The Kelly Criterion: How Edge Sets Size, and Why Overbetting Destroys Growth.
The Kelly criterion sizes each bet in proportion to its edge, so no edge means no bet; betting above it lowers long-run growth even when the edge is real, and a record chosen after a good run can overstate the edge, and so the bet. Here is what the science actually says, and what to do with it.
01The Opening
The Kelly size is only as sound as the edge estimate behind it
A bettor can win most bets, size every one of them by a fixed rule, and still see capital tend toward zero over a long enough run, if the fixed size is large enough.[1] Stake a fixed share of capital on an even-money bet, win once and lose once, and capital ends below its start: a 10 percent gain followed by a 10 percent loss leaves 99 percent of the original.[2] Whether a favourable bet builds capital depends on its size as well as on its edge. The Kelly criterion is the rule that sets that size from the edge.[4]
Two quantities set the Kelly size. The edge is the average gain per unit staked, net of costs; the odds are what a win pays per unit staked. For a bet that either wins the odds or loses the stake, the Kelly share of capital is the edge divided by the odds.[1] In trading, the stake is the risk unit (R), the amount lost when a trade fails at its planned exit, so the formula reads straight from a trade record: win rate, average win in R and average loss in R.
The formula has a consequence for selective trading. Zero estimated edge gives zero size, so the Kelly bet and the correct rejection are the same decision.[1] In signal detection theory, a correct rejection is passing on an option that really was bad. A statistical theory of bet selection reaches the same rule: take only bets with positive expected profit.[5]
Kelly sizing is selectivity written as arithmetic: a setup with no demonstrated edge earns a size of zero.
The originating paper asked how fast a gambler acting on a noisy private signal can grow capital, and showed that, for bets at fair odds, the maximum growth rate equals the rate at which the signal carries information.[4]
The originating paper showed that betting everything on each favourable bet maximises expected value, the average final wealth across all possible sequences, and also leaves the bettor broke with probability one if the betting continues.[4] A few extremely lucky sequences carry that average; almost every actual sequence ends at zero. Kelly instead maximises the long-run growth rate of capital, the compound rate at which capital grows per bet.[4][1]
That target describes the typical path. Over many bets, the Kelly bettor's capital, divided by that of any essentially different strategy, grows without limit with probability one, a result later work proved in general.[1][3][6] For repeated independent bets, the Kelly strategy also maximises the median of wealth, the level that half of all paths end above and half below.[7]
Kelly targets the growth of the typical path, not the average outcome, which a few lucky sequences dominate.
This article builds on the companion deep dive The Arithmetic of Selectivity: Expectancy, Costs and How Often You Trade, which estimates the edge per trade net of costs. That piece asks whether a setup has an edge; this one asks how much capital the edge supports, and what happens when its estimate is wrong.
The answer has three parts. Overbetting, betting above the Kelly size, lowers long-run growth even when the edge is real, and in the continuous approximation with no risk-free return, twice the true-edge Kelly size brings growth to zero.[2][1] A record chosen after a good run can overstate the edge; because any estimate is noisy, full Kelly on it can overshoot the true Kelly size.[8][9][1] And betting a fraction of the Kelly size gives up some growth for much smaller drawdowns, the falls in capital from a previous peak.[1][10]
Each result assumes repeated independent bets, known probabilities and payoffs, and a preference for long-run growth.[1][2] A trade record meets the first only roughly and the second never, so the input, not the formula, decides whether a Kelly size helps or harms.
The Kelly size is only as sound as the edge estimate behind it, and an estimate that overstates the edge overstates the bet.
02The Mechanism
The Kelly Criterion Growth Curve: Why More Is Not Faster
In the continuous model with no risk-free return, growth stops near twice the true-edge Kelly size, though every bet is favourable.
Long-run growth rises with bet size up to the Kelly fraction and falls beyond it; in the continuous approximation with no risk-free return, half Kelly keeps three quarters of the growth and twice Kelly keeps none.
