# Tag Info

15

To respond to your questions in order: The formula looks deceptively simple. Does it actually work? That depends on what you mean by "work". Chan spends the rest of the chapter discussing the pitfalls of investing at "full Kelly". Do professionals use it at all? Professionals may maximize geometric growth, but I don't know anyone who does so with ...

12

First of all a very warm welcome to Quantitative Finance Stack Exchange :-) Concerning your question there are some basic points that seem to be unclear. In general "Quantitative Trading" by Ernie Chan is a good starting point for learning about quantitative trading strategies. The problem is of course that in this small book there are many concepts whose ...

9

The Sharpe ratio $S_i$ of a strategy indexed by $i$ is given by the ratio of the mean excess return $m_i$ to the standard deviation of returns $\sigma_i$, The formula you have quoted is the discrete Kelly criterion. That's not so useful in trading, where the outcomes are continuous. The continuous Kelly criterion states that for every $i$th strategy with ...

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The optimal growth portfolio is obtained by applying the Kelly criterion which is one of the pillars of the sound risk management. Ed Thorp's weekend forays to Las Vegas to play blackjack were one of the first historically documented cases of successful practical implementation of the Kelly strategy. Since then this method and its modifications have been ...

5

I would not put too much weight on any relationship between Sharpe ratio and Kelly criterion. The two are simply not logically related other than they both share common inputs. Kelly relates to sizing your position while Sharpe ratios relate your excess returns to the volatility of those. As long as you find common inputs you can always setup a ...

5

You are trying to apply the Kelly Criterion, supposedly to maximize how aggressively to bet, and you are having trouble when the Kelly Value turns negative. The naive answer to your question is that when your kelly value turns negative, then $f=\frac{bp-q}{b}$ turning negative means the instantaneous expected return is negative, which means you should not ...

4

The Kelly criterion is just one approach to portfolio construction (or bet sizing) that considers the risk-return tradeoff. There are many possible strategies (static or dynamic) that incorporate other criteria such as the maximum drawdown, probability of ruin, etc. As pointed out by @John, Kelly is maximizing the log of wealth, which is equivalent to ...

3

If you have K strategies and each strategy has an expected return, a variance, and you can measure the covariance of your strategies performance then a mean-variance optimization would answer how to optimally allocate capital amongst your strategies. Key to this approach is accurate estimation of your the input parameters identified above.

3

I hope this help you. We have to start from the very first step, namely how the Kelly formula is calculated. We have the chance to make a bet on a event $A$ that as an odd (decimal odds) $O_A$. We want bet only a fraction $f$ of our capital $V_0$. How much of our capital we have to bet? Well, if we win will face with a capital $V_1$ $$V_1=(1+(O_A-1)f)V_0 ... 3 Here is an interesting example which makes use of these concepts in emerging markets. Emerging markets are ideal because volatility tends to be higher so it can better be harvested: Diversifying and rebalancing emerging market countries by David Stein et al. Abstract: We discuss the diversification and rebalancing of Emerging Market countries. Emerging ... 2 Here you have a example "applying Volatility Pumping to real stock market". http://parrondoparadox.blogspot.com.es/2011/02/parrondos-paradox-stock-market.html 2 The Kelly Criterion was derived for two-outcome events (binomial). Assuming it "works" for anything else (including "normal" events) is asking for trouble. 1 Kelly calculates optimal leverage for maximising geometric growth. At the same time, any change in leverage does not lead to a change in a risk-adjusted return (i.e. Sharpe). Therefore Kelly cannot be used to improve risk-adjusted return. Talking about the excess vola, in practive one rarely applies Kelly. The bet is usually Kelly/2, Kelly/4 or even less. ... 1 They are the same. The maximum growth rate is achieved when the Sharpe ratio is maximized. For the proof, see here. 1 Maybe you could find pretty interesting the following papers: Laureti, P., Medo, M., and Zhang, Y.-C. (2010). Analysis of Kelly-optimal portfolios. Quantitative Finance, 10(7): 689–697. and Nekrasov, Vasily, Kelly Criterion for Multivariate Portfolios: A Model-Free Approach (September 30, 2014). The last is available at SSRN. Particularly, ... 1 What are you saying is not completely correct. What kelly criterion maximizes is the average growth of the capital invested. In fact, if I want to invest a fraction f of my 1000 units the amount that I will have after M trades will be 1000\Pi_{i=1}^{M} (1+f\phi_i) What we need to maximize is expected long-term growth rate. Growth rate is given by ... 1 As the paper suggests, the results that are shown in table 2 are taken from (if you read the caption) Ziemba, William T., and Donald B. Hausch, Betting at the Racetrack (New York: Norris M. Strauss, 1986) The citation is not included for some reason, hence your confusion. Your code works fine by the way. Thanks 1 Others may have different views, but I've tried applying Kelly formula/fractional Kelly strategies to capital allocation, and find it rather unpractical and risky. I would honestly suggest a three-tier optimization framework that I am myself adopting: Assuming you have M number of models covering multiple instruments and strategies. Your goal is to pick ... 1 Bayesian Odds Ratios can be used to compare models and allocate wealth to various models based on the relative probability that each particular model is "best." You could begin to look into it more on the wiki site. 1 Have a look at my paper http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133 I checked Kelly formula and found the answer from it is exactly as Markowitz's theory. >Thus, most issues on mean-variance theory (e.g. noise of estimation for mean and >variance) applies here. Kelly is not exactly as Markowitz's theory but they are indeed closely ... 1 See Ralph Vince's excellentbook: Handbook of Portfolio Mathematics where he goes through explicit, worked examples of using an appropriate modified-Kelly system in dollar / contract terms (Optimal F). He even gives Excel examples for the programmatically uninitiated. 1 Well, the first formula on the wiki page gives you a straight forward answer in absolute terms (you do know your bankroll so its pretty much absolute): http://en.wikipedia.org/wiki/Kelly_criterion Simple as that, sometimes it does not pay but only causes headaches to overcomplicate things :-) Happy Thanksgiving!!! Update as requested by OP: ... 1 It helps to think about what the Kelly criterion is attempting to achieve. The purpose of the Kelly criterion is to find a betting strategy that maximizes the geometric growth rate. In a portfolio management context where the investment universe contains a risk-free asset, it would be equivalent to (ignoring constraints)$$ w\equiv argmax\left\{ ...

1

It was discussed long ago by Claude Shannon and discussed a bit in Fortune's Formula. In the 1960s, Shannon gave a lecture in a hall packed with students and teachers alike in MIT, on the topic of maximizing the growth rate of wealth. He detailed a method on how you can grow your portfolio by rebalancing your fund between a stock and cash, while this ...

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