The Trader’s Ruin Problem

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You may have already heard that leverage is something dangerous, but on the other hand, it also boosts gains. Trading in the markets using leverage is commonplace among traders because it generates a potential return that justifies all the efforts made by these professionals. However, if leverage is not well used, it can be devastating in a trader’s life. Therefore, how to use leverage safely in order to get good profitability with low risk?

Easy To Lose, Hard To Win

First of all, the problem of leverage is not the leverage itself, but the level of exposure to losses, which tends to be higher, the greater the position taken in a trade, or the greater the volatility of the traded asset.

If a trader has initially $100.00 and accumulates a loss of 10%, he will end up with $90.00. To go back to $100.00 he needs to accumulate a profit of more than 11%. This effect is more problematic, the greater the loss. For example, if the trader loses 50%, he needs to get 100% gain to go back to the same amount of money he had before. This mathematical effect can play against the trader’s aims since several losses in a row eventually happen and it may cause a good trading system to lose money and it may result in the ruin of the trader’s capital.

Staying In The Game

An approach that can be used to avoid the losing bias mentioned before is by instead of making the size of each trade proportional to the capital, one should reserve a fixed amount of capital to cover eventual losses of the trading system and define a size for each trade. Once the size for each trade is defined, it won't be changed when eventual losses reduce the capital.

After reserving the capital, what would be the ideal trade size?

In order to avoid losing all capital and consequently be put out of the game, the trader must define the trade size and calculate the risk of ruin to make sure that it is small enough.

Example:

Let's say the initial capital is $100.00. The trading system is set to return $8.00 in profit or loss per trade and the probability of gain is 55% while the probability of loss is 45%. The risk of losing all capital can be calculated as follows:

The result is 0.0814, meaning that the probability of losing all capital is 8.14%. This result is too high for any serious trader. In this case, the initial capital must be greater, or the size of trades must be smaller.

Let’s take the same example, but now changing the size of trades in such a way that the trading system is now set to return $1.00 in profit or loss per trade. The risk of losing all capital can be calculated as follows:

The result is 0.000000002, meaning that the probability of losing all capital is 0.0000002%.

When comparing these two cases, it is clear that in the second case the risk of ruin has decreased dramatically. So, in the second case, as long as the trading system continue working the trader will stay in the game, since the risk of ruin is negligible.

Having good risk management is as important as making profitable trades. Systematize the management of risk allows the trader to stay in the game by preserving his capital, ensuring that the trading system will bring gains to the expected level.

Obs:

The calculations that were shown here consider that the results of each trade are like a simple random walk. For a different scenario, the way of calculating may change.