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# P1.T3.716. Arbitrage and the cost of carry model (Hull Chapter 5)

#### Nicole Seaman

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Learning objectives: Differentiate between investment and consumption assets. Define short-selling and calculate the net profit of a short sale of a dividend-paying stock. Describe the differences between forward and futures contracts and explain the relationship between forward and spot prices. Calculate the forward price given the underlying asset’s spot price, and describe an arbitrage argument between spot and forward prices. Explain the relationship between forward and futures prices.

Questions:

716.1. In April 2017, Portfolio Manager Jeff believed that the shares of Chorizo Fast Casual Restaurants Incorporated ("Chorizo Inc"), trading at $380.00 per share, were over-valued. He instructed his broker to short 1,000 shares. In May, Chorizo Inc paid a dividend of$6.00 per share. In July, due to a food contamination incident, the shares plummeted to 333.00, when Jeff closed out his position. The total borrowing fee was $1,500.00. What was Jeff's net profit? a.$39,500
b. $45,000 c.$47,000
d. $51,500 716.2. An investment asset has a current price of$60.00 while the risk-free rate is 3.0% per annum with continuous compounding. The asset pays income twice a year and the income is equal to 2.5% of the asset price at the time of income payment; in other words, the asset's yield is 5.0% per annum with semi-annual compounding. If a one-year forward contract on the asset has a price of $58.00, and if we make the typical theoretical cost of carry assumptions (e.g., no trading transaction costs), then which of the following best summarizes the arbitrage opportunity? [note: inspired by Hull's Example 5.3] a. Cash and carry will realize$1.92 in future profit
b. Cash and carry will realize $2.44 in future profit c. Reverse cash and carry will realize$3.83 in future profit
d. There is no arbitrage opportunity: the forward is not mis-priced

716.3. The spot price of wheat is $5.00 per bushel while the risk free-rate is 3.0% per annum with continuous compounding. The cost to store wheat is 12.00% per annum as a proportion of the spot price. The traded (observed) price of a nine-month wheat futures contract, F(0, 0.75), is$5.430. Among the following choices, which of the following scenarios is the most likely?

a. Arbitragers will immediately compel the futures contract price to increase by $0.165 b. Arbitragers will immediately compel the futures contract price to increase by$1.370
c. We can currently conduct a cash-and-carry arbitrage, borrowing to buy the asset at the current spot price, for a future profit of about \$0.316 per bushel
d. The market is concerned that a possible shortage (i.e., lack of supply) in wheat might occur and this is reflected in a convenience yield of about 4.0% per annum as a proportion of the spot price