Chartist Claims Debunked With Simple Math

A chartist I know sees a massive top formation in S&P 500. I replied to him that he has been wrong several times in the past with such random formations. He argued that although he is frequently wrong, almost 70% of the time, if he can make 4 times what he loses on the average then he can profit longer-term. Math says forget about it.

It can be shown that traders of classical chart formations that take several weeks or even months to form have to trade more frequently than short-term traders to realize the same profit. Given the relevant timeframes, chartists must trade in many different uncorrelated markets and that may be hard or even impossible. In order to see that, let us consider a chartist and a short-term trader with the following parameters.

Chartist: win rate = 30%, reward = 4, risk = 1

The chartist has low win rate but the claim is that he makes 4 times more than he loses on the average.

Short-term trader: win rate = 65%,  reward 2, risk =1

The short-term trader has payoff ratio of 2 but at a higher win rate.

The average trade for the chartist, avgTc is given by:

AvgTc = 0.3 x 4 – 0.7 x 1 = 0.5      (1)

The average trade for the short-term trader, avgTs is given by:

AvgTs = 0.65 x 2 – 0.35 x 1 = 0.95   (2)

Note that the average trade is equal to the mean of the population only for sufficient samples. Only in that case the average trade values become the expectation.


(1) The average trade of the chartist is nearly half that of the short term trader. Thus, the chartist must trade twice as much to make the same profit.

(2) Since on the average trades from classical chart patterns last weeks or even months, the average trade will converge to the expectation in a long time. For example, if we assume that a typical chart pattern takes 3 months to form, then for a sufficient sample of 30 trades it will take 7.5 years of data in all markets combined. In contrast, a short-term trader needs a few months to accumulate a sufficient sample to test a trading method

The conclusion is that any claims of high payoff ratios (average win to average loss) to justify charting and trading based on formations that take several weeks or even months to form come in conflict with simple math and usually involve denial of reality. Ruin when trading with low win rate is highly probable and most likely to occur before the average trade converges to expectation.

The simple math above explains why trading with classical chart patterns has been one of the most unsuccessful methods and basically it has acted as a wealth transfer mechanism to market makers and other professionals.

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7 Responses to Chartist Claims Debunked With Simple Math

  1. Bo says:

    Your claim is correct if "Given the relevant timeframes, chartists must trade in many different uncorrelated markets and that may be impossible". However for someone who trades purely on charts formation, this is precisely the point. For a chartist, there is no difference between S&P500, GOLD, Hogs, EURUSD, Bond and individual stock. It's just a chart formation. So it is entirely possible to trade many different uncorrelated markets. I have seen people making money consistently purely on chart formations. Of course there is no predicting power in the charts but for them the chart provides a logical reference point for entry, stop level and profit target.

    • Hello Bo,

      I have talked about people who make money trading chart formations in past blogs. They are a small group who have experience with price action and some of them use the formations for confirmation and risk management. However, math is math and on top of that scanning many securities for patterns eventually increases data-mining bias for those who do not have the experience in identifying the significant formations.


  2. Ryan says:

    People focus on how "hard" it is to market time, but I think that you have found the real problem. Even if you have a statistical edge, opportunities arise so infrequently that it can never really be a winning strategy.

    Also remember that the market goes up. Unless you are beating an equivalent buy and hold strategy net of fees (and preferably on a risk adjusted basis over a meaningful time period) you haven't achieved anything.

  3. ellisg says:

    In 1989 my wife and I were sailing on our own boat through the Tuamotus in French Polynesia. At one anchorage I got bored with the daily ritual of snorkeling beautiful coral lagoons and spear fishing. I created a little program in Excel using the random number function. Beautiful charts unfolded before my very eyes. I saved a few and showed them to a fellow sailor on his boat, whilst keeping mum about the source. He was a former commodities trader who believed in classical chart functions. Some of the charts showed beautiful head-and-shoulder formations, and he waxed eloquent on their significance. I never told him where they came from.

  4. Dyson says:

    There were distinct times when the chartists were saying breakout and I was channeling Obi Wan Kenobe to say this is not the breakout you re looking for. It does not refer to retail-sized products, which can have very large premia sometimes, due to inelastic manufacturing capacity.

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