CALCULATE YOUR RISK OF DRAWDOWN/RUIN
Below is a calculator that implements risk of ruin or risk of drawdown calculations based on the two methods described therefafter (the risk of ruin is calculated from both a Monte-Carlo simulation and from the formula).
RISK OF DRAWDOWN
A couple of volumes on my bookshelf discuss drawdowns and how to calculate their probability.
Balsara, in Money Management Strategies for Futures Traders, publishes tables of calculated risk of ruins based on different parameters.
However risk of ruin is different from risk of drawdown. Ruin is usually defined as a fixed capital level, representing a large percentage loss on initial capital. For example, a risk of ruin at 60% is the probability that your initial capital falls to 40% of what you started with. As the equity grows, the risk of hitting that “ruin threshold” decreases.
Risk of drawdown, on the other hand, stays constant regardless of how high the equity grows, because the drawdown “capital barrier” keeps moving up in line with the equity.
Both risk of drawdown and risk of ruin increase as the track period or backtest length increases. However, the risk of drawdown tends to 100% as track period length increases, whereas the risk of ruin is bounded at a value determined by the characteristic of the trading system results (probability of win, payoff, trade risk, etc.).
Vince expands the concept of risk of ruin by modifying the calculation to derive the risk of drawdown (in The Handbook of Portfolio Mathematics)
Monte-Carlo simulation allows for estimating the risks of drawdown and ruin by iterating a random process governed by characteristics such as probability of win, payoff ratio, percentage of capital risked on each trade.
RISK OF RUIN FORMULA
Perry Kaufman, in New Trading Systems and Methods, presents a formula to calculate the risk of ruin. This is more convenient than having to run a Monte-Carlo simulation but it does not allow for calculating a risk of drawdown.
The formula is as follows: