Tutorial on trading futures

This is a small tutorial on how to make arbitrage profits from trading futures.

What are futures?
The futures contract calls for delivery of a commodity at a specified delivery or maturity date, for an agreed-upon price called the futures price, to be paid at contract maturity.

How to get the price information?
Let us take Gold for example. We can get the spot price (current trading price of the commodity) and the futures price from various sources. We also need the risk-free rate or Treasury Bill rate. Let us use Wall Street Journal market place.

Here is the information after th bell today, 2/2/2007.

Gold spot price - $647.45 (So)
6-month T-bill rate - 5.152% (Rf)

You will also find the list of all Gold futures prices here.
(From there, I got
Gold August-07 price (6 months from now) - $663.9 (Fo)
We will not need this information now, it is for comparison)

How to make arbitrage profits by trading Gold futures?
If the markets were efficient, the Spot-Future parity must hold good.
Fo = So (1 + Rf)^T

where T in our case = 0.5 years, as I'm estimating the 6-month futures price of Gold.
Plugging in the data we got from WSJ,

Fo = 647.45 * (1+.05152)^0.5
= $663.91

Now if we check what the 6-month Gold future contracts are trading in the market at, we see that it is $663.9 too ! If it were selling for less than $663.9, people could make arbitrage profits. Since the market is efficient, in that case, there will be buying and selling of such contracts till the market corrects itself to sell 6-month futures at $663.9, and that is what has happened here.

Now for argument sake, let us suppose, Gold is trading at $663.0 instead of $663.91. I'll show you how to make profits

1. Today
(a) Long the Gold futures. So there is no cash flow now. You have just entered an agreement to buy at a future date for $663.0
(b) Go short on Gold. ie. sell Gold at its current spot price. You get $647.45.
(c) Invest this money in T-bills maturing at the end of 6 months from today

2. After 6 months
(a) You will get 647.45(1.05152)^0.5=$663.91 from the T-bills
(b) Use $663.0 out of that to pay for the futures contract and get the Gold
(c) Use this Gold to cover your short position
(c) $0.91 is your profit left on the table! Enjoy!

Contest -1 and Prizes...!!

Updated - There are a few corrections, they are in red. Also, please keep looking at the comments section, there are a few clarifications there...But in short:
STEP-1 : Decode the numbers to form words as described below
STEP-2: Unscramble the 9 words, ask me for clues (post a comment, I'll not publish)
STEP-3: Now, take the first chars of these 9 rightly-arranged words and rearrange them to form the final word.
I just posted the clues in the comments section

Ok, this is a small contest, open for all. But the prizes are restricted to first year McCombs MBAs. The first 5 correct respondents can claim one of the following from me:

(1) Competitive Strategy by Porter
(2) Barney (another strategy text)
(3) Bodie Marcus (Investments)
(4) Financial Strategy (Titman)
(5) Fredrickson Strategy course packet (otherwise worth more than $200!)
(6) If you require any other course packet or text, I will try to arrange it for free from my friends if I don't have it

DISCLAIMER - After you use them free of cost for the next semester, I would like them to be returned.

Contest Closes Sunday 11/26 with TG, after which I will post the results...

'Orite enjoy! This is purely for fun! Happy ThanksGiving!


STAGE-A
I'm trying to develop a mapping between every possible word from one to twenty characters and unique integers. A very simple mapping, with the ordering done first by the length of the word, and then alphabetically. Assume they are case-insensitive. The list goes...

a 1
b 2
...
...
z 26
aa 27
ab 28
...

UPDATED: Please note, there are a few corrections in the identifiers. Sorry.
I had to change most of them, becuase of a problem with Excel. Excel rounds off numbers with more than 15 digits! I didn't know about that. Here is the related Microsoft bug
Thanks Microsoft! :) However, those who are interested in a fix for that, you can use the XLPrecision plugin
Apparently, it displays precisely more than 37,000 digits! I just tried it, it works fine...

'Orite, now I don't want you to go through the process of installing plugins for the purpose of solving this small puzzle, hence I went ahead and changed the identifiers and words, however retaining the final word I had in mind. Use this updated list. It's got a lot easier now...

Thanks!

