Carrying charges remain very large in the CBOT wheat market – “too large” considering the possibilities of arbitrage that exist in the market. I want to discuss the calculation of carrying charges in futures markets for storable commodities, then look at the current situation in CBOT wheat.
Carrying charges are the price differences between futures delivery months (e.g. May and July corn futures, July and December wheat futures, etc.). A positive carrying charge occurs when deferred contracts are trading at a premium to nearby contracts. If you want a great example of positive carrying charges in the market, look at the CBOT wheat market, where the nearby May’10 contract closed Friday at $4.93 per bushel and the Jul’10 contract closed at $5.05. Every subsequent deferred contract shows a positive carrying charge, all the way out to the Jul’12 contract, which closed at $6.69 per bushel. A negative (or inverse) carrying charge is the opposite – deferred contracts trade at a discount to the nearby contracts. The soybean futures market is showing an inverse, with May’10 futures closing at $10 per bushel last Friday, while the new crop Nov’10 contract closed at $9.79.
In theory, positive carrying charge cannot exceed “full carry,” or the cost of carrying grain delivered on a nearby futures contract to the next delivery period. “Full carry” can be calculated based on commercial storage costs and interest, using the following formula:
full carry = [(nearby futures price * interest rate)/12 + (monthly storage rate)] * # months
The first part of this equation (nearby futures price * interest rate)/12 is an attempt to calculate monthly interest costs. It seems simple enough but it raises a question: What interest rate is correct? Should we calculate full carry based on the prime rate (currently 3.25%)? An old friend in the grain business always used the 3-month commercial paper rate (currently .25%). Recently I read a newsletter from a private grain firm that used the 3-month LIBOR plus 2.25 basis points (0.25%+2.25%=2.5%).
The second part of the equation is commercial storage (aka premium charges in the CBOT rulebook). From the rulebook…
The premium charges on Corn [and soybeans] shall not exceed 16.5/100 of one cent per bushel per day [4.95 cents per bushel per 30 day month, or 5.115 cents for a 31 day month].
The wheat market is transitioning to a variable storage rate. Again, from the rulebook…
Chapter 14 Wheat Futures 14108. PREMIUM CHARGES The premium charges on Wheat shall not exceed 26.5/100 of one cent per bushel per day during the period from July 18 through December 17 [7.95 cents per bushel per 30 day month, or 8.215 cents for a 31 day month]. The premium charges on Wheat shall not exceed 16.5/100 of one cent per bushel per day during the period from December 18 through July 17 [same as corn and].
The possibilities of arbitrage define a full carrying charge, or the maximum amount by which the price of distant futures may exceed the nearby futures. To illustrate the possibilities of arbitrage, let’s assume that today (April 26), the July wheat contract is trading at a 16 cent premium to the May contract (it’s actually closer to 12 cents). Using the prime rate for an interest costs, a full carry to July is…
[($4.90 * 3.25%)/12 + ($.05 per month)] * 2 months = $0.138 or 13.8 cents
If this were the case, wouldn’t a savvy trader buy the May contract ($4.90) and sell the July contract ($5.06) at a 16 cents carry - this transaction offers a risk-free profit! On May 1, stand ready to take delivery of May wheat, write a check for the grain and pay storage and interest costs for two months (13.8 cents), then deliver on the July contract. The net result should be a 2.2 cent profit on every bushel (16 cent carry – 13.8 storage costs).
This sort of “no brainer” trading opportunity should not happen because market spreaders would quickly take advantage of the situation, and their collective action of bidding for May wheat and selling July wheat would narrow the spread to the maximum carrying charge. At least this is the way I teach it in my class.
With your understanding of a full carry now taken to a higher level, can you help me explain what’s happening in the Dec’10/Jul’11 wheat spread? On Friday, April 22 the following closes were recorded in CBOT wheat futures; Dec’10 @ $5.52¾, Jul’11 @ $6.11 – a 58¼ cent carry. Let’s calculate a full carry in the CBOT wheat market from December to July. We will start with interest costs, using the more conservative prime rate for interest.
($5.52¾ * 3.25%)/12 * 7 months from December to July = 10.5 cents
Commercial storage costs get trickier, as the variable “premium charges” apply.
17 days in December @ 26.6/100 cents per day = 4.505 cents
195 days to from Dec 18 to July 1 @ 16.5/100 cents per day = 32.175 cents
Total premium charges = 4.505 + 32.175 = 36.7 cents
Full storage costs from Dec. 1 to July 1 = 10.5 cents interest + 36.7 cents storage = 47.2 cents
Conclusion? Based on Friday’s closing prices and a conservative (aka “high”) interest rate, the Dec’10/Jul’11 carry is trading at 123% of full carry!
What am I missing?