From: pcw@access.digex.net (Peter Wayner)
Date: Tue, 19 Apr 94 14:43:43 PDT
To: cypherpunks@toad.com
Subject: More futures trading analysis...
Message-ID: <199404192143.AA07277@access2.digex.net>
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Here is a paper analysis based on my phone calls
to a few brokerage firms and a forage through the stack
of old newspapers. If anyone has the time to read through
the rest of it, I would appreciate it if you could alert
me to any errors in either judgement or execution. 


Here are the prices for the June S&P 500 Index Futures.
These contracts have a value of $500 times the cost of
the index when they expire in June. That means the person
who bought the contract gets $500 times the index value.The person who sold
a contract would have to pay that amount. The clearing
house is responsible for making sure the money gets from
one place to another.  If the contract expired on April 6, 
for instance, then it would be worth $224,025.

Here are some prices gathered from a stack of newspapers
waiting to be recycled. They show the S+P 500 

   date           open   high   low    close   open-close     range
March 25 1994    464.70 466.50 459.80 459.95   -4.75         (+1.80 - 4.80)
March 29 1994    461.35 461.35 451.00 451.65   -9.70         (+0.00 -10.35)
March 31 1994    451.85 453.60.445.60 446.15   -5.70         (+1.75 - 6.25)
April  4 1994    435.80 441.75 434.75 439.25   +3.45         (+5.95 - 1.05)
April  6 1994    448.45 451.00 440.80 447.25   -1.20         (+2.55 - 8.35)
April  7 1994    447.10 452.00 445.90 450.50   +3.40         (+4.90 - 1.20)
April  8 1994    450.60 450.95 444.95 447.25   -3.35         (+0.35  -5.65)
April 11 1994    447.25 450.90 446.30 450.45   +3.20         (+2.65  -0.95)
April 14 1994    446.05 448.00 442.90 445.95   -0.10         (+1.95  -3.15)
April 18 1994    446.05 447.80 440.70 442.40   -3.65         (+1.75  -5.35)

{There are other days out there, but the newspapers were thrown away or
whatever.}

In practice, you can usually buy futures contracts by only putting
up 5% of the current value of the contract. You can (and usually
want to) put up more because the banks and brokerage houses want
that amount available to cover losses. You need to maintain
5% of the current value. That means that if the price goes the wrong
way and you have less than 5% on hand you have to add more money 
to your account. This is known as a margin call.

Let's assume:

   Assume that the market will move at least +/- 3 points in
   a day.
   
   Assume that the market isn't moving too fast so you're
   able to close out a position moving the wrong direction at 3 points off. 
   (There is not as much need to really worry about this
   because the money isn't disappearing. It's just moving 
   in the wrong way too fast to stop it.)
   
   If you want to move $50,000 in _one_ day by opening the
   transaction in the morning and closing it in the evening,
   then you would need to move 34 contracts.
   
   The 10% margin requirements for these 34 contracts would
   mean that you must have about $800,000 on hand to cover losses.
   
   
   The cost of borrowing $800,000 for a day at a 10% annual rate
   is about $220 in interest.
   
   Let's assume that the market inefficiencies are about .10 to
   open the position and .10 to close the position. That means
   that the difference between the price you buy the futures
   and the price you sell them is different by .10 in the morning
   and .10 in the evening. (.10 in the wrong way.)
   
   That means you could lose $3400 in trading costs if you can't
   execute the 34 contract trades successfully at the same price. 
   

This gives me the following approximate transaction costs:
       
                                 

        Day 1        
         Commissions          $200 x 2         
       on 34 Contr. 
       (guess)
       
     Interest Costs       $220 x 2      
       on $800,000
       
     Market               
      Inefficiencies     $1700 x 2      
                        ---------            
                          4240              


Chance of Succeeding: 50%.

So if things go wrong:
     
                                   

        Day 2        
         Commissions          $400 x 2         
       on 68 Contr. 
       (guess)
       
     Interest Costs       $420 x 2      
       on $1,600,000
       
     Market               
      Inefficiencies     $3400 x 2      
                        ---------            
                          $8480              
 
     Assume you guess that the market will move correctly: 50%.
     That means you will have moved the $50,000 by now in 75% of
     the cases. 
          
But if things still go wrong:
     
 
        Day 3        
         Commissions          $800 x 2         
       on 136 Contr. 
       (guess)
       
     Interest Costs       $840 x 2      
       on $3,200,000
       
     Market               
      Inefficiencies     $6800 x 2      
                        ---------            
                        $16920   
                             
     Assume you guess that the market will move correctly: 50%.
     That means you will have moved the $50,000 by now in 87.5% of
     the cases. 
          
   
If these conservative calculations are correct, then it is possible
to move $50,000 for $4240n in all but 2^{-n} of the cases. 

Note, there were about 60,000 S&P 500 contracts traded in the 
average day. I would guess that even 544 contracts wouldn't make
a too much of a difference. Especially since half would be buying and the
other half would be selling. 

There are many places where these numbers may be off, but I believe
that I've erred on the side of extreme conservatism by putting up
10% of the contracts' value. Many people who do day trading
have low margin requirements. As you can see, the net profits or 
loss in the day was never more than 3% in the days I included. And
the list included a big trading day when the market lost plenty. 

I've also assumed that the market inefficiences would always move
against me. In one sense, this is probably fair because brokers are known to
buy a contract and then resell it to a customer for a fraction more. 

This leads me to the following conclusions:

  *) It is not cheap to do this well. You could  do it 
  for less with some more risk.
  
  *) It may take very good timing to execute the straddle effectively.
  The market inefficiencies are the biggest cost. Being a floor broker
  may be essential. 

  *) If you can open the position at the same price
  i.e buy and sell the contracts at the 
  same price, then you've got a good deal. 

   
  
I would appreciate any questions or comments about the details in
this very approximate estimate. 


-Peter Wayner