Position Sizing . Kelly Criterion

Monday morning. Friend forwards a WhatsApp on a "high conviction" trade. Sixty forty win rate, even money payoff, the kind of setup he had been waiting four months for. He wanted to size it. His instinct said half his book. Maybe a third on a more cautious day. He asked the one question worth asking. How much.

Kelly says twenty pct. Half Kelly says ten. The math says he was about to over-size the trade by a factor of two on the chart he was right about.

The Kelly formula on a discrete payoff is fraction equals win probability times payoff minus loss probability, divided by payoff. At sixty forty even money that reads zero point six times one minus zero point four over one, which lands at zero point two. Twenty pct of the book on the highest conviction trade of the quarter. The number reads small because Kelly is not optimising for the bet. It is optimising for the long-run geometric growth of the bankroll across thousands of bets like this one. Optimising for log wealth.

The reveal is in the next column. Full Kelly compounds at the theoretical maximum, but the expected long-run drawdown on the way to that maximum is roughly half the bankroll. Half Kelly captures about three quarters of the geometric return for roughly half the drawdown. Quarter Kelly takes about half the return for one quarter of the drawdown. The relationship between size and drawdown is convex. Doubling the bet does not double the pain. It roughly quadruples it.

That is why every quant fund that knows the formula does not use the formula. They use Half Kelly. Or quarter. The drawdown profile of Full Kelly survives in a spreadsheet. It does not survive in a fund that has investor mark-to-market windows.

For equity holders the continuous version reads f-star equals mu over sigma squared. Plug in long-run Nifty 50 numbers, mu around twelve pct, sigma around eighteen pct, and the formula hands you three point seven times leverage. Almost nobody actually runs three point seven times. A 100 pct equity SIP, no margin, no leverage, is already running at roughly quarter Kelly on that math.

That is by design, not accident.

The size is the strategy