πŸ’ Leverage and The Line Between Aggressive and Crazy

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In probability theory and intertemporal portfolio choice, the Kelly criterion also known as the The general result clarifies why leveraging (taking out a loan that requires paying interest in order to raise investment capital) decreases the optimal.


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The Kelly Investment Criterion and Optimal Leverage - Cash Chronicles
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R: calculate Kelly criterion ratio (leverage or bet size) for a strategy
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The Kelly Criterion. Now that we've explored the counteracting forces in leverage, we can discuss the Kelly Criterion. The Kelly Criterion is a.


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The Kelly criterion is based on the assumption that you can borrow at the risk-free rate. In your example, if you borrow at 4% over the risk-free rate.


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Details. The Kelly Criterion was identified by Bell Labs scientist John Kelly, and applied to blackjack and stock strategy sizing by Ed Thorpe. The Kelly ratio can.


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Within this article the Kelly Criterion is going to be our tool to control leverage of, and allocation towards, a set of algorithmic trading strategies that make up a.


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For the multi-asset portfolio, Kelly criterion provides an insightful perspective on. Risk Parity strategies, which can be extended for the assets with fat tails. 1 Head​.


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In probability theory and intertemporal portfolio choice, the Kelly criterion also known as the The general result clarifies why leveraging (taking out a loan that requires paying interest in order to raise investment capital) decreases the optimal.


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While the Kelly formula requires an estimate of the probability After reading Poundstone's book, I wanted to apply the Kelly criterion to my own investing. The problem in the real world is twofold – first that the leverage.


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kelly criterion leverage

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The Kelly criterion is based on the assumption that you can borrow at the risk-free rate. In your example, if you borrow at 4% over the risk-free rate.


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The end-result: keeping a constant leverage (which is some fraction of your Kelly criterion as we saw in previous articles), requires you to.


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kelly criterion leverage

Combining all these estimates, we can create a simple model of how a Kelly investor should have traded in real time over the course of our sample period. In my last post I railed against levered ETFs, investment products that have collectively cost investors billions of dollars. But its first extension was to gambling. Post Views: About the Author: Colby Davis. View Larger Image. Not to mention I have not accounted for transaction costs here, which could be significant with daily rebalancing. There is also a vast academic literature on forecasting volatility, with a cornucopia of elaborate statistical models developed by Ph. Though in reality transactions costs would have created a significant drag, and future returns are likely to be less than the ones seen here, an investor could also improve upon these simplistic models by incorporating additional asset classes and shifting allocations between them dynamically based on forward-looking risk and return estimates, at least in principle. Previous Next. Thus the zigs of government bonds largely offset the zags of the stock market, and so including them in a portfolio can greatly reduce overall volatility. Though not pictured here, using 5x leverage would have lost money in absolute terms, turning a dollar into 89 cents over 24 years. The expected return on bonds can be more easily and accurately estimated by simply looking at the current yield to maturity of the bond market. Among the scientists and engineers at its New Jersey campus, Kelly stood out due to his Texan drawl, chain-smoking habit, and penchant for firearms, firing homemade bullets at parties to impress guests, as well for his sharp intelligence; many people at Bell Labs at the time said he was the smartest person there after Claude Shannon. I calculate the expected return on long-term government bonds as the latest available yield on the 20 year treasury bond. You should keep making this bet for as long as I will let you. Kelly had heard about a gambling scam on the news in which the outcome of a quiz show was being telephoned to confederates and bet upon before the show aired. John Kelly died young and supposedly never put his own formula to use. Now, the best way to reduce portfolio volatility is through diversification, especially by including assets with low or negative correlations with each other. Less intuitively, using more than 2. Colby brings passion to the investment management process and takes no shortcuts when it comes to delivering investment value to our clients. Despite this we at RHS Financial have had positive things to say about leverage before, and leverage is an integral part of the investment strategies we employ. Far from betting everything on heads or tails, the Kelly Criterion says the optimal bet size is 2. That translates to a Kelly leverage ratio of 4. Still, the performance is rather erratic, and the vast majority of it comes in the years following the financial crisis. Just as Shannon deduced that a communication channel always contains some amount of random noise that reduces the information content of the message transmitted, Kelly reasoned that there was always some chance that our gambler could receive a bum tip, or that there would be some other error β€” or noise β€” in the system, and the first time there was the gambler would surely lose everything if he were betting everything. Join 1, readers, never miss a fresh perspective on financial matters that matter, and get two FREE investing tools. This means the Kelly leverage ratio is now a whopping This represents a return of Well, math plus some completely unrealistic assumptions, an additional one this time around being the fact that no broker will ever let you use this much leverage on these securities. The Line Between Aggressive and Crazy. Disclosures: This post is solely for informational purposes. Thus the leverage increases decreases when expected returns are higher lower and leverage decreases increases when recent volatility is higher lower. But if you bet too much, you will eventually go bust. Information theory has found applications in fields as far ranging as thermal physics, molecular biology, and artificial intelligence. One is a full Kelly investor trying to maximize returns regardless of risk. At PNP, Thorp ran various arbitrage strategies while keeping a fastidious focus on risk, consistent with his mathematical background in bet-sizing. In each case I used a random number generator to simulate a coin flip and ran trials for each gambler, then plotted the median wealth after each flip. I assume expected volatility is equal the trailing 60 day realized volatility. This is a task fraught with uncertainty, but not necessarily futile. This Goldilocks bet is given by the following formula, what has since come to be called the Kelly Criterion:. SPY gave individual investors the ability to trade virtually the entire stock market in continuous, real time, which means it also gave individual investors the ability to adjust their leverage to the market in real time as well, so it will serve as our baseline. Colby holds the Chartered Financial Analyst designation. John Kelly, Jr. Next time we will continue pursuing this thread and ask, how can we profit by betting against those who bet too much? The results were perhaps the greatest risk-adjusted returns any hedge fund had ever delivered before or since. He also recommended that Thorp look into the work of John Kelly. Between and Princeton Newport had a compound annualized return of All the while, Thorp continued to publish mathematical research, including elaborations on the Kelly Criterion and its extensions to other situations like stock investing. Because my bet is only valuable to you for as long as you have money to keep making it. A popular ETF based on this index, SPLV , launched in , but I want to look at the same period since so I will use the index data itself with the additional caveat that indexes are not directly investable and so this backtest will be even less realistic than the last one. Indexes are unmanaged, do not incur fees and expenses and cannot be invested in directly. Comparing against the rate on 3 month treasury bills over this period, SPY had an average excess daily return of 0. Accounting for the higher moments of the distribution will generally result in lower optimal levels of leverage, but for moderate leverage levels applied to broadly diversified portfolios, the differences are generally trivial. In his paper, Thorp demonstrated the first mathematical proof that the game of blackjack could be played so as to move the odds in favor of the player instead of the dealer, something most mathematicians had long assumed was impossible. Thorp showed that by keeping track of the cards as they are dealt and betting more when the deck contains relatively more favorable cards and less when contrariwise, a player could obtain a substantial edge over the dealