Probability approach to trading

A state lottery is conducted in which 10,000 tickets are sold for $1 each. Six winning tickets are randomly selected. One grand prize winner of $5000, one second prize winner of $2000, one third prize winner of $1,000 and three other winner of $500.

a) Construct a probability distribution, with the random variable X equivalent to the net return.

b) Compute the expected value of playing this game.

c) Would you play this game? Why or why not?

A)
$4999 $1999 $999 $499 -1
0.0001 0.001 0.0001 0.0003 0.9994

B) Expected Payoff -0.05

C) The player's contribution to the game is the answer: Would he participate or not. If the ticket price is $1 he might not care the loss, if the ticket price is $1000... he might care and not choose to participate in the game.

Why this math wiz type question is relevant to trading?

Answer: Coming soon.

I would imagine the answer is similar to my personal style of playing poker.

You can't win a hand unless you play it. And at the same time, you have no idea whether or not the cards dealt to you are going to be good or not. When I play Texas Holdem poker, I always try to get to see the flop (first three cards in the community) with as little money as possible. Basically the big blind.

My strategy is to see as many hands for as little money as possible, and only increase my bet when I have a higher chance of winning--or know what all my opponents have =D.

The same I suspect applies to this lottery ticket example--if loosely:

Almost anyone here in the states can afford to spare one dollar. And the potential to beat the odds and win the jackpot always keeps them buying. As for $1000, not too many people can spare that on a regular basis, so they don't.

consider it as high risk investment, you think they do it fair and square, and it is taxed,,,, so it is investment

It has been a month.

The example I gave from a quantitative point a view to compare trading with a game of lottery is only relevant if we use pre-defined stop loss.

My answer is, trading is not similar to lotto. Buying a ticket means you know your sunk cost already. In trading many veteran traders try to imitate the game of lotto by putting fixed stop loss to know their sunk cost in advance.

That way they can know their expected pay off... win loss percentage... risk to reward ratio and many other fancy term that *I think* has nothing to do with profitable trading.

Two main reason of this is, a) the trader is not sure about the trend and b) the trader is afraid to lose more than x% of his account.

Now Ronald said a very interesting thing, if he can see the initial cards with little to bet then as his odds increases he can increase his bets and win big and loss small.

Some traders try to start with the smallest lot he can put with a fixed stop loss then try to add on to the position as the trend develops, this is similar to playing poker the way Ronald mentioned.

Again, two main reason of this is, a) the trader is not sure about the trend and b) the trader is afraid to lose more than x% of his account.

The market has two state of mind. a) Either is is ranging or b) it is trending.

Range traders try to put a short on top and long at bottom with sunk cost stop loss. At least that makes sense. But how a trend trader can put stop loss? The only way a trend trader can convince himself to take a sunk cost loss of the "chance" is again the same two reasons. He is not sure of the trend's direction and he is afraid to lose due to the first reason.

Trading the trend is very difficult for people who take trading like a game of lottery with probability approach aka. fixed stop loss approach.

The Art of War teaches us that every war is won before it is ever fought. For trend traders, every trade is a winner even before he puts the first position. The probability of win is absolute 1 and loss is 0.

And how that is done? Coming soon.

Don't leave us hanging like that...

Personally I am starting to smell a "as long as there's a trend, we don't need no steenkeen' stop losses" coming...

Along with the binary outcome being tied to either the trend is still on - any random buy/sell wins eventually, some time - or it isn't - you lose a completely random amount of money due to not having used stop losses and potentially, depending on how deep you buried yourself, more than you ever bargained for. Especially if emotions begin kicking in, the classic "should resume the trend any minute now" etc phenomena add to it...

Let's see whether this turns into yet another "stop losses are for people who don't know what trading/trend/$anyotherexcuse is" thing.

IMHO stop losses don't generate the losses, they generate the insane leverage for bigger wins than anything else, INCLUDING stoploss-less "trend trading".
If it comes down to "Can trading without a s/l work?" then the simple answer is sure, and the addon is: But why trade inefficiently?

And - if it turns up, which I'm sure it will eventually, ANY exit criteria other than the margin call telling you to get out is one way or another a "stop loss" anyway. So let's see what is to come..


Miser-Man out

Brilliant
Nothing the stop-less trend trader does can out do the gains possible using stoploss defined risk to maximize returns. limiting risk is the way to make profits. without defined risk your position size needs to be so small you'll be lucky to beat bank interest and thats providing the trend doesent reverse. Ive heard trends sometimes do that

I'm trying to develop this thread in a way that I can use it as reference. So, sorry for being slow. If you are interested to contribute, I would suggest getting a basic idea regarding normal distribution first.

I (and hopefully other contributors) will be talking about Post Modern Portfolio Theory soon in context of trend trading.