– Michael Harris, Price Action Lab Blog
Shortly after my post on Kelly maximization I received a number of emails from traders who are developing systems but are, understandably so in my opinion, a bit confused about which performance criterion or criteria to use when evaluating them. I understand why those traders are confused, or to be more exact, what or who has confused them and why.
The most important criterion to use when measuring the performance of a trading strategy is its success rate, a.k.a. win rate. A year ago, in the post “What Every Trader Should Know About the Win Rate, Profit Factor and Payoff Ratio“, I mentioned a formula I derived 20 years ago that first appeared in a book of mine published in 2000 and in a few papers in popular magazines. The formula describes the relationship between the win rate, payoff ratio and profit factor:
w = pf/(pf+r) (1)
where w is the win ratio, expressed as the ratio of the number of winning trades to the total number of trades, pf is the profit factor calculated as the sum of winning trades divided by the sum of losing trades and r is the ratio of average winning trade to average losing trade, also known as the payoff ratio.
Now, a frequent argument is that the win rate can be low, such as, for example, 30%, but the ratio r can be high enough so that the resulting profit factor is greater than 1, i.e., a profitable strategy. The formula for the profit factor can be derived from equation (1):
pf = w x r /(1-w) (2)
We can see from equation (2) that if w =0.4 and r = 1.5, then pf = 1.0. Thus, if r is kept above 1.5, then the strategy will be profitable. Then the argument is that r is maybe more important than w, and strategies should be developed for maximum r. For example, trend-following strategies have usually low w but high r.
I will try to shed some light on these issues; Trend-following strategies need to have high r but there is no guarantee for it. It is not up to strategy to decide what value of r it will have as that depends on market conditions. If the market moves sideways, then trend-following generates a profit factor less than 1. This was the case during 2011 with most trend-following funds. The ratio r is not something that can be controlled by the trader. If you rely on hopes then you can measure performance based on the ratio r. But if you rely on skill, then you measure performance based on win rate and for maximum achievable ratio r.
The Source(s) of the Confusion
Why do most traders and system developers prefer to use metrics such as net profit, Sharpe ratio, payoff ratio, profit factor, max drawdown, etc., when developing systems instead of the straightforward win rate?
The answer in my opinion is that finding strategies with high win rate for maximum achievable payoff ratio r is extremely difficult where use of the other ratios often facilitates curve-fitting but the strategies usually have low win rate, in the range of 40% to 60%, but high payoff ratio r, as a result of the optimization. As a matter of fact, this is what most strategy development tools based on neural networks, genetic optimization and programming usually accomplish because of their nature. These algorithmic approaches have been successfully applied to many fields but are misapplied in the case of trading system development. One reason is that they generate TYPE-I optimized systems and the data-mining bias is too high.
Even more important is the fact that the risk of ruin of a trading strategy depends primarily on its win rate. The lower the win rate, the highest the risk of ruin. In the special case of ruin due to consecutive losers, this can be seen from this simple equation:
RoR = (1-w)^R
where ROR is the risk of ruin, w is the win rate and R is the inverse of risk percent. It may be seen that for fixed risk percent, for example 2% of capital, the risk of ruin decreases as w increases. However, consecutive losers are a special case of ruin and in general the probability is higher. This special case was used to show the importance of win rate.
If you cannot develop a strategy with a sufficiently high win rate, higher than 70% in my opinion, regardless of the value of a sufficiently high payoff ratio, the risk of ruin is high. Strategies with low win rate that appear good during backtesting or even perform well during the first couple of years of actual trading may rely on luck and specifically on the payoff ratio remaining high. Software vendors who implement various types of metrics to assist traders in developing trading systems often do so because that offers many more choices of curve-fitting strategies that appear to have a high profit factor and payoff ratio at the expense of win rate. Such strategies carry high risk of ruin because they make unrealistic assumptions about the future behavior of the markets, such as, for example, that the market will keep on rewarding a trader with a low win rate for an extended period of time.
– Michael Harris, Price Action Lab Blog
Update: Jeff here…I’ve coded the Win Rate into a function which you can use in your own strategies. Download it here.