity of the contract is not knowable so this can't be computed directly. There are ways of estimating it...

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