Stock Market Scam

Date: 02/08/2001 at 11:28:19
From: Amy Gray
Subject: Statistics

One Monday morning you receive in the mail a letter from a firm with 
which you are not familiar, stating that the firm sells forecasts 
about the stock market for very high fees. To indicate the firm's 
ability in forecasting, it predicts that a particular stock, or a 
particular portfolio of stocks, will rise in value during the coming 
week. The prediction proves to be correct. This routine continues for 
seven weeks: Every Monday morning you receive a prediction in the 
mail from the firm, and each of these seven predictions proves to be 
correct. 

On the eighth Monday morning you receive another letter from the firm. 
This letter states that for a large fee the firm will provide another 
prediction, on the basis of which you can presumably make a large 
amount of money on the stock market.

Since you have taken a course in probability and statistics, you 
reject this letter. Why? How might this scheme work? If the cost of 
printing and postage is $0.50 per letter, and the "firm" expects the 
rate of ignorance of basic probabilistic principles within the US 
population to be 10% and to your knowledge stock market predictions 
are correct 50% of the time, how large should the "fee" be so that it 
breaks even (given your implementation)? (You do not need to factor 
in costs of bribing law enforcement or SEC officials, maintaining 
offshore accounts, retaining a "fee collection agency," etc.)

Date: 02/08/2001 at 14:35:12
From: Doctor Shawn
Subject: Re: Statistics

Amy,

Funny how real problems and stat problems sometimes coincide, isn't 
it? The SEC gets scams like this all the time. Since you just quote 
the problem, I don't know where it's giving you trouble, so I'll just 
throw in a little bit to get you started:

Suppose that I start with a pool of, say, 16,384 people. To half of 
them I then send out letters predicting that a given stock will rise; 
to the other half I send out the same letter, predicting that it will 
fall. Since the stock must either rise or fall, 8,192 people will get 
a letter with good investment advice. For those 8,192, I then send 
out two more sets of letters the next week with more advice. (The 
people to whom I gave bad information I just ignore.) And so on, and 
so on, for seven weeks. At the end, how many people got seven weeks 
of good advice? I can expect 10% of those people to pay up. How much 
postage is that? Can you take it from here?

Hope that helps! Feel free to write back with any other questions you 
have, or if you want to talk about this some more. 

- Doctor Shawn, The Math Forum
  http://mathforum.org/dr.math/