Only a PowerPoint document is required for the final report. Use futures and spot relationship to find an arbitrage opportunity.

F = S*erT We learned in the class that when future price is deviated from the price determined from the above formula, an arbitrage opportunity will arise. You will use this case to illustrate if you can find an arbitrage opportunity in a real world.

You may define the parameters on your own or use the following assumption for the parameters:

Interest rate is 5%

Transaction costs for a trade on futures (selling or buying) is a flat fee of $25.

Transaction costs for a trade on spot (selling or buying) is a flat fee of $25.

Transaction costs for a trade on bonds (selling or buying) is a flat fee of $25.

Trading margin requirements: Futures 5% Bond 50% Spot 100% You may use 365 days a year to calculate interest.

To find a commodity spot price and initial margin requirement, you may Google search to find them. For example, for gold spot price, you may google "spot gold price."

Prepare your report in MS PowerPoint: You will prepare a report that includes an Introduction of your selection of the derivatives (You may choose any commodity asset or any financial instrument), explanation of any theory you applied, the data sources (please include a screen shot of the Futures quote from CME.com), and your summary conclusion. Include everything, Excel calculation, in a PowerPoint document.

Assume you have $1,000,000 trading credit to conduct the arbitrage.

Your report will be assessed by the following Assessment Matrix 3 component:

1. Case Introduction, Explanation, and Parameter Assumption:

2. Arbitrage calculation in Excel:

3. Summary of your arbitrage results:

(including arbitrage profit per contract, total arbitrage profit)

Make sure your report includes each element in the matrix above for the grading

The following example will help you understand the project data collection.

GO to CME.com for futures information. In case you have trouble getting the quote page on CME.com, then try to Google like this : "cme.com live cattle quote" or "cme.com pork or lean hog quote"

We choose Live Cattle Futures Contract for this example. We choose Oct 2019 contract.

(For your case, you may use any futures on any products such as energy, or on agricultural products, or on metals, or anything that’s traded in the exchange.)

Live Cattle

Futures and Options

Quote page from CME.com, November 15, 2018. You may Google “cme delayed quotes” to get to its quote page.

CALCULATIONS MUST BE SHOW LIKE THIS SAMPLE BELOW

Today (t=0) is November 15, 2018.

One contract = 40,000 pounds

Price unit: Cents per pound I choose Oct 2019 Live Cattle contract Futures Contract for this example.

Oct 2019 contract

Futures price: F=113.125

Number of Months= 11 (from November to October)

T=11/12=.9167 r=5%

Spot price: S=112 (google “live cattle spot price”)

Future-spot Parity: F = S erT

Test if there is an arbitrage opportunity

F = S erT

Left=F=113.125

Right= S erT=112*e.05*.9167=117.253

Ask if the left is equal to Right?

The Right is not equal to the left. There is an arbitrage opportunity when the Futures and Spot parity is violated.

How to trade with arbitrage? The rule is: Buy low and sell high

What is low here? Futures of 113.125 is low and the other side of Spot of 117.253 is high.

So the arbitrage strategy will be: Long futures, short spot, and lending money

The arbitrage profit will be high minus low: 117.253-113.125=4.128

The following table is used to prove the arbitrage profit (We randomly choose 120 (price is up) and 50 (price down). You may choose any other up and down numbers, you will get the same profit.

Live cattle price=130 price=40

T=0 t=1

CF CF

Long Futures 0 +16.875 (130-113.125) -73.125 Short Spot 112 -130 -40 lending money 112 117.253(112* e.05*.9167) 117.253

0 +4.128 +4.128

(Question: We derive the arbitrage profit of 4.128 per pound at t=1. How much is the profit in today’s dollar? The profit in today’s dollar: PV0=CF1* e-.rT=4.128* e-.05*.9167= 3.943 per pound)

Please refer to the Excel example file for the following margin calculation to derive the total profits for the arbitrage trade.

interest rate=	5.0%
div yield: q=	0.0%
spot price: S0=	1.12	per unit
futures price: F0=	1.13125	per unit
t=	11	months
T=11/12=	0.9166667
contract size	40000	units
initial margin per contract (trading Futures)	5%
initial margin per contract (trading bonds)	50%
initial margin per contract (trading spot)	100%
trading credit	1000000.00
F0 = S0 e(r-q)T	1.1725
F0 =	1.13125	Spot is too high
S0*e(r-q)T	1.17	futures is too low
Arbitrage Profit=High-low	0.04128
Present Value arbitrage Profits per unit: A15*e-rT	0.0394
Arbitrage Profit per contract: A15*A7	1651.1161
PV of Arbitrage Profit per contract	1577.148
Arbitrage Strategy as follows: Buy Low and Sell High
long Futures	0.00
Short Spot	1.12
buying a bond (lending money)	-1.12
Total Cash Flow at t=0	0.00	no investment needed
cash requirement to trade
Cash trading requirement per contract to trade futures	2000
Cash trading requirement per contract to trade spot	44800
Cash trading requirement per contract to trade bonds	22400
total cash requirement per contract	69200
With a total trading credit of	1000000.00
Total # of contracts to be traded: A30/A29	14.450867
take a whole # of contract	14
Arbitrage Profit per contract from above:	1651.12
Total profits: multiply by 21 contracts	23115.63
Present Value of Total Profits: Total Profit *e-rT	22080.07
Total profits after transaction fees
PV-$25-$25-$25=	22005.07
Note:
Transaction costs for a trade on futures (selling or buying) is a flat fee of $25.
Transaction costs for a trade on spot (selling or buying) is a flat fee of $25.
Transaction costs for a trade on bonds (selling or buying) is a flat fee of $25.

With the trading credit of $1000000, your total arbitrage profit in today’s dollar will be $33,045.