The Kelly fraction is the share of capital to put at risk on each bet: for an even-money bet, the win probability minus the loss probability; in general, the edge divided by the odds.[1] Take an invented setup that wins 55 percent of the time and pays 1 R per win against 1 R per loss. Its edge is 0.55 minus 0.45, or 0.10 R per trade, and its Kelly fraction is 0.10 of capital at risk.[1]
Win rate alone does not set the size. A second invented setup wins 40 percent of the time, with an average win of 2 R against 1 R. Its edge is 0.40 times 2 minus 0.60, or 0.20 R per trade; divided by odds of 2, that also gives a Kelly fraction of 0.10. A third setup wins one third of the time at the same payoff, and its edge and size are both zero. The payoff ratio, average win over average loss, matters as much as the win rate.
The fraction comes from the growth formula. Over a long run of independent bets, capital compounds at a rate equal to the average logarithm of what each bet multiplies it by, so maximising growth and maximising the expected logarithm of wealth are the same goal.[4][1] The two-outcome formula ignores the spread of results around each average; in the continuous version the Kelly fraction is the mean excess return divided by its variance, so a wider spread means a smaller size.[1]
The Kelly fraction is edge divided by odds: the size comes from the net gain per unit risked and from what a win pays.
In the standard continuous approximation, which treats capital as moving smoothly rather than in discrete jumps, and with no risk-free return, growth is a parabola in the bet size with its peak at the Kelly fraction.[1] In that model, a bet of c times the true-edge Kelly fraction keeps c times (2 minus c) of maximum growth, and a bet with c below 1 is called fractional Kelly.[1] The share in that model is 0.75 at half Kelly, 1 at full Kelly, 0.75 at 1.5 times Kelly and 0 at twice Kelly.[1]
That zero is the article's central number. In the continuous approximation, when the size is computed from the true edge, betting twice the Kelly fraction brings long-run growth down to the risk-free return, which is zero when no risk-free return is available.[2][1] With no risk-free return, growth beyond that point is negative. For a single even-money bet the zero comes slightly earlier, at about 1.95 times Kelly for a 60 percent coin.
Equal distances either side of Kelly cost about the same growth: in the continuous approximation with no risk-free return, half Kelly and 1.5 times Kelly both keep 0.75 of maximum growth, and in an exact even-money bet the cost above is slightly larger, 0.746 at 1.5 times Kelly against 0.749 at half Kelly for the 55 percent setup.[1] Halving the bet keeps about three quarters of the growth rate and doubling it removes about all of it, in the continuous approximation with no risk-free return and the size computed from the true edge.[1][2]
In the continuous model with no risk-free return, halving the bet costs a quarter of maximum growth and doubling it costs all of it.
Bet size rises from left to right, in multiples of the Kelly fraction; the arrows mark a larger bet, not a cause. Growth is shown as a share of the maximum: c times (2 minus c) at c times the Kelly fraction, so 0.75 at half Kelly, 1 at the Kelly fraction, 0.75 at 1.5 times Kelly and about 0 at twice Kelly, with negative growth beyond. The chance of ever halving capital is 1 in 2 at the Kelly fraction and 1 in 8 at half Kelly, and half Kelly has half the volatility of full Kelly. Continuous approximation, true edge known, no risk-free return, unlimited horizon. Growth against bet size in the standard continuous approximation with no risk-free return, with the size computed from the true edge; exact even-money bets cross zero slightly before twice Kelly.
Diagram
Signal. The peak sits at the Kelly fraction. Edge divided by odds gives the fastest long-run growth when the edge is known.
Coordination. Below the peak, growth stays positive. With no risk-free return, half Kelly keeps three quarters of the growth with half the volatility.
Breakdown. With no risk-free return, growth reaches zero near twice Kelly. Every bet stays favourable; the size erases the growth.
Past the zero point, favourable bets shrink capital over a long run. With repeated independent bets and known odds, a positive growth rate sends capital toward unlimited growth with probability one, a negative rate sends it toward zero with probability one, and at exactly zero capital swings between both extremes.[1][3][11] These are limit statements. Over a finite run a bettor above the zero point can stay ahead for a long time, which hides the error in a short record.
The loss comes from volatility drag, the gap between average return and compound growth that widens with bet size. At a fixed fraction f, each pair of one win and one loss on an even-money bet multiplies capital by 1 minus f squared.[2] In the continuous approximation the average gain rises with bet size and the drag with its square, so beyond the Kelly fraction the drag outgrows the gain.[1]
In the continuous approximation, risk scales with the bet: half Kelly has half the volatility of full Kelly, and 1.5 times Kelly has 1.5 times as much.[1] Overbetting buys more risk and less growth at once.
