How big to bet
You have an edge. How much of the fund do you put behind it? Bet too little and you leave growth on the table; bet too much and volatility compounds against you until you're going backwards. The gives the single leverage that maximises long-run compound .
The trap: the payoff is a parabola, not a ramp. Doubling your leverage past doesn't double your return — it takes it to zero while doubling your risk. And because investors redeem on losses, real funds run — giving up a little growth to make a fund-ending drawdown unlikely.
Skill × how often you use it
You never know a stock's true alpha — you have a noisy score. Two numbers govern everything: how correlated your forecasts are with reality (the ), and how many independent bets you get to make (). The combines them.
Why concentration loses: raising means being smarter — hard. Raising just means making the same-quality bet more often — a process problem. Ten deep-dive names at IC 0.10 give IR ≈ 0.32; five hundred systematic names at IC 0.04 give IR ≈ 0.89. The diversified book wins, and people hate it.
The optimiser fights your gut
Given expected returns and how assets move together, the weights maximise return per unit of risk. The inverse rewards low volatility and low correlation — so the lower-returning asset often gets the bigger weight.
B has lower return but lower vol and modest correlation, so the optimiser leans on it. Push ρ toward 1 and watch it refuse to hold both.
Keep the alpha, shed the market
This is the whole reason "hedge fund" is a phrase. You like a stock, but you don't want to bet on the whole market coming with it. Short the index in proportion to the stock's and you strip out market risk while keeping your stock-specific edge — the .
The dial that matters is ρ. Since you remove ρ² of the variance, a stock 90% correlated to the index lets you delete 81% of its risk with a single short. A stock at ρ = 0.3 barely hedges — there's little market risk to remove, so it's nearly a pure single-name bet whether you hedge or not.
The size of a bad day
Risk managers speak in and . VaR is the loss you won't exceed on 95% of days; ES is the average loss on the 5% of days you do. The catch: both assume a bell curve, and markets have — so the real number is worse.
Why ES beat VaR after 2008: VaR tells you the edge of the cliff; it says nothing about how far you fall past it. Two books can share a VaR and have wildly different . And the normal-curve number is the optimistic one — under fat tails the same 95% shortfall is ~40% larger.
Your own success shrinks your edge
Buying moves the price against you. The says the cost of trading grows with the square root of how much of the day's volume you demand. So there's an optimal trade size — and past it, becomes the real boss fight of a growing fund.
The invariant: at the optimal trade size, market impact always eats exactly two-thirds of your gross alpha — no matter the numbers. Grow the fund and every position must grow with it; impact scales like Q1.5, so net alpha per dollar decays. That ceiling, not your cleverness, is what caps a strategy's size.
A great backtest from pure noise
If a researcher tries enough strategies, one will look brilliant by luck alone. The expected best from worthless strategies grows with how many you tried — so the right question about any backtest is never "how good?" but Then you the survivor back toward zero.
Deflated Sharpe: a 1.6 backtest over 5 years is exactly what 1,000 coin-flip strategies produce. When the research team is proud of a number, the number is often just a count of attempts wearing a disguise.
Whose money is it?
The classic takes 2% of assets and 20% of profits above the . That last clause turns the manager's pay into a call option on the fund — which means when the fund is underwater, the manager's incentive is to take more risk while the investor wants less.
The margin spiral ties it all together. A fund with $500M of assets on $100M of equity runs 5× levered. A 4% loss on assets wipes 20% of equity → leverage jumps to 6×. To get back to 5× you must sell $80M — into the very market that just moved against you, paying on the way out. This is how one bad quarter becomes a dead fund.
Play it out: five years, one decision
Now put it together. Pick your skill and how hard you press the pedal, then run the fund through 20 quarters with random markets, occasional where correlations spike, 2-and-20 fees, and — the killer — that fire when you're deepest underwater. The lesson lands fast: the fund that wins isn't the one with the highest return, it's the one that survives its worst drawdown.
Try this: set your Sharpe to 1.5 and run 500 funds at Full Kelly, then at ¼ Kelly. Full Kelly posts a higher median — and closes far more often. Quarter-Kelly gives up a little upside to keep the survival rate high. Same skill, same edge; only the bet size changed. That trade-off is the job.
Point the model at a real market
Everything so far came from random draws. Now pull actual price history off the internet — a crypto coin or a currency — measure what it really did (return, , ), then run the same fund model at four settings and watch where reality lands inside the simulated cone. Does the model that kills most funds also bracket what the market actually delivered?
Reading it right. The cone is what the model — 2-and-20 fees, a 5%-a-quarter , at a 25% drawdown — expects from a fund with this asset's skill. The bold line is what actually happened. Sit high in the cone and the market was kinder than the leverage; plunge through the floor band and the model's risk was optimistic. Crypto usually pierces the floor near full Kelly; a major currency barely leaves the centre. Data is live from the internet — CoinGecko (crypto) and the ECB via Frankfurter (FX) need no key; equities come from Alpha Vantage (weekly closes, full history) with a free key you paste once (stored locally, sent only to Alpha Vantage). Free-tier closes aren't split-adjusted, so clean splits are corrected automatically — index ETFs like SPY/QQQ are the safest read.