What is the Chance of Losing All My Money Short-Term Trading Stock? According to a Statistical Concept: the Gambler's Ruin Problem
Ideally, we want to be able to "buy low, sell high" when doing short-term stock trading.
However, there is a chance we will "buy high, sell low" and lose money.
According to a statistical concept, the gambler's ruin problem, tradning stock can be very dangerous and we may lose all our money trading.
The Gambler’s Ruin Problem
The gambler's ruin problem can be described as two gamblers, A and B, gamble 1
dollar each time. A has x dollars, and B has n - x dollars. They
have total of n dollars and they gamble until one of them loses
all his or her money.
Let the probability that gambler A wins a game be p, then the
probability of A losing a game is q. p + q = 1, since A either
wins or loses a game.
If p does not equal to q, The probability of A wining all
the money is
If p equals to q, The probability of A
wining all the money is
Analysis of 3 scenarios of trading
Assume each trade is either wining or losing 1 dollar for calculation
purposes.
scenario 1: short-term trading with the probability of making money in each trade being 50%.
Let gambler A be a short-term trader and every time A conducts a trade, A's
probability of making money in each trade is 50%.
Assume A will continue trading until he or she loses all his or her money, the
probability of A losing all the money is 100%!
This results from n being very large as in the equation
scenario 2: short-term trading with the probability of making money in each trade being 49%.
If A's probability of wining in each trade is 49%, A will lose all the money
more quickly. Even if A is not trading against a lot of people that together have
almost infinite amount of money.
Below is a table of A's probabilities of losing all A's money with
respect to how much money his or her trading competitors have:
| A's Money | Other People's Money | Chance of Bankruptcy |
|---|---|---|
| $100 | $10 | 33.4% |
| $100 | $50 | 86.7% |
| $100 | $100 | 98.2% |
| $100 | $200 | 99.9% |
scenario 3: short-term trading with the probability of making money in each trade being 51%.
If A's probability of wining in each trade is 51%, can A make money in the long run? Refer to the probability table below:| A's Money | Other People's Money | Chance of Bankruptcy |
|---|---|---|
| $1 | $1,000,000 | 96.1% |
| $2 | $1,000,000 | 92.3% |
| $5 | $1,000,000 | 81.9% |
| $10 | $1,000,000 | 67.0% |
| $20 | $1,000,000 | 44.9% |
| $50 | $1,000,000 | 13.5% |
| $100 | $1,000,000 | 1.83% |
| $200 | $1,000,000 | 0.03% |
Conclusion
If one wants to do stock short-term trading, one needs a wining
probability in each trade greater than 50% and has enough money to be able not to lose all
one's money.
If one's probability of making money in each trade is 50% or lower, one will
go bankrupt in the long run if one keeps trading .
Suggested reading: Probability calculator: gambler's ruin problem
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