Can you help me out with finding the words for the following unique identifiers ?
(1) 1,539,790,545,915
(2) 145,052,901,271
(3) 88,813,741,261,667
(4) 76,631,734,754
(5) 85,991,506,864,985
(6) 84,420,066,965,242
(7) 136,062,431,514,661
(8) 2,044,464,824,521
(9) 1,189,799

STAGE-B
Now, unscramble these 9 words.

STAGE-C
If you've got this far, this is hardly anything. Take the first letters of each of these, arrange them in some order and form a new word. Post that word in the comments section, with the 9 words too, and claim your prize!

NOTE:
(1) Once you reach STAGE-B, if you post the words, with your full name, I can email you clues if you're stuck on unscrambling any. I'm not posting the hints for all, since I've seen some terrific anagram solvers. Don't worry about posting your answers as comments, I will not publish them till the end-date
(2) Obviously, you CAN use any anagram engine, but you MAY not. Since the game is for fun, it is against the honor code.
(3) If you have any generic questions, feel free to post them as comments and I'll reply as soon as I can.
(4) For any post, sign off explicitly with your Full Name and write (McCombs) in paranthesis if you are a McCombs first year.
(5) Remember, contest closes on Sunday, but only the first five winners will be given prizes. So hurry! I will try to keep the post updated if as and when people complete
(6) Again, this is just for kicks!

The Exxon Fallacy

I keep hearing people ask this question or pass this comment quite often these days. "How is it fair for Exxon Mobil to report a $30 billion profit per annum in 2005 , while gas prices had been sky rocketing? Can't they take a cut on their net income and pass their profits to the public through lower gasoline prices? Why is the government not taking any action?"

I was unclear about these questions too, until I stepped back and did some quick and simple analysis. So, what is Exxon first?

Company: Exxon Mobil (NYSE:XOM)
Primary line of Business: Oil and gas exploration
No. of employees: 123,000
Currently trading: $67.32
Market cap: $400.21 Billion (pretty big huh!)
Revenues: 2005 - $339 billion, up 25% from 2004 (again, largest by any company!)
Fortune 500 Rank: #1
2005 Profits: ~$36 Billion (I worked for a Fortune 150 company whose annual 'revenues' were ~$15 Billion. Just mentioning for a scale comparison)

The public wonder how can Exxon be allowed to make such enormous profits, while on the other hand gasolines prices are so high. Is it a fair policy to allow them to do so?
The answer is simple. Their profits are up, only becuase their revenues are up. If you take a look at their 2000-2005 financials,
you will observe that although their net income has grown at a CAGR of 55.23% ($17,720 to $36130) from 2000 to 2005, their net income as a percentage of annual sales has been relatively constant around 8-10% for the past 6 years. So, they have not done anything unethical or illegal to raise or artificially boost their profits. I've summarized this in the table below too.

	2000	2001	2002	2003	2004	2005
Revenues	$227,596	$208,715	$200,949	$237,054	$291,252	$358,955
Net Income	$17,720	$15,320	$11,460	$21,510	$25,330	$36,130
NI % sales	7.79%	7.34%	5.70%	9.07%	8.70%	10.07%

And this increase is their revenues or sales, is primarily due to demand. Demand for oil and gas has been growing tremendously in these years, and that's not Exxon's fault!


Thus I argue that Exxon is doing a fair job. It's not its fault that there are 3 energy companies in the Fortune 10 list - with Exxon leading the way at #1, Chevron at #4 and Conocco Phillips at #6.

SAP: How does Broadway price a ticket?

For those who've been wondering why a Broadway ticket is so expensive, here's why. In this post, let us analyze how Broadway Theatres prices a ticket for its world-famous live musical shows like The Color Purple and Dirty Rotten Scoundrels.

• In this industry, the pricing strategy cannot be determined by looking at the competitors becuase there aren't many.
  
• Although we have to focus on supply and demand to an extent to price a ticket here, the price-based costing technique will not work here too because there are no economies of scale in these plays. There are huge costs associated everytime a musical is performed, which cannot be controlled by demand.
• So, that leaves us with one approach - to analyze the total costs involved with a musical and price the ticket accordingly.

