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When Random Traders Profit, It is Hard to Prove Skill

It is shown that random, long-only position trading in SPY based on a biased coin has resulted in 100% winners. The simulation results also confirm that proving trading skill requires returns in excess of buy and hold return.

The simulation environment

  1. A biased coin with p{heads} = 0.9
  2. Toss a coin before the close of each day
  3. Buy at the close if heads show up
  4. Exit long positions if tails show up
  5. Repeat the coin tossing until the end of price history
  6. Trading commission is set at $0.01/share
  7. Equity is fully invested at each long position
  8. The simulation is repeated 20,000 times

Case 1:  Adjusted SPY data from inception (01/29/1993) to 06/26/2015

Results of the simulation

SPY_inc

The distribution of net returns of each random trader is shown above. The maximum return is 897.68% and the minimum is 268.15%. Therefore, 100% of random systems profit. The mean return is 581.26% and the standard deviation is 69.23%. The kurtosis is low and there is positive skew. This distribution is nearly normal. The average holding period of long positions is 10 days.

Note that 10.94% of random traders perform better than a test return of 500%. The buy and hold return is 625.75% and the minimum significant return to support skilled trading is at 694.91%, or about a difference of 69%. This means that for a trader or fund manager to prove skill would have to generate an excess return of about that amount. Only then the return would be higher than that of about 95% of the random traders. This is true even when about a quarter of random traders return more than the buy and hold.

The above results show that in markets with a structural positive bias, such as the U.S. high cap stock market, it is easy to profit even with random position trading but due to that, proving skill is exceptionally hard.

Next, let us see if the same results held true during the last uptrend in stocks.

Case 2:  Adjusted SPY data from 01/04/2010 to 06/26/2015

Results of the simulation

SPY_2010

The distribution of the net returns of the random systems is leptokurtic in this case with a negative skew. The maximum return is 138.17% and the minimum is 5.23%. Therefore, 100% of random systems profit also in this case. The mean return is 98.67% and the standard deviation is 12.16%. Also in this case about a quarter of random traders (23.20%) make returns above buy and hold.

Note that 48.69% of random traders performed better than a test return of 100%. The buy and hold return is 106.91% and the minimum significant return to support skilled trading is at 115.07%. This means for proving skill a trader or fund manager would have to generate an excess return of about 8%. Only then the return would be higher than that of about 95% of the random traders.

The above results show that also in this time period and in a market with a structural positive bias, such as the U.S. high cap stock market, it is easy to profit even with random position trading but due to that proving skill is hard because returns above buy and hold are required.

Discussion

Markets that reward random traders usually punish professionals by raising the skill standard. This is true only in the equity markets and it is not the case in forex and futures markets, where random traders get a harsh punishment, as was shown in a series of recent articles. One of the reasons that random, long traders get rewarded in equity markets is the strong upward structural bias. Many such traders profit because of the upward bias although they mistakenly attribute that to technical methods they use, as it was argued in another article.

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© 2015 Michael Harris. All Rights Reserved. We grant a revocable permission to create a hyperlink to this blog subject to certain terms and conditions. Any unauthorized copy, reproduction, distribution, publication, display, modification, or transmission of any part of this blog is strictly prohibited without prior written permission. 

4 Comments

  1. Rich

    The only conclusion I can draw from this is that traders should have a long bias to stocks because stocks have a bias to go up. Is there some other lesson here?

    • Comment by post author

      Yes, see the discussion part. One other lesson not discussed is that wrong application of technical methods and risk management can result in losing the benefits from the long bias. Trading randomly the long side is at times better than applying random technical methods because they can result in worse than random results, or what some authors have referred to as "spoilers".

      • Rich

        "Trading randomly the long side is at times better than applying random technical methods because they can result in worse than random results"

        Two clarifying questions please:
        The worse than random results you describe are a from random technical trading or randomly long only?
        Is the random technical trading long and short in equal amounts, or long only?

        Thanks