Vijay Rajakumar is a commodities trader for Sloane Murchison, a global commodities firm based in Australia. Although Sloane Murchison does trade commodities for physical delivery on behalf of its clients, it focuses the bulk of its dealings on the futures markets. Rajakumar has clients across a variety of industries, both mining- and petroleum-related and agricultural. He routinely calls his larger accounts when movements in futures prices related to their businesses might create a trading opportunity for the client. Recently prices for both petroleum and soybean products have been rising sharply, and an unusually large calendar spread is developing. Rajakumar believes that this change in spread represents a trading opportunity for his clients with inherent business risk in either the petroleum or soybean market. Rajakumar telephones Anita Chang, his counterpart in the London office of Sloane Murchison. He notifies Chang that the forward markets in petroleum products are in flux. He predicts, “The crude market should go into contango, since the lease rate is higher than the risk-free rate.” “Once the market is in contango,” Rajakumar elaborates, “The forward rate will be greater than the spot rate.” He points out that the increase in the level of interest rates will increase basis risk for buyers of commodity futures. And since convenience yields are consequently rising, he expects forward prices to rise as well. Chang asks Rajakumar about the current market conditions that underlie his expectation, and he provides her the data below: Spot Price Price of One-month Futures Price of Two-month Futures Crude oil(/barrel) 60 61 62 Diesel fuel(/barrel) 70 72 74 Gasoline(/barrel) 78 80 82 Kerosene(/barrel) 90 92 95 Heating oil(/barrel) 82 84 86 Soybeans (/bushel) 7.00 7.50 7.75 Soybean oil (/pound) 0.30 0.32 0.34 Soybean meal (/ton) 225 230 235 Chang remarks that the soybean markets also appear to be in contango. She points out to Rajakumar that the contango of the soybean markets has implications for firm clients in agricultural industries. “When the soybean markets are in contango, any increase in storage costs will increase forward prices.” She suggests that they propose appropriate hedging strategies to their agricultural clients who need to inventory soybeans to address the possibility of increasing storage costs. Chang wonders about an increase in interest rates as well. She points out to Rajakumar, “An increase in interest rates will drive forward prices down since it increases the discount rate on the contract.” She and Rajakumar decide to advise their commodity clients to trade now in anticipation of developing contango in the forward markets. 1. Basis risk is least likely to arise in a commodity futures contract because of: A) transportation costs. B) the general level of interest rates. C) differences in grade. 2. Is Rajakumar correct in his description of a contango market with respect to the relationship between: The Lease Rate and Risk-Free Rate Forward Rate and Spot Rate A) Correct Incorrect B) Incorrect Incorrect C) Incorrect Correct 3. Which of the following is the best example of convenience yield? A) The increase in corn prices as a function of time after the harvest. B) A coin dealer that lends out gold coins. C) A manufacturer of copper tubing that holds copper in inventory. 4. Is Chang correct about the response of forward prices in contango to increases in: Storage Costs Interest Rates A) Correct Correct B) Incorrect Incorrect C) Correct Incorrect 5. Assuming it takes one month to produce the products, the profit that can be locked in today on a 7-4-3 crack spread for delivery in two months is closest to: A) $16.43 per barrel. B) $1.21 per bushel. C) $22.71 per barrel. 6. Does the upper bound of the range of prices that represents the no-arbitrage cash-and-carry opportunity for an investor who recognizes a convenience yield depend on: Convenience Yield Storage Costs A) No Yes B) No No C) Yes Yes
- C 2. C 3. C 4. C 5. C 6. C
- B 2. C 3. C 4. C 5. C 6. A
B C C C C A
- B 2. C 3. C 4. C 5. C 6. A My head hurts from reading these types of questions on AF.
Nice work! Answers: BCCCCA
c c c c c a
- B 2. C 3. C 4. C 5. C 6. A
"1. Basis risk is least likely to arise in a commodity futures contract because of: A) transportation costs. B) the general level of interest rates. C) differences in grade. " “6. Does the upper bound of the range of prices that represents the no-arbitrage cash-and-carry opportunity for an investor who recognizes a convenience yield depend on: Convenience Yield Storage Costs A) No Yes B) No No C) Yes Yes” ^Anyone care to explain these two? Guessed on #1 but felt pretty solid about #6.
For #6 the lower bound depends on convenience yield not the upper bound.
heer Wrote: ------------------------------------------------------- > For #6 > > the lower bound depends on convenience yield not > the upper bound. Still don’t get it.
The convenience yield is actually subtracted from the Rf when calculating the Futures price. So it will affect the lower bound of the arb zone, but not the upper. The storage cost will be a factor in both the upper and lower amounts.
Transportation costs, timing of delivery, and grade differences are all sources of basis risk in a commodities futures contract. The level of interest rates affects price but does not create basis risk in commodity futures. The upper bound depends on storage costs but not on the convenience yield. The lower bound adjusts for the convenience yield.
mwvt9 Wrote: ------------------------------------------------------- > The convenience yield is actually subtracted from > the Rf when calculating the Futures price. So it > will affect the lower bound of the arb zone, but > not the upper. > > The storage cost will be a factor in both the > upper and lower amounts. I understand the different effects on the futures price, what I don’t get is why the convenience yield doesn’t affect the arbitrage price in both directions. We have: F(0, T) = S0 * e ^ [(Rf + storage costs - convenience yield - lease rate) * T] So in cash-and-carry arbitrage, we are purchasing the asset and selling the futures contract, then holding the asset until the expiration of the contract. I would think that a decrease in the convenience yield would shift your entire range of arbitrage profit opportunities downward.
Convenience yield is only available to those who have a valid business purpose for holding the commodity. And I believe - Convenience yield - storage costs = lease rate but I am not sure.
mwvt9 Wrote: ------------------------------------------------------- > Convenience yield is only available to those who > have a valid business purpose for holding the > commodity. > > And I believe - Convenience yield - storage costs > = lease rate > > but I am not sure. The problems states that the investor: “recognizes a convenience yield”. Still not sold.
yeah, but it asks for upper bound, not lower bound.
KRochelli Wrote: ------------------------------------------------------- > yeah, but it asks for upper bound, not lower > bound. I understand that. My argument is that if the convenience yield changes that would shift the range of arbitrage opportunity prices. -If the convenience yield increases then the lower range of prices will shift down and the upper range of prices will shift down as well. -If the convenience yield decreases then the lower range of prices will shift up and the upper range of prices will shift up as well. It affects the prices on both ends…
Dwight Wrote: ------------------------------------------------------- > mwvt9 Wrote: > -------------------------------------------------- > ----- > > Convenience yield is only available to those > who > > have a valid business purpose for holding the > > commodity. > > > > And I believe - Convenience yield - storage > costs > > = lease rate > > > > but I am not sure. > > > The problems states that the investor: > “recognizes a convenience yield”. > > Still not sold. Well…I have been getting beat up all day today. I am not going to try to sell you.
mwvt9 Wrote: ------------------------------------------------------- > Well…I have been getting beat up all day today. > I am not going to try to sell you. Haha don’t let me discourage you. Thank you for your help trying to figure out questions. I’m just not willing to roll over on this one. I don’t think the math supports the conclusion.