Past Kelly, extra size buys risk and loses growth; past about twice Kelly, in the continuous model with no risk-free return, it shrinks capital.
10,504 median: dollars: median bankroll in a hypothetical, uncapped 300-flip run of a 60 percent coin at the Kelly fraction from $25, against a mean of about 3.2 million, in one experimental paper's arithmetic[12]. Hypothetical uncapped arithmetic · 300 flips at the Kelly fraction · median against mean
The mean in that arithmetic is about 300 times the median because a few extreme sequences carry it.[12] Kelly sizes for the middle of the distribution of paths, not for its rare top end.[7]
The Kelly fraction applies to current capital. In the coin experiment's own example, 20 percent of a $25 bankroll is a $5 bet; after a win, 20 percent of $30 is $6; after a loss, 20 percent of $20 is $4.[12] For the 55 percent setup with capital of 10,000, the Kelly stake at risk is 1,000; after one loss, capital is 9,000 and the stake falls to 900. After a loss capital is smaller, so the Kelly size in money is smaller, and sizing up to recover is the opposite of Kelly.[1][12]
A recovery stake is an overbet when it exceeds the Kelly stake on current capital. Doubling the stake to 2,000 after that loss does: against a Kelly stake of 900, it puts 22 percent of capital at risk, 2.2 times the Kelly fraction, where the 55 percent setup has negative long-run growth. In experiments with real money, prior losses made bets that offered a chance to break even especially attractive.[13]
The Kelly stake shrinks after a loss and grows after a gain; a recovery bet runs the rule backwards.
03Evidence
What the Kelly Criterion Evidence Proves, and Where It Stops
01Context
Before the rankings
The evidence on Kelly sizing comes in three kinds
Proofs establish what follows from stated assumptions: repeated independent bets, known probabilities and payoffs, and capital that can be divided without limit.[1][2] One controlled experiment, in which all players faced one game under fixed rules, shows how people size a bet when told its win probability.[12] Analyses of estimation error, the gap between an estimated input and its true value, show what happens when the edge is measured rather than given.[9][14]
Each kind has a limit. A proof says nothing about a setting that breaks its assumptions, and a trading record breaks the most important one: the edge is estimated, not known. The experiment observes one small group under one protocol.
The ranking below puts a proof with stated assumptions above an experiment, and an experiment above a single analysis. The critique ranks last because it limits the claim rather than carrying it.[15]
The mathematics is exact under its assumptions; the open question is what happens when the edge is an estimate.
02How we ranked
Ranked, not scored
Criteria (4, in rank order)
Design quality. A proof from stated assumptions ranks above a controlled experiment, which ranks above a single analysis.
Measurement precision. Exact derivations and observed bets rank above results stated only in words.
Causal clarity. Results that bear on bet sizing with less interpretation rank higher.
Replication value. Results restated or reproduced in independent work rank higher.
Order of weight
03At a glance
The Evidence at a Glance · 04 Findings · 21 Sources
What the Growth Mathematics Proves
Four proved results, each assuming repeated independent bets with known odds; three also use the standard continuous approximation.
01 · Half Kelly · Proved result · 75% of full-Kelly growth, no risk-free return. In the continuous approximation with no risk-free return, betting half the true-edge Kelly size keeps three quarters of the maximum long-run growth rate and halves the volatility of growth.[1]
02 · Twice Kelly · Proved result · 0 growth at twice Kelly, no risk-free return. In the continuous approximation, betting twice the Kelly size computed from the true edge brings long-run growth down to the risk-free return, zero when that return is zero; larger bets push it lower, though every bet is favourable.[2][1]
03 · Drawdown · Proved result · 1 in 8 chance of ever halving, half Kelly, no risk-free return. In the continuous approximation with no risk-free return and an unlimited horizon, the chance of ever falling to half of starting capital is 1 in 2 at full Kelly and 1 in 8 at half Kelly.[1]
04 · Past the Zero Point · Proved theorem · 1 probability, in the limit. With repeated independent bets and known odds, a bet large enough to make the growth rate negative sends capital toward zero with probability one over an unlimited run.[1][3]
Sources cited
21
Proof 9 · Experiment 3 · Analysis 8 · Review 1
04The signal
Evidence signal
Editorial judgment
The core results are proofs that independent derivations restate; the one human experiment shows people sizing a stated edge badly.
