Feedback from this post:
If it helps, a mathematical “proof” for the efficacy of trend following might be simpler than supposed. In any given trading system (trend-following or otherwise), your long term win-size to loss-size ratio (essentially your “betting odds”) must be greater than the ratio of your number of losses to number of wins in order to be a worthwhile endeavor. When the ratios are equal, you win 50% of the time, and your wins are the same size as your losses. No point in trading that system. If the win-to-loss ratio is less than the number of losses-to-wins ratio, then you’re losing money, and there’s no point in trading that system either. Unfortunately, a real proof would have to demonstrate that all the systems that your reader defines as “trend-following” behave in such a way as to exhibit that positive win-to-loss : losses-to-wins inequality. Perhaps your reader could define all systems that can be labeled “trend-following” first. It would then be up to the same reader to find an example of trading data that was statistically significant (more than 50 trades, let’s say) wherein any of those given systems does not produce a positive effect. Given the instance of a losing system, your reader could then triumphantly conclude that not *all* trend-following systems “work,” but merely a percentage of them.