# The Risk of Ruin

### Turning your fortune into nothing

How long will it take to turn \$5,000 into \$0?

### Introduction

This article follows The Edge (How long will it take to turn \$5,000 into \$100,000?) and will hopefully show you how to calculate and take into account the risk of wiping out your account completely.

The risk or ruin (also known as the probability of ruin) is the probability that you will lose sufficient trading capital that you deem it impossible or unwise to continue trading. This point does not need to be bankruptcy (it often is) but is where you throw in the trading towel and close your trading account.

### How probable?

If you pursue any occupation or endeavor for long enough you may witness events that are once-in-a-lifetime or at least very rare events. A bird watcher, may for example, rarely if ever see an Aplomado Falcon. However, the chances of him/her seeing an Aplomado Falcon increase the more bird watching he/she does.

Trading is no different. If you pursue a trading career for long enough and you execute a sufficiently large number of trades you will most likely see long losing and wining periods. The longer you expose yourself to trading the more likely you are to see those extreme events.

### Losing

I back tested a gap fade strategy for the E-mini S&P 500 (What profit would have been achieved if all gaps were faded during the study period?) and it showed that on trading day 82 your account would have stood at a loss of 72.25 points. This back test is a good example of how a marginally winning strategy (I believe the strategy returned an average of 2 tick per day profit over 2 years) can show an extreme loss after 4 months of trading and the account only returned to breakeven after 5.5 months of trading.

Once you have back tested a trading system do the following. Select the period with the largest draw down and start your simulation account at the beginning of that series. When the draw down reaches its maximum sit back and look at the amount of money (or percent) that has been lost and the time period over which you have traded it and ask yourself how you would emotionally feel at that point.

Consider the Gap Fade strategy that I did in the E-mini S&P 500. After trading this strategy for 4 straight months, starting with \$10,000 and trading 1 contract per trade, you account is close to a 40% draw down. What do you feel at that point? Obviously devastated. Do you have the mental and emotional resolve to continue trading that particular strategy?

It's very important that you back test you strategy over a sufficiently large sample of data and see what the worst starting case scenario has been in the past and you tell yourself that it IS possible that after 4 months of trading your account could have lost 40% of its capital and that this is a reality.

To return the the title question in this article (How long will it take to turn \$5,000 into \$0?) the answer is about 4 months trading the gap fade strategy if you start at the wrong time. Granted there would still be \$1,387 left in the account but that's not much of a capital base to work from. Still we're looking at around a 70% loss in the account at that point.

### Some calculations

On page 66 of Smarter Trading, Perry Kaufman discusses the risk of ruin and provides us with a formula to work with. He considers the following 2 premises:

• In real trading, once profits accumulate, the chance of ruin decreases. The greatest risk is at the beginning.
• If we plan to withdraw profits, thereby maintaining the same relative commitment to the market then the risk of ruin must be greater than if we accumulate profits and keep the trading position the same.

Kaufman gives us the following formula for calculating the risk of ruin:

risk_of_ruin = ((1 - Edge)/(1 + Edge)) ^ Capital_Units

Edge is the probability of a win.

We can see that the mechanics of the formula are such that the larger the value of Edge the lower will be the risk of ruin. This is also intuitively logical because the greater your edge in any strategy the more likely you will have more winning trades. Also, the greater the number of capital units employed the lower the risk of ruin. Again this should be obvious: The smaller the amount you risk for any one trade relative to your capital base the lower the risk of ruin.

### Why is risk greatest at the beginning? (added 11 July 2005)

As mentioned above, the risk of ruin is greatest at the beginning.

One reason is because your capital base is smallest at this point and if you immediately hit a string of losses it will take a smaller string of losses to wipe out your account - this is discussed in detail below in Our Example.

There is another reason why risk might be greatest at the beginning. This may be because of lack of experience. An experienced trader who has survived for a long time will have overcome losing habits that a new trader may still have. These losses may be from simple things such as not operating the trading platform correctly to more complex discretionary decisions about when to override the system.

### Our example

One of the assumptions that I made in the The Edge was that for each \$5,000 profit that we accumulated in our account we would increase the bet size by 1 contract and using this pyramiding scheme our time for moving a \$5,000 to \$100,000 accelerates over time. This, however, maintains the same amount of risk per trade relative to our capital base and fits under Kaufman's second premise where he states that the risk of ruin is greater. i.e. By constantly risking the same percent of the portfolio we increase our risk of ruin. However, it doesn't take into account the fact that we also scale back the trading as our capital base diminishes and therefore reduces the risk during losing phases.

If we start with \$5,000 risk capital in our account (practically assume that we have \$6,000 and our broker requires us to maintain a minimum balance of \$1,000) and we risk 2 E-mini S&P points per trade then we are risking \$105 (if we add \$5 commission) per trade. After 47 straight losing trades we've lost \$4,935 and have to cease trading.

Now assume that our account has accumulated to the value of \$18,000 before we hit a losing streak. (We are now trading 3 contracts per trade while our capital base is between \$15,000 and \$20,000.) Each losing trade now costs us \$315 so after 10 losing trades our capital drops by \$3,150 and is back below \$15,000 at \$14,850.

Because our capital base has moved back into the \$10,000 to \$15,000 range we move back to trading 2 contracts per trade and each loss costs us \$210. The next 24 losing trades (at \$210 per trade loss) reduce the account to \$9,810 where we scale back trading to 1 contract per trade which gives us a loss of \$105 per trade.

It will now take 93 consecutive losing trades to wipe out the remaining \$9,810. The total number of consecutive losing trades required to eliminate the account from \$18,000 is 10 + 24 + 93 = 127 losing trades.

### Conclusion

In agreement with Kaufman the risk of ruin is greatest at the beginning. The risk of ruin also increases the longer your remain a trader because the risk of experiencing a series of losses increases.

The risk of ruin in our example would remain the same as the risk at the beginning if we did not scale back when we started to hit a series of losing trades. By scaling to smaller trade sizes as our portfolio is reduced we lower the risk of ruin and improve our survival rate.