The mathematics holds under its assumptions; the danger is the input, an edge that a trading record only estimates.
The 5 Strongest Sources on Kelly Sizing
Ranked on four criteria, in the order shown below; no points score was assigned.
01Anchor
Reference chapter deriving the growth curve, fractional Kelly and drawdown results[1]
3/4 of maximum growth at half Kelly, no risk-free return: share of the maximum long-run growth rate kept by betting half the Kelly size, in the continuous approximation with no risk-free return.
This chapter gives the growth formula, the theorem that positive growth compounds and negative growth ruins over an unlimited run, the fractional Kelly trade-off and the drawdown probabilities, crediting the general proofs to earlier work.[1][3][11] In the continuous approximation with no risk-free return, betting c times the true-edge Kelly size keeps c times (2 minus c) of maximum growth.[1] It also works the case of an edge half as large as estimated, in which full Kelly on the estimate gives zero growth in the continuous approximation with no risk-free return.[1]
What this proves. The growth curve has one peak, at the Kelly fraction, and smaller bets trade growth for much lower drawdown risk.
Why it ranks first. It states every result the article relies on in proved form, with its assumptions.
Limitation. Its fractional Kelly and drawdown results rest on the continuous approximation with no risk-free return; with a risk-free return the formulas change.[1]
Rubric breakdown
Together the five establish the growth curve and its limits, show people misbetting a stated edge, and show, in one analysis, a smaller bet doing better out of sample on an estimated edge.
Evidence Hierarchy · Ranked by methodological weight
02
Balanced statement of strengths and harms
0 growth at twice Kelly, continuous model, no risk-free return. In the continuous approximation, betting twice the Kelly size computed from the true edge brings growth to the risk-free return, zero when that return is zero, and larger bets push it lower.[2] The review lists harms beside benefits, including that equal numbers of wins and losses at a fixed fraction leave capital below its start.[2]
Proves: full Kelly is not safe by default; the rule that maximises growth also brings deep drawdowns.
Why ranked here. It states limits the founding papers do not, but some of its figures come from other studies.
Not scored
03
Only controlled human experiment in the set
28% went bust (under $2 at the end), of 61 players. Players started with $25 and 30 minutes, with payouts capped at $250; 28 percent went bust, and 21 percent met the paper's definition of maxing out, ending with at least $200.[12] It is an unreviewed working paper.
Proves: in one group told the win probability of a simple repeated bet, sizing was erratic and often ruinous.
Why ranked here. It observes bet sizing directly, but it is one small, capped, unreviewed experiment.
Not scored
04
Kelly under an estimated edge
Smaller bet than the raw Kelly fraction, out of sample. In this analysis, a win probability estimated from data gave worse results out of sample than in sample, and shrinking the bet improved them.[9]
Proves: in one analysis of Kelly with an estimated win probability, a bet below the raw formula did better out of sample.
Why ranked here. It is the one peer-reviewed source here on Kelly with an estimated probability, but its result is stated in words, not numbers.
Not scored
05
The critique that sets the scope
Any finite number of bets, for the stated preferences. For preferences in which satisfaction rises with a power of wealth other than its logarithm, the growth-maximising strategy is not optimal for any finite number of bets and is never a good approximation to the optimum.[15]
Proves: Kelly is the right rule for long-run growth, not for every preference.
Why ranked here. It narrows the claim rather than carrying it, which places it last.
Not scored
04Stakes
The Edge Is Real and the Account Still Shrinks
Four routes turn favourable bets into slower growth or shrinking capital: overbetting, deep drawdowns at the right size, an edge smaller than the record shows, and chasing.
Leverage concentrates these costs. When the continuous Kelly fraction, mean excess return over variance, exceeds one, the formula asks for more than the capital in the account, which means leverage, betting with borrowed capital.[1] That is where estimation error bites hardest: the size moves in direct proportion to the estimated mean, and in the mean-variance comparison above, errors in means are the costliest.[2][18] This article recommends no leverage level.
Overlapping positions add a quieter overbet. Two independent bets made at the same time each warrant a slightly smaller fraction than one bet made alone: with an edge of 0.10 on each even-money bet, the fraction falls from 0.10 to about 0.099 each.[1] Positive correlation, the tendency of two positions to move together, lowers the fraction further; negatively correlated positions can warrant a larger combined fraction, and bets that are not mutually exclusive have to be sized together.[1][19] Two positions that move together completely are one bet; sized at full Kelly each, together they sit at twice Kelly.
