Monday, February 17, 2025

The Rewards of looking at Risk:Reward

One of the things I've come to somewhat despise is the non-specificity in "folksy" trading aphorisms. Let's choose a few and interpret what they really amount to (and why they are not universal truths):

"cut your losers and let your winners run" -- pretty much assumes everyone is a trend trader with low win % (excludes scalping, mean reversion, or wide stop loss strategies)

"don't fight the trend" -- excludes mean reversion strategies or market neutral strategies

"buy when there's blood in the streets" -- never defines when it's actually bloody in the streets, lots of hindsight bias baked in

Trading ultimately comes down to precisely definable mathematics performance numbers that, save for a strategy that is solely dependent on black swans, can be proven to be viable with back or forward testing. "Letting your winners run" could much better be translated to "ensuring you have a winning risk:reward ratio given your winning %". Yes, one would ideally want winners to run forever, but there has to be an observable, repeated average reward obtained for each trading strategy (yes, also accounting for the occasional runner). Similarly, there is an average losing dollar amount that one must not exceed in order to be profitable. 

Some people even give sensible advice like defining a max loss per trade, max daily loss, etc. without going through the math. Make it too small, and your winning percentage may dwindle to the point of unprofitability, and make it too big, you may win more often but blow up with just a few max losses in a row (or get so psychologically compromised that you're prone to go on tilt). These numbers are also not universal, i.e. they differ per person and strategy. Even advanced techniques like asymmetric position sizing can thought of as taking advantage of a high probability scenario to effectively execute multiple winning trades at once (so one's win rate may improve due to the 'parallel' trades being executed, but the average winner per risk unit may remain the same).

It took me a hot minute to start to translate trading advice/common knowledge into mathematical principles, but doing so seems to have been a game changer in mitigating emotionally charged trades. The engineer in me sees things objectively, and I should have tapped into this a long time ago. When I am a purely human trader without any mathematical sense, a high-volatility spike screams "money making opportunity." The mathematically savvy trader in me sees an average dollar amount (winner or loser) spiking, but not necessarily probability of actually making money unless the event or pattern is very obvious. If it's both high-vol and high-probability, it would just be dumb to not trade. It's usually somewhat random, in which case either a much smaller position size or avoidance altogether is warranted. 

The bottom line is that viewing trading opportunities and scenarios through a mathematical lens is a game-changer for those with impulse control issues or those who just inevitably find themselves self-sabotaging their results at just the wrong time given enough trades. Yes, the story stock or headline of the day coupled with high-volatility price action becomes a lot more "dry" when viewed in terms of risk and reward and expected value, but the outcome is steady progress and not going 10 steps back in one's PnL journey! I'll take that any day. Especially looking at the cumulative dollar amounts I'm making after a string of sensibly traded days.

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