Optimal Bet Size

One of the unique aspects of risk management is that it is not linear.  Doubling your risk doesn't normally double your returns.  And reducing your risk in half doesn't normally reduce your return in half.  Below are 3 charts that show returns for 2 good traders that have a 100% return over 2 years.  There is trader A, a risky trader who takes bigger risks, and trader B, one who takes smaller risks.  Their returns are the same for their usual bet sizes.  But if you reduce their bet size in half or double their bet size, the returns change drastically. 

Trader B's returns scale up better when more risk is taken, but scales down worse when less risk is taken.  I think most traders that have lasted more than a few years have returns more similar to trader B than trader A.  These traders should take more risk. 

What I'm trying to show here is that there is an optimal bet size for trades.  You bet too small, you will have less than optimal returns.  If you bet too big, you will have less than optimal returns.  But what I've noticed is that compared to the risk management literature, the bigger your expected returns, say 100% return over 2 years, you should be willing to bet big and deal with big drawdowns.  But not too big.  Look at the double volatility chart.  Good aggressive trader A gets crushed despite doubling up on risk compared to conservative trader B. Traders should look at their own returns over the past few years and decide, am I optimizing my growth rate of account value?  I would guess that most good traders are too conservative.  If you are not a good trader, betting small is the best way to go until you learn to become  a good trader.