23 votes

Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?

The short answer is that: Maximizing the expected logarithm leads to more wealth almost surely in the long run. In contrast, maximizing expected return can easily lead to going broke almost surely in ...
Matthew Gunn's user avatar
  • 6,934
14 votes
Accepted

Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?

Maximizing $E[\log(G)]$ which corresponds to a concave utility function is a subtle way of incorporating risk aversion in the utility. Maximizing $E[G]$ is basically saying that you have linear ...
Ezy's user avatar
  • 2,187
10 votes
Accepted

Kelly criterion for normally distributed returns

This problem can be expressed as the original Merton's portfolio problem. Consider wealth process defined by SDE $$ d X _ { t } = \frac { X _ { t } \alpha _ { t } } { S _ { t } } d S _ { t } + \frac ...
starovoitovs's user avatar
9 votes

Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?

The original paper was concerned with optimizing the long run geometric return. In fact, he does not explicitly optimize either $\mathbb{E}(G)$ or $\mathbb{E}(\log(G))$. He also assumes the ...
Dave Harris's user avatar
  • 4,299
5 votes
Accepted

Question about quadratic form of f* in the Continuous Kelly Criterion

The Kelly Criterion aims to maximise the expected value of the logarithm of terminal wealth. The derivation starts off by assuming that there is a risky asset that is following a Geometric Brownian ...
Tim Wilding's user avatar
  • 1,406
5 votes

Why does Kelly maximise $E[\log\space G]$ rather than simply $E[G]$?

This is indeed a very good question! There were (and still are) very hefty debates, where even academic champions like Paul Samuelson were involved! A very good starting point to get some main ...
vonjd's user avatar
  • 27.4k
3 votes

How do market makers chose the size that they quote?

@chrisaycock raises a valid point about the process not being particular rigorous. There are reasons why it is not a rigorous or optimized sizing mechanism. 1) most market makers are quoting many ...
kdragger's user avatar
  • 541
3 votes

How to apply Kelly criterion to a portfolio made by a stock plus a option?

Kelly is mostly based upon assets with zero correlation made independent of each other. The way I approximate Kelly for multiple bets with correlation is: Assume after your first bet the capital is ...
Mike's user avatar
  • 31
3 votes

Volatility pumping in practice

In the following blog post the analytical results of the following paper and reproduced by simulation with real market data: Michael Stutzer: The Paradox of Diversification Abstract The current ...
vonjd's user avatar
  • 27.4k
2 votes

Am I calculating my Kelly Criterion correctly?

When it comes to Kelly, I've always liked the explanation at http://www.financialwisdomforum.org/gummy-stuff/kelly-ratio.htm. At this link there are three versions of Kelly explained, if you don't ...
babelproofreader's user avatar
2 votes

Am I calculating my Kelly Criterion correctly?

According to Skiena (link page 21) the Kelly fraction in the case of wins all equal to W and losses all equal to L is: $$f=\frac{pW-qL}{WL}=p/L-q/W$$ where $q=1-p$ and $p$ is the probability of a ...
nbbo2's user avatar
  • 11.2k
2 votes

Can a Kelly Criterion Percent be very high?

I think your calculation is right and the Kelly criterion is very aggressive. Note however that it is meant to apply to the situation where you win exactly your last bet times 299 84% of the time and ...
spaceisdarkgreen's user avatar
2 votes

Questions on continuously compounded return vs long term expected return

There are two communities that parametrize the random variables of the returns and levels differently. And unfortunately, they both use the same notation. One community uses $\mu$ to denote the mean ...
Taylor's user avatar
  • 544
2 votes

Utility-optimal leverage with costs

I hope my computations are correct. Let $u(t,x)=\max_{(f_s)_{s\geq t}}\mathbb{E}[(b+X^{f_.}_T)^\gamma]$. Using HJB (you have to prove that it is ok to use it). $$0=\max_{f}\partial_t u(t,x)+(\mu f ...
M. Jeunesse's user avatar
  • 2,422
2 votes

Optimize portfolio of non-normal binary return assets

For a single period, I would consider scenario optimisation: simulate your assets' returns (which you can do since you know their statistical properties, including correlations), and in this way ...
Enrico Schumann's user avatar
2 votes

How can the Kelly Criterion be adjusted for making Angel Investment Decisions?

