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Kaufman gives us the following formula for calculating the risk of ruin:
risk_of_ruin = ((1 - Edge)/(1 + Edge)) ^ Capital_UnitsNote: "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.
The risk of ruin is greatest at the beginning of a trading career. 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 an 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.
Example
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.