Let us first break up the costs as follows -
(a) Costs in getting to the opening night

• Sets, costumes and lights - $4 M
• Salaries and expenses in the theatre - $2 M
• Salaries for creative team, staff - $1.5 M
• Rehearsal salaries - $1M
• Advertising and promotion - $1M
• Administrative - $700,000
• Advances for writers, director and designer - $350,000
• Casting / rehearsal expenses - $150,000
• Reserve - $1M

TOTAL = $12M
(b) Costs per week in keeping the show on

• Theatre expenses - $200,000
• Salaries - $150,000
• Advertising - $50,000
• Maintenance of physical production units - $50,000
• Administrative - $25,000
• Fees and royalties - $5,000

TOTAL = $0.5 M / week


Let us assume an average play shows for around 5 months, successfully running 7 shows / week including weekend special shows.
A Broadway Theatre's capacity = 1750 (app.)

Total costs for this show = 12M + 0.5*20 = $20M

Estimate total tickets sold = 1750 tickets/show * 7 shows/week * 4 weeks/month * 5 months
= 245,000 tickets

So, Break-Even Price = $20M / 245,000 = $82

Let us assume Broadway wants to see a profit-margin of 20% per show, which is very reasonable. That brings the price of a ticket to $100

We know that there is pretty good demand for these shows and they run at full capacity most of the days in New York. Three-fourths of the demand is fulfilled by visitors to the city. So, as long as visitors rush to New York, Broadway will continue to survive even by charging these high prices.

What can it do to bring down the price? (1) Increase the capacity of the theatres? -NO, becuase those are historical landmarks. (2) Increase the number of shows per week? -NO . First, producers cannot add shows to the schedule as they like becuase of union rules and second since there are costs associated with every show, it does not guarantee more profits.

So, unf0rtunately, Broadway has to charge us around a $100 for its musicals.

NOTE: The numbers used in this post are estimates and assumptions

SAP: 3 economists in one cab

WSJ Uncut

Thats's a terror, I know, but let's see what happens. Three economists get into a cab, they're each getting off at different places along the route. How will they share the fare?
Assumptions:
(1) There is no rush hour
(2) cabs are plentiful
(3) each one can reach his destination at atleast the same speed, if not faster. So they have come together becuase the total fare would be cheaper than if they had travelled separately.
(4) A and B are allowed to jump out at no cost at their destinations on the way to C's.
(5) Also, say A's usual fare = $1, B's usual fare = $5 and C's usual fare = $9
(so, rather than paying $15, they would pay $9 now)

Now, how do you allocate costs and benefits among 3 people who have come together for mutual benefits. Let us explore the various ways they may think doing this.

(a) Easiest solution, all 3 share A's fare, then B and C share the fare from A's to B's, and C should pay the remaining fare from B's to C's. So, A's fare = $0.33 ; B's fare=$2.33 ; C's fare = $6.33

(b) The benefit of travelling together is the total savings of $6. They can split that up proportionately. A's savings = (1/15)*6 = $.40 ; B's savings = (5/15)*6 = $2 ; C's savings = 6-(0.4+2) = $3.6.
So, A's fare = $0.6 ; B's fare = $3 ; C's fare = $5.4
Here, every passenger pays an amount proportional to what he would have paid w/o the savings. Proportional split up of surplus and debts is a common practice under U.S law, seen mostly in bankruptcy cases

(c) Now, lets introduce the beauty of negotiations. Heard of John Nash? Yeah, the Beautiful Mind guy, some economists dug into his work on negotiation strategies in game theory to propose a solution.
Each passenger would negotiate his best outcome which turns out to be an equal split of the savings. Why? Because this whole deal of travelling together to obtain mutual benefits, would be nullified if any one party walks away. So, A has the highest bargaining power in this case.
So, A is paid $1 to travel along ; B's fare = $3, C's fare = $7

(d) The above solution is problematic because one party is paid to travel. Instead, B and C would negotiate with A and give him a freebie and split up rest of the savings equally.
So, A's fare = $0 ; B's fare = $2.5 ; C's fare = $6.5

(e) The negotiation gets further interesting if B and C form a coalition. They would argue with A that, if they travel without A, they would save $5, so they have to make atleast that now, which means only the remaining $1 of savings is up for equal splitting.
So, A's fare = $0.67 ; B's fare = 5 - (2.5+0.33) = $2.17 ; C's fare = $6.17

The conclusion one would derive, as indicated by Jonathan Gruber, Prof of Economics, MIT, is that there really is no one single solution to this problem, it depends on individual preferences and bargaining power.