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13

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 ...


10

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 ...


8

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

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 ...


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 ...


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.


2

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 ...


2

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 ...


2

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.


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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