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Money Management Using the Kelly Criterion

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Money Management Using the Kelly Criterion Money Management Using the Kelly Criterion An Application of the Kelly Criterion on an Intraday Trading Strategy Based on the Swedish Stock Market Index OMXS30 Mårten Hagman Student Spring 2014 Master thesis I, 15 ECTS Master’s program in Economics, 60/120 ECTS Supervisor: Christian Lundström Abstract This paper highlights the importance of money management. Firstly, we show how an intraday trading strategy based on Swedish stock market index OMXS30 can be developed given market ineffectiveness. Secondly, we maximize the profitability of this technical trading strategy by applying the Kelly money management criterion. We estimate a concave relationship to find the optimal leverage factor. The main finding is that the profitability can be increased substantially for the given trading strategy. Key words: Breakout filter, Day trading, Future contracts, Kelly criterion, Market inefficiency, Money management, Optimal leverage factor, Relative strength index Acknowledgements I would like to thank my study companions for the support and the great company, enabling me to get through the long days of studies. I would also like to express my big gratitude towards Christian Lundström for all the inspiration he has given me and also for guiding me, with his expertise, through the financial jungle. Table of content 1. Introduction ......................................................................................................................................... 1 1.1 Background ................................................................................................................................... 1 1.2 Structure ........................................................................................................................................ 3 2. Money management ............................................................................................................................ 3 2.1 Previous studies ............................................................................................................................. 3 2.2 The Kelly criterion ........................................................................................................................ 5 2.3 Application of Kelly criterion on future contracts......................................................................... 8 3. Technical analysis ............................................................................................................................... 9 3.1 The efficient market hypothesis .................................................................................................... 9 3.2 RSI ............................................................................................................................................... 11 3.3 Daily breakout filter .................................................................................................................... 11 3.4 The trading strategy ..................................................................................................................... 12 4. Empirical results ................................................................................................................................ 14 4.1 Data ............................................................................................................................................. 14 4.2 Profitability test ........................................................................................................................... 15 4.2.1 Model.................................................................................................................................... 15 4.2.2 Results .................................................................................................................................. 16 4.3 Applying the Kelly criterion on the trading strategy ................................................................... 18 4.4 Comparing the optimized θ to θ=1 .............................................................................................. 19 4.5 Using a high leverage factor ........................................................................................................ 20 4.6 Test of robustness ........................................................................................................................ 21 4.7 Overview of results from the test period ..................................................................................... 23 5. Conclusions ....................................................................................................................................... 23 References ............................................................................................................................................. 25 Appendix ............................................................................................................................................... 28 A. How to practically obtain θ ....................................................................................................... 28 B. Relative strength index .............................................................................................................. 29 C. Frequency histogram of returns .................................................................................................. 30 1. Introduction 1.1 Background What do a risk neutral gambler and an investor have in common? Both want to make as much money as possible. By using money management this paper shows how the capital or wealth of an investor can be maximized. Money management can, as we partly will demonstrate, be seen as a field that in many aspects ties gambling theory together with financial theory. The main goal of money management is to maximize the capital growth by applying an optimal leverage factor without risk of ruin. We define the concept of ruin as substantial losses of capital that limits the amount we can reinvest. If ruin occurs it thereby causes a constraint in possible capital growth. In his paper we test the theory Kelly criterion. This theory is suggested by many high achieving investors as a way to handle the money management. Among these investors we find John Maynard Keynes, Warren Buffet and Bill Gross (Lundström, 2014). The contribution of this paper to the field of money management is the application of Kelly criterion on an intraday trading strategy based on the Swedish stock market index OMXS30. 1 By involving money management when studying a trading strategy we highlight a flaw of many similar studies. What can be noticed when observing previous studies of investment strategies is that they are often simplified. Many studies are limited to investing the same amount for every trade and not allowing for reinvestments (e.g. Wang and Yu, 2000). In this study we allow for reinvestments of capital gains and thereby, unlike earlier simplified studies, we present a more reality based study. Using reinvestments, the capital grows or shrinks at an exponential speed (Kelly, 1956). Given that an agent is utility maximizing and risk neutral, it should be of importance that we maximize the profit in the long run without risk of ruin.2 Under the assumption that one possesses an investment strategy that generates a positive average return, determining the size 1 The index corresponds to the 30 most traded stocks listed on the Stockholm stock exchange, corresponding to 65% of the trading volume and 45% of the market value. 2 Risk of ruin can be defined as the probability of losing sufficient trading or gambling money to the point where continuing a trading strategy or game is no longer considered an option to recover losses. 1 of the investment is essential. It can analogously be seen as a bet size decision of a blackjack player who is exploiting an edge he or she has in the game (Anderson and Faff, 2004). To practically perform a strategy like the one we present in this paper a financial instrument is needed. Future contracts are a financial instrument that well suits for active trading. There are a several reasons why future contracts are a facilitating instrument for this study. At first trading futures is very common and frequently used for agents acting on the financial markets. For instance, trading futures is a multi-billion US dollar industry (Lundström, 2014). Some primary reasons behind the wide prevalence are the low transaction costs and the liquid market of futures. Future contracts do also have the advantage that it is just as easy to make long trades as short trades. Its flexibility to make long and short trades also offers an opportunity for people who want to hedge against risk. Moreover, future contracts also offer the investor to set their own risk by allowing for different leverage factors. When trading futures, determining the investment size can equally be seen as determining what leverage factor to use (Sewell, 2011). When referring to investment size when observing future contracts, we from now on refer to it as leverage factor and denote it by the Greek letter . Thus, setting is the same as not involving money management. By being able to adjust the leverage factor without any additional transaction costs, futures offer a great flexibility. For an example of how is obtained practically, see appendix A. Since we have chosen to use future contracts of OMXS30 we now need a trading strategy that gives us empirical returns and a way to determine the optimal leverage factor. The optimal leverage factor
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