Questions tagged [kelly-criterion]

The kelly-criterion is a risk management strategy (or wagering system) providing an optimal risk apportionment system that relies on having 2 calculated probabilities.

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71 views

Kelly Criterion in correlated stocks

I would like to ask if there exist any mathematical proof or model which addresses how the Kelly criterion can be applied to find portfolio weights when the stocks are correlated.
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Is optimising for the Final Wealth is the same as optimising log of growth rate in Kelly Criterion?

A direct, brute force approach could be used to find the Optimal Portfolio. Consider simple play. There's a biased coin with 55% probability of win. The simulator play as a single person with 100$ ...
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How do market makers chose the size that they quote?

A typical quote in the derivatives market may be 2.00 bid at 2.50 ask with a size of say 100x100. How do practitioners go about choosing the size of the market (how many contracts) to quote? It seems ...
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Connections between Merton Fraction & Kelly Criterion

What are the theoretical and practical connections between the solution to the Merton's Portfolio problem and a bet-sizing tool such as optimizing the expected value of the logarithm of wealth (aka ...
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Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?

Given $G=\frac {C_n} {C_0}$, with $C_0$ the initial capital and $C_n$ the final capital after $n$ trades, the Kelly criterion derives the optimal fraction of capital to invest in each trade, by ...
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431 views

Kelly criterion for normally distributed returns

If the returns of my strategy are distributed like 𝒩[μ,σ], what is the optimal fraction of capital to invest in each single trade, as a function μ and σ? Help! PS. I know that normally distributed ...
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Question about quadratic form of f* in the Continuous Kelly Criterion

I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free. The derivation begins by assuming that the risky assets follows a GBM (a ...
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1answer
184 views

How to use Kelly Criterion to place an order in financial market

I tried to write a real-time trading system, however do not know how to fit a Kelly model into the system. The system will automatically calculate everyday 12AM while I want to add another function ...
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76 views

Can you clarify Kelly's derivation in Paul Wilmott Introduces Quantitative Finance?

Can anybody explain how the $\phi_i$ became $\mu$ and how $\phi_i^2$ became $\sigma^2$. Am I correct to assume that since $\phi_i$ is the outcome, $\mu$ is the average of the outcome? But I don't ...
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How can the Kelly Criterion be adjusted for making Angel Investment Decisions?

1 Context Consider the Kelly Investment Criterion, which "is a formula used to determine the optimal size of a series of bets in order to maximize the logarithm of wealth". Put differently, the Kelly ...
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Applying the Kelly Criterion - Targeting Specific Capital Gains

I keep reading that the expected time for your capital to reach any predefined number is minimized by the strategy that sizes bets according to the Kelly Criterion. But it seems trivially easy to come ...
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Am I calculating my Kelly Criterion correctly?

I'm taking a look at my trading history over a particular time period and have 500 trades on with an win rate of 82%. My average win is $W$. My average loss is $L$. So am I correct in assuming the ...
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381 views

Can a Kelly Criterion Percent be very high?

This is my personal record trading options (selling spreads) over a certain time period: Win Rate: 83.94% Average Win: $299 Average Loss: $1,181.40 The formula for the Kelly Criterion is: $$ f=\frac{...
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Questions on continuously compounded return vs long term expected return

I have reading a paper from Oliver Grandville on long term expected return. I am trying to reconcile what I am reading in that paper vs what I see under "Application to Stock Market" in Kelly ...
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Kelly's maximum for G(f)

In Thorpe's paper, Thorpe derives the Kelly criterion $$f^* = p - q$$ and plugs this into the equation $$G(f^*) = p \times \log(1+f^*) + q \times \log(1-f^*)$$ to get the following expression $...
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Optimal f (position sizing) without look ahead bias

My goal is to identify a systematic way to position sizing in the futures market. Let assume that I'm an investor with log utility. In addition, let assume that I'm reluctant in estimating the ...
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What is the Kelly Criterion for continuous probability case?

Given return of a portfolio or a single asset modeled as a continuous, but not necessarily gaussian, probability distribution, what's the Kelly criterion equation? I've heard that it's simply the ...
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Utility-optimal leverage with costs

Say I have a portfolio, $X_t$, using a leverage of $f$, such that the dynamics are given by \begin{equation} dX_t = \mu f X_t dt + \sigma f X_t dW_t \end{equation} I want to optimize the expected ...
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Optimize portfolio of non-normal binary return assets

I am facing t = 1,..T investment periods where each period I have x$ to invest. Suppose each period I can build a portfolio from thousands of assets (some are uncorrelated whilst some are highly ...
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Questions on Kelly criterion

I am new to asset allocation problems and have some concerns regarding the derivation of the continuous-time Kelly criterion (i.e. not the original version destined to discrete sports betting/Casino). ...
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How to apply Kelly criterion to a portfolio made by a stock plus a option?

First of all, assuming a Gaussian, Markowitz, well behaved world. Extensions for non-well behaved world will be welcomed. I know that by a portfolio made by only by one stock (and a risk free bond) I ...
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Implementation of Kelly in multivariate case using modeled distributions

I am exploring how to determine an "optimal" portfolio in the context of real life data and systems. Specifically, I want to calculate a Kelly Optimal Portfolio (see this paper, especially section 8.4 ...
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242 views

Risk Adjusted Kelly Ratio?

The Kelly Ratio maximises the expected cumulative return. However, it has been criticised for leading to excessive volatility. Is there a version of the kelly formula that maximises the risk ...
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Full Kelly portfolios having same weights as tangency portfolios

I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ...
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446 views

Combining modern portfolio theory and Kelly betting?

I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth. I'm looking for a ...
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the incremental value of Kelly Criterion under difference circumstances

I know that the Kelly Criterion maximizes bankroll, but i was wondering how much value it contributes to the total return and under what circumstances. I'm trying to understand the difference between ...
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Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
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Kelly Capital Growth Investment Strategy (Example in R)

In the paper Response to Paul A Samuelson letters and papers onthe Kelly Capital Growth Investment Strategy pages 5 and 6 Dr William T Ziemba, gives a praticle example on Kelly Growth. I’m trying to ...
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Capital Allocation for Portfolio of Multi-Strategy and Multi-Instrument

I would like to know if there is a way (or theory) to manage a multi-strategy, multi-instruments portfolio that would calculate the optimal weight to allocate capital for each combination of strategy ...
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Kelly criterion and Sharpe ratio

Whats the relationship between the Kelly criterion and the Sharpe ratio? $$ f=\frac{p(b+1)-1}{b} $$ where $f$ is a percentage of how much capital to place on a bet, $p$ is the probability of success,...
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Absolute Dollar Form Of Kelly Criterion

Is there a absolute dollar form of the Kelly equation $f=\frac{m}{s^2}$? (i.e. one that does not use percent returns).
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How to apply the Kelly criterion when expected return may be negative?

My concern is how to handle a negative value for the Kelly formula. Even when you have a system that has positive expectancy, you can (and usually will) sustain a number of losses, sometimes ...
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How to optimally allocate capital among trading strategies?

I'm trying to find an optimal way to allocate capital among trading strategies. "Quantitative Trading" by Ernie Chan claims on page 97 that the optimal fraction of capital to allocate to a given ...
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Optimality of Kelly criterion in non-normal environment

It is a not so well known fact that the Kelly criterion is only optimal in a nice and well-behaved Merton-world. It is far from optimal when things are getting non-(log)normal (i.e. more realistic!). ...
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Volatility pumping in practice

The fascinating thing about volatility pumping (or optimal growth portfolio, see e.g. here) is that here volatility is not the same as risk, rather it represents opportunity. Additionally it is a ...