Bankroll Management for Prediction Markets: Kelly, Fractional Sizing and Ruin

Bankroll management is the part of prediction-market trading that decides whether you survive long enough for an edge to matter. The central tool is the Kelly criterion, which gives the bet size that maximises long-run growth. The central problem is that Kelly assumes you know your edge. You do not, so the practical answer is a fraction of Kelly, a hard cap per position, and a separate cap per event.

Get this wrong and the outcome is not a smaller profit. It is a blown account after a streak that was always going to happen.

Kelly in one paragraph

For a binary contract bought at price c with true probability p, the growth-optimal fraction of bankroll is:

f = (p − c) divided by (1 − c).

The derivation maximises expected log wealth. The intuition is that a bet worth taking at all is worth sizing in proportion to the edge, but scaled down by how much of your capital is exposed to a total loss.

A few values make the shape clear. At a price of 0.50 and a true probability of 0.55, the fraction is 0.05 divided by 0.50, or 10%. At 0.20 with p = 0.24, it is 0.04 divided by 0.80, or 5%. At 0.40 with p = 0.46, it is 0.06 divided by 0.60, or 10%.

Thorp's exposition of the criterion remains the standard reference for the practical details, including the difference between full Kelly, fractional Kelly, and overbetting. The key result is that betting more than Kelly does not increase long-run growth; it reduces it while increasing risk.

Why the formula is fragile in binary markets

Three features make prediction markets a harder setting than the textbook.

Your probability is an estimate. Kelly treats p as known. If you are two points off, the recommended size can change by a factor of three. At 0.50, p = 0.53 gives a fraction of 6%, p = 0.51 gives 2%. The formula is linear in the edge and inversely proportional to the price, so small errors in the numerator produce large changes in the answer.

The outcome is all or nothing. There is no partial credit and no stop-loss that fills inside a gap. A position that is "only" 8% of bankroll can lose the entire 8% in one resolution. In a continuous market, a stop limits the loss; here it does not.

Costs reduce the edge before the formula sees it. Fees and spread are paid on entry and exit. A 6-cent gross edge at 0.40 can become a 4-cent net edge after a round trip, which cuts the Kelly fraction from 10% to about 6.7%.

Fractional sizing

The standard practical response is to bet a fixed fraction of Kelly: half, a third, or a quarter. This is not a claim that Kelly is wrong. It is an admission that p is uncertain, that the model ignores correlation and resolution risk, and that a drawdown large enough to force you to stop trading has a cost the formula does not capture.

Half Kelly captures about three-quarters of the growth rate with roughly half the volatility of full Kelly, under the model's assumptions. Those assumptions are strong, but the direction is robust: the growth you give up is smaller than the drawdown you avoid.

A second layer is a hard cap. Even a half-Kelly calculation can produce a large number when the estimated edge is large, and large estimated edges are often estimation errors. Cap any single market at 2% to 5% of bankroll, and cap total exposure to a single event at 10%.

Binary outcomes and ruin

Ruin is not a single bad bet. It is a sequence of them at a size that compounds.

If you risk 10% of bankroll per trade and lose seven in a row, you are down to 0.9 raised to the seventh power, or 47.8% of your starting capital. A 52% drawdown requires a 109% gain to recover. If you risk 2% per trade, the same seven losses leave you at 86.8%, a 13% drawdown.

At a 45% loss rate, the chance of seven consecutive losses in a given seven-trade window is about 0.37%, roughly one in 270. Over a few hundred trades, a run of that length is more likely than not. The streak is not a tail event; it is a feature of the sample size.

This is why "risk 10% because the edge is large" fails even when the edge is real. The strategy can be profitable in expectation and still bankrupt the trader who sizes it for the expectation rather than for the path.

Correlation is the hidden multiplier

Kelly assumes bets are independent. Prediction markets rarely are.

"Candidate wins the presidency," "the party wins the presidency," and "the candidate wins a specific state" can all be separate contracts, but they resolve on the same underlying event. Sizing each at 5% of bankroll creates 15% of exposure to one outcome, not three independent 5% bets. The effective Kelly fraction for the cluster is much lower than the sum.

The fix is to budget by event, not by market. Assign each event a maximum loss, then divide that budget across the positions that express the same view. If you want to hold several correlated contracts, treat them as one position with several legs.

There is a second correlation: resolution risk. Markets resolved by the same oracle, in the same dispute window, can fail together. A 50/50 resolution on one contract is a loss; a 50/50 resolution across a cluster is a portfolio event.

A worked example

Bankroll: $10,000. A contract trades at 0.40 and you estimate the true probability at 0.46. The gross edge is 6 cents.

Full Kelly is 0.06 divided by 0.60, or 10%, which is $1,000. But the round trip costs about 2 cents including fees and spread, so the net edge is 4 cents and full Kelly is 6.7%, or $670.

Now account for estimation error. Your credible range for p is 0.42 to 0.50. At the low end, the net edge is 2 cents and Kelly is 2 divided by 60, or 3.3%, about $333. At the high end it is larger, but you should size to the low end, not the point estimate.

A quarter to a half of the conservative Kelly gives $85 to $170, or 0.85% to 1.7% of bankroll. That feels small. It is also the size that survives being wrong about p, a correlated second position, and a resolution dispute. If the cap is 5%, the calculation, not the cap, is binding, which is what you want.

A simple rule set

1. Compute the edge net of fees and spread, not gross.
2. Use the low end of your probability range, not the midpoint.
3. Bet a quarter to a half of that Kelly fraction.
4. Cap any single market at 2% to 5% of bankroll.
5. Cap total exposure per event at 10%, including correlated markets.
6. Keep a cash reserve and value open positions at the bid, not the mid.
7. Recompute after every resolution. Do not let a winning streak automatically increase size; increase it on a schedule, not after a good week.

What Kelly does not tell you

Kelly does not tell you whether your probability is right. It does not model platform risk, resolution risk, or the possibility that the market is right and you are wrong. It assumes you can rebalance continuously, that bets are independent, and that you can tolerate the drawdowns it produces.

It also maximises long-run growth, which is not the same as maximising the chance of reaching a specific goal. A trader saving for a house in two years should not use the same fraction as a fund with a ten-year horizon, even with the same edge.

The honest summary is that Kelly is a boundary, not a target. It tells you the maximum you should ever bet under ideal assumptions. In a market where the assumptions are shaky, the useful number is well below it.