View Full Version : easy question - just a test...

12-08-2001, 07:56 PM
Consider a binomially distributed price chart, where you can do unlimited size at the immediate price. Once every five minutes the price jumps 1 dollar, either up or down.

If the price is twice as likely to jump in the same direction as the last jump - meaning your necessary information is accumulated in one jump - what is your expected profit after 9+1 jumps?

Don't worry: If anyone answers, next question is harder...


12-09-2001, 03:56 AM
What does this have to do with investing in the market? Will this ever make you money?

Stop short term trading..you will not overcome the friction.

12-09-2001, 11:14 AM

12-10-2001, 09:46 PM
1) this is not binomialy distributed by your later assumption.

2) It is also impossible to determine expected profit - for several reasons: For starter one could bet $100 on each of the 9 jumps (after the first). This method has an expectation of $300.

By increasing the bet amount one can increase this expectation.

3) Suppose you have just $1000 - now what strategy has the best possible expectation?? back at you..

12-11-2001, 10:34 AM
1. As you know, you answered the question correctly. But I cannot reciprocate by answering yours:(Shall I take my ball and slink home?)

2. By what rule, going back in history, must the alternate terms in a "binomial" distribution be symmetric? It is only necessary that there are exactly 2 to choose from, rather than an infinte number as in "continuous." If someone only chose to teach you the simplest condition satisfying "binomial," you should have gone back and taken Stats 102. Now I am reminded why I did not take 101.

Would you have been happier if I used symmetric probabilities and asymmetric jumps? I could then have correlated time intervals to jumps, or some other contrivance satisfying your looser condition and my narrower one, and still constructed the same problem and achieved the same result.

3. You can't answer your question #3. Apparently, the Kelly Criterion can be used to determine at what bet level for each consecutive bankroll you can "expect" the highest rate of bankroll expansion. But that does not address a portfolio of competing opportunities (temporally-exclusive or non-temporally-exclusive, correlated or non-correlated), the non-finite nature of bankrolls, dependent utility curves for volatility/uncertainty, etc. - all shaping strategy. If interest rates were extremely high, you might want to front-weight your returns at some additional risk. Someone may actually "want" to go broke!

Obviously, my question implied that A) given a particular strategy, and B) given that particular strategy dictates a certain amount of bankroll put at risk, C) what is your expectation, as expressed in terms of bankroll?

Which you answered:)

Would you have given me a hassle if I expressed it in terms of apples and trees and seasons? You are free to express the equation in any terms you like, be they meters squared, or what-have-you.

I never asked what you wanted to do with that expectation, of what use it might be to you.

I cannot solve for Kelly because I cannot do math:( But you may construct an equation with any inputs you like, call it a strategy, and express exepctation in terms of them. I am actually looking forward to seeing this! You have the tools to become a very wealthy man - if you have not already - at your disposal, and many will envy you.

You will live in Mighty Castle on a Hillside stocked with the Greatest Luxuries civilization can offer. The lights of the ships and of the city will be as twinkling stars in your solitary universe.

Finally, I'm wondering what else you had in mind when you used the word "several?" Because, it is clear you are probably smarter than me, and we could all benefit from your insights. I may not be that smart, I just happen to know something about the markets:)

And I would seriously like to see you make 100 million dollars! Only, I'm too busy to construct problem #2 right now...


P.S. To answer John Ho, - whoops, no time...