One analysis of published return factors argues that, once multiple testing is counted, a new factor needs a t-ratio, its distance from zero in units of sampling error, above 3.0 rather than 2.0.[20] A personal record is a small version of that search, and the overconfidence deep dive covers why an estimate feels more certain than it is.
Overbetting hides in leverage, overlapping positions and optimistic estimates, and each pushes the real size above what the true edge supports.
Overbetting a Real Edge
Past the zero point near twice true-edge Kelly in the continuous approximation with no risk-free return, growth is negative, and over an unlimited run capital tends to zero with probability one, though every bet is favourable.[1] In one experiment of 61 players told a coin lands heads 60 percent of the time, 28 percent went bust.[12]
What it feels like · right on most trades and still going backwards; losses out of proportion to the win rate
Deep Drawdowns at the Right Size
Even at full Kelly with a known edge, in the continuous approximation with no risk-free return and an unlimited horizon, the chance of ever falling to half of starting capital is 1 in 2; at half Kelly it is 1 in 8.[1] In an example reported in a review, 700 bets with a 14 percent edge each can take 1,000 down to 18 at full Kelly and to 145 at half Kelly.[2]
What it feels like · the account halves before it recovers; pressure to abandon the method at the bottom
An Edge Smaller Than the Record
In portfolio choice, plugging sample estimates into an optimal rule can produce very poor out-of-sample performance.[14] For mean-variance allocations at average risk aversion, a review reports cash-equivalent losses in a 20:2:1 ratio for errors in average returns, variances and covariances.[2][18]
What it feels like · a method that worked for months and then stopped; sizes the record looked strong enough to justify
Chasing and Erratic Sizing
In the coin experiment, 18 of 61 players bet everything on a single flip at some point.[12] In real-money experiments, prior losses made bets offering a chance to break even especially attractive.[13] After a loss the Kelly stake on current capital is smaller, and a recovery stake above it is an overbet.[1]
What it feels like · one big bet will put me back; stakes rising as the account falls
05Protocol
A Four-Step Kelly Criterion Protocol for the Selection Ledger
This protocol adds one column, size against cap, to the Selection Ledger, the record of every setup seen, taken or rejected; the column and the four steps built on it are this article's method, and no study has tested them as a whole. Every number in it is the reader's own.
The protocol, as a sequence.
Before sizing → Before each trade → When positions overlap → At the weekly review
Size From a Conservative Edge
Compute the size only from a conservative estimate of net edge in R; where the record shows no edge, the size is zero.
Recompute From Current Capital
Size every trade as a fraction of current capital, and never raise the stake to win back a loss.
The Kelly stake moves with current capital, so after a loss it is smaller, and a recovery stake above it is an overbet.[1][12] Betting a fraction of Kelly on all capital equals betting full Kelly on that fraction of capital with the rest set aside.[2]
Sizing up after a loss, the pull toward break-even bets that real-money experiments document.[13]
Count Correlated Positions as One Bet
Add up the risk of positions that tend to move together, and size the total against the cap.
Simultaneous independent bets each warrant less than a lone bet, and positive correlation lowers the fraction further.[1][19]
Sizing each position as if it stood alone.
Choose the Drawdown, Then the Fraction
Decide the deepest drawdown you will sit through, then choose the fraction of Kelly that fits it; the fraction is yours.
In the textbook illustration, in the continuous approximation with no risk-free return and an unlimited horizon, half Kelly keeps three quarters of the growth rate, and the chance of ever losing half of capital is 1/8 against 1/2 at full Kelly.[1] A proved bound ties the chance of a drawdown to the bet size, and every fraction trades growth against security.[21][10]
Choosing size from the growth curve alone and being forced out at the bottom of a drawdown.
06Verdict
The verdict.
Bottom line
The Kelly size is the edge, stated in capital; where the edge is zero, so is the bet.
