# 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 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 (

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

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

- 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

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.

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