Risk · Instrument 02
Most sizing tools ask what percent you feel like risking. This one starts from the only sizing rule with a mathematical claim behind it — the Kelly criterion — then walks it back with a conservatism fraction, an upside tilt, and a risk budget that shrinks your size automatically as a position moves against you.
Expected log growth per trade at every possible position fraction. The peak is full Kelly. Everything to the right of it takes more risk for less growth — the part of the curve that ends careers.
Your edge, repeated. Each faint line is one possible sequence of wins and losses at your recommended size; the band is the 10th-to-90th percentile. Log scale, so a straight line is steady compounding.
Recommended risk as a percent of capital, across win probabilities and reward-to-risk ratios. Your current inputs are highlighted. If small changes in p swing the size wildly, your edge estimate is doing too much work.
Everything downstream depends on three numbers taken from your entry, stop and target. Expressed as fractions of the price you pay, they are the loss if you're stopped out, the gain if the thesis works, and the ratio between them:
Defining g and l against the entry price is what makes the rest coherent. Kelly's fraction is a share of capital committed, so the money at risk is that fraction times l, and the share count falls straight out of the position value. Skip this step and it's easy to build a sizing tool that quietly conflates the money you commit with the money you can lose.
Kelly asks a specific question: what fraction of capital maximises the long-run growth rate of wealth, assuming you can repeat this bet many times? For a binary outcome it has a closed form:
For a continuously distributed return rather than a binary one, the equivalent is f* = (μ − r) / σ² — expected excess return over variance. Same idea: edge divided by the cost of carrying it.
Two properties matter more than the formula. First, if p·g ≤ q·l the edge is negative and Kelly returns zero or less — no size is the correct size. Second, and less intuitive: betting more than Kelly is strictly worse than betting Kelly. Growth rises to the peak and then falls away, so an overbet buys extra volatility and a lower compounding rate. There is no upside to the right-hand side of that curve.
Full Kelly assumes your inputs are exact. They are estimates, and Kelly is punishingly sensitive to the win probability. It also produces drawdowns most people badly overestimate their tolerance for. Half Kelly captures roughly three quarters of the growth rate at roughly half the volatility — an excellent trade, and the reason frac defaults to 0.5.
The RRR^k term deserves an honest caveat. Kelly has already used your reward-to-risk ratio — g and l are both inside the formula. Multiplying by it again is a second helping of the same information, so any k above zero pushes you toward, and past, the point where growth starts falling. It's defensible as a conviction knob if you believe a binary target understates a genuinely fat right tail, which is often true of deep-value and special-situation positions. It isn't defensible as an optimisation. That's why k defaults to zero here and the gauge above shows exactly what percentage of full Kelly you've landed on.
The risk budget is the part of this framework that does the most practical work. Decide up front the largest total loss you'll accept in one idea. As unrealised losses accumulate, size tapers:
With m = 1 the taper is linear: burn half the budget and your next add is half size. Raise m to 2 or 3 and it collapses far faster. Understand what this rule is really doing — it deliberately penalises averaging down. For a value investor whose whole method is buying more as price falls, that's a genuine tension, not an oversight. The rule's answer is that conviction should be expressed by sizing correctly at the start, and that the position which keeps getting cheaper is also the position most likely to be telling you something. Set m low if you want room to add; set it high if your losses tend to come from doubling down.
Two hard limits sit on top of everything: a maximum dollar risk per trade as a share of capital, and a maximum position size. They exist because every layer above them depends on an estimated win probability, and estimated probabilities are wrong in correlated ways precisely when it hurts. The caps are the only part of this calculator that doesn't care how good your idea is.
The Monte Carlo panel is the reality check on all of it. Same edge, same size, four hundred different orderings of luck — the spread between the best and worst path is almost always wider than people expect, and it is entirely down to sequence.
A formula for the fraction of capital that maximises long-run wealth growth given a known edge. For binary outcomes, f* = (p·g − q·l)/(g·l). Its key property is that betting above the Kelly fraction increases risk while reducing growth, so the optimum is a ceiling worth staying below rather than a target to reach.
Because full Kelly assumes perfect knowledge of your edge, and nobody has that. It also produces drawdowns of 50% or worse as a matter of routine. Half Kelly gives up about a quarter of the growth rate for about half the volatility, which is why fractions between 0.25 and 0.5 are standard practice.
Whatever your own record supports, not what the thesis feels like. If you haven't tracked outcomes, the sensitivity table is the useful part of this page — it shows how much the answer moves across a range of p, and if it swings dramatically, that's a signal to size smaller until you have data.
The arithmetic works for any instrument where you can state an entry, a maximum loss, and a target. For defined-risk option trades, use the debit paid as the effective entry with a stop of zero if you intend to hold to expiry. Be aware that the win probability for options is often knowable from the pricing itself, which makes the Kelly edge much harder to claim.