Consider the following scenario:

• There are three investors interested in trading in the same stock.
• Any Sell order tends to decrease the stock price.
  (For each Sell order, the price decreases by 1%.)
• Any Buy order tends to increase the stock price.
  (For each Buy order, the price increases by 1%.)
• Examples:
      For two Sells and one Buy, the stock will decrease by 1%.
      For three Sells (and no Buys), the stock will decrease by 3%.
      For three Buys (and no Sells), the stock will increase by 3%.

>Okay, so the changes in stock price look realistic, buy I still think ...
Patience. Our objective is to see whether we can devise a "best" strategy, given that stock prices fall when there's lots of selling and rises when ..
>Yeah, yeah. So?
I'm thinking.
In the meantime:

Consider stock price changes as described above (Up or Down depending upon whether the majority of investors Buy or Sell) ... and suppose:

• All investors (A, B and C) begin with $1000 invested in the stock.
• Investors A and B Buy and Sell at random.
• Investor C Buys (or Sells) when the price drops (or rises).
• When any investor Sells, all his money in stock goes into Cash.
• When any investor Buys all money in Cash gets invested in stock.

>Yeah, So?
I'm thinking.
In the meantime:

Consider stock price changes as described above (Up/Down depending upon whether the majority of investors Buy or Sell) but with a random component.
Suppose, further, that a certain percentage of investors are in each class:

• All investors (type-A, type-B and type-C) begin with $10,000 invested in the stock and $50 per month to invest.
• Investors of type-A buy every month ... with payroll deductions.
• Investors of type-B buy when the price goes up, thinking it's an upward trend. (They sell when the price falls.)
• Investors of type-C buy (or sell) when the price drops (or rises).
• When any investor sells, all his money in stock goes into Cash (plus the $50).
• When any investor buys all money in Cash gets invested in stock (plus the additional $50).

This game #3 is interesting. In it, you can decide what fraction of investors are of types A, B or C. When a particular type dominates, then that type often controls the stock price, as in Figure 1A where type B is in the majority and his buying causes the price to drop (except for that random component) and, abiding by his strategy, he sells, driving the price down and eventually is putting his money into Cash (as the market collapses).

Figure 1A

In Figure 1B, C is the major player. She buys when the stock goes down and that buying tends to make the stock price increase in which case she sells ... and the stock oscillates and she's buying and selling (and profiting) on the swings.

Figure 1B

In Figure 1C, A is the major player, constantly buying and driving the price up (except, of course, for that random component) and that makes B buy (which also drives up the price) ... and C falls behind. >Buy C is still making money! Actually, she's waiting for the price to drop and, when it doesn't, she just puts everything into Cash. Remember, they all have $50 a month to invest (or put into Cash) so, after 25 months (the time scale in the charts) they'd put 25*50 = $1250 somewhere. Together with their initial $10,000 that makes $11,250 and not too many of these scenarios end up with a $11,250 portfolio.

Figure 1C

>What's this random component thing?
I just subtract, from the weighted average of Buy / Sell numbers ("1" or "-1"), a random number from 0.00 to 0.01, meaning 0% to 1% and ...

>Do those random numbers have a Normal distribution or ...?
Uh ... no. Okay, we'll do it this way:

• We'll assume a percentage of the investor population is one of three types.
• Types A and B have strategies as above.
• However, to make things more interesting, we'll assume that C investors Buy when the current price falls below some Moving Average of stock prices (and they Sell when it's above the Moving Average).
• We'll Assume that the monthly returns are calculated as follows:
  • Monthly Return = a (Net Buys/Sells) + b Random(Mean,SD)
  • where Net Buys/Sells is the weighted average of those "1" and "-1" values
    (weighted by the percentages of each investor type)
  • Random(Mean, SD) is a normally distributed return with prescribed Mean and Standard Deviation
    (which, although we prescribe as Annual values, we'll change to Monthly)
  • and we can choose, via a and b, what fraction of each we want.
• Finally, the number of Months Back (to use in the Moving Average) is prescribed by the user.

You can play with this Excel spreadsheet, where each F9 generates another scenario, including percentages of each investor type and number of Months Back.

>Can I choose my own?
Be my guest, but keep pressing F9 to see the parameters which are efficacious to C or to the other ...
>Efficacious? Is that some kind of medical affliction?
Yes.

for Part III