The Kelly criterion sizes each bet as its edge divided by its odds, so a setup with no edge gets no capital, and for repeated independent bets with known odds it maximises the long-run growth rate of capital. Above the Kelly size growth falls, and in the continuous approximation with no risk-free return, twice the true-edge Kelly size brings it to zero, though every bet is favourable. A trader never knows the true edge; a record chosen after a good run can overstate it, and full Kelly on an overstated edge is an overbet. Fractional Kelly gives up some growth for much smaller drawdowns, and the fraction is each trader's own choice.
The criterion joins whether to trade and how much, the second called position sizing. A setup with zero estimated edge gets zero size, the same verdict as a correct rejection.[1] At a fixed payoff, a larger edge raises the Kelly fraction, and the stake moves with current capital, falling after a loss and rising after a win.[1][12] The strategic inaction guide covers the wider case for not acting when no edge is present.
Halving the bet keeps about three quarters of the growth rate and doubling it removes about all of it, in the continuous approximation with no risk-free return.[1][2] And the rule has a scope: it serves long-run growth.[15][2] A goal to reach a wealth target by a deadline can call for a different policy, and a low drawdown tolerance argues for less.[17][10] Choosing a smaller fraction buys security with growth, the growth-security trade-off.[10]
Kelly sizing makes the size match the edge the record shows: no raise without a record, no bet without an edge, a smaller stake after a loss.[1]
Growth peaks at the Kelly size and is about zero at twice it
Size Follows Edge
The Kelly fraction is edge divided by odds, and it maximises long-run growth for repeated independent bets with known odds. No edge means no bet.
Overbetting Costs Growth
Above Kelly, growth falls; in the continuous approximation with no risk-free return, twice the true-edge Kelly size brings it to about zero, and beyond it capital shrinks over a long run. A record chosen after a good run can overstate the edge, and so the bet.
Size From a Conservative Edge
Use a conservative estimate, recompute from current capital, combine correlated positions and fit the fraction to a chosen drawdown. The fraction is the reader's own choice.
07Bibliography
The bibliography.
-
01
Chapter
doi: 10.1016/s1872-0978(06)01009-x
Chapter 9 The Kelly Criterion in Blackjack Sports Betting, and the Stock Market
-
02
Journal
doi: 10.1080/14697688.2010.506108
Long-term capital growth: The good and bad properties of the Kelly and fractional Kelly capital growth criteria
-
03
Chapter
Optimal gambling systems for favorable games
-
04
Journal
doi: 10.1002/j.1538-7305.1956.tb03809.x
A new interpretation of information rate
-
05
Journal
doi: 10.1371/journal.pone.0287601
A statistical theory of optimal decision-making in sports betting
-
06
Journal
doi: 10.1214/aop/1176991793
Asymptotic optimality and asymptotic equipartition properties of log-optimum investment
-
07
Journal
doi: 10.1239/jap/1101840570
The Kelly system maximizes median fortune
-
08
Journal
doi: 10.1090/noti1105
Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance
-
09
Journal
doi: 10.1287/deca.2013.0271
Optimal betting under parameter uncertainty: Improving the Kelly criterion
-
10
Journal
doi: 10.1287/mnsc.38.11.1562
Growth versus security in dynamic investment analysis
-
11
Journal
doi: 10.2307/1402118
Optimal gambling systems for favorable games
-
12
Journal
doi: 10.2139/ssrn.2856963
Rational decision-making under uncertainty: Observed betting patterns on a biased coin
-
13
Journal
doi: 10.1287/mnsc.36.6.643
Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice
-
14
Journal
doi: 10.1017/s0022109000004129
Optimal portfolio choice with parameter uncertainty
-
15
Journal
doi: 10.1073/pnas.68.10.2493
The "fallacy" of maximizing the geometric mean in long sequences of investing or gambling
-
16
Journal
doi: 10.1037/h0031322
Belief in the law of small numbers
-
17
Journal
doi: 10.1239/aap/1029955147
Reaching goals by a deadline: Digital options and continuous-time active portfolio management
-
18
Journal
doi: 10.3905/jpm.1993.409440
The effect of errors in means, variances, and covariances on optimal portfolio choice
-
19
Journal
doi: 10.1515/jqas-2020-0122
Kelly criterion and fractional Kelly strategy for non-mutually exclusive bets
-
20
Journal
doi: 10.1093/rfs/hhv059
... and the cross-section of expected returns
-
21
Journal
doi: 10.3905/joi.2016.25.3.118
Risk-constrained Kelly gambling
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