Unfortunately, the solution isn't simple in that you can pick up a piece of paper or pencil, but with software it isn't actually as bad as it is about to sound. To begin with, note that the Kelly ...
Dave Harris's user avatar
  • 4,299
2 votes

Kelly criterion for normally distributed returns

ok I found it 🙂and this works for any distribution, not just the normal distribution $f^*=\frac μ {σ^2 + μ^2} \approx \frac μ {σ^2} \space if μ\llσ$ here the steps: https://www.dropbox.com/s/...
elemolotiv's user avatar
2 votes

Kelly Criterion in correlated stocks

Luenberger's book has a discussion on growth-optimal (i.e. Kelly) portfolios, also for the multivariate case with correlated assets. ...
Enrico Schumann's user avatar
2 votes
Accepted

Calculating M in Kelly portfolio optimization

Thorp defines $g_{\infty}$ as the mean long run logarithmic portfolio return. He argues that this is maximized when the portfolio is set $$F^{*}=C^{-1}(M-R)$$ Here is $M$ a vector of drift rates $m_i$ ...
fes's user avatar
  • 1,727
2 votes

Kelly Criterion — maximize expected value and minimize the variance in card game with $x$ red and $y$ black cards

This is what I would do without access to pen and paper. I don't know whether this strategy is optimal but it is easy to execute and I invite others to do better :) The problem in this setup is that I ...
Bob Jansen's user avatar
  • 8,552
2 votes

Why not calculate Kelly using semivariance? As w Sortino

The underlying assumption to your mu/simga^2 formula is that the pricing process follows geometric Brownian motion, so your returns are therefore symmetric and normal. The existence of a very high ...
Mild_Thornberry's user avatar
2 votes

Kelly Criterion for Multiple Simultaneous Correlated Bets

A natural question which was likely studied in academic literature (even though Kelly is not particularly popular among portfolio managers). I guess you could generalize Eq. (6.87) of this book. If $...
Michael Isichenko's user avatar
2 votes

Kelly Criterion applied to portfolios vs Markowitz MVA

As correctly mentioned in the comments, Kelly tends to be more aggressive than MVA. Its main weakness is a focus on a single bet/security and ignoring serial correlation of returns, something which ...
Michael Isichenko's user avatar
2 votes
Accepted

Can I apply the Kelly criterion directly, without fitting any distributions?

I think that your worries regarding normality, in general the right choice of a distribution, and the headache regarding high-dimensional distributions are valid. However, how could you maximise the ...
FP0's user avatar
  • 251
2 votes

Kelly Criterion for cash game poker (normally distributed returns)

Well it took me a while but I found the answer.
Tom Boshoff's user avatar
2 votes
Accepted

Did I derive the Kelly criterion correctly?

Might be a typo but you dropped the $\alpha$ on the noise term after solving the SDE: in $\exp(...)$ you should have $\alpha \sigma W_t$ instead of $\sigma W_t$. For deriving the Kelly criterion, it ...
Nap D. Lover's user avatar
1 vote

Kelly fraction for discrete distributions

I’ve already made a comment about how to find the Kelly bet size, f, but I guess that misunderstood the question. I come by it honestly though, because it is so vague. There are an infinite number of ...
Mild_Thornberry's user avatar
1 vote

Kelly Criterion in correlated stocks

This post provides a model for the Kelly Criterion under no leverage and no short constraints, and yields the following quadratic program: $$\max_f g = r + \sum_{i=1}^n f_i(\mu_i - r) - \frac{1}{2} \...
hubbs5's user avatar
  • 111
1 vote
Accepted

Is optimising for the Final Wealth is the same as optimising log of growth rate in Kelly Criterion?

As you suspect, you have a mistake. You say that: $$R_{average} = W^{1/n} = (\prod_{i = 1..n}R_{i})^{1/n} = {1\over n} \sum_{i = 1..n}log(R_{i}).$$ Notice that you took a log and kept the equation ...
AvidLearner's user avatar
1 vote

How do market makers chose the size that they quote?

The minimum size can be enforced on the market maker by the exchange or regulator. For example, some bond markets demand that market makers show a minimum size and spread for a certain period of the ...
river_rat's user avatar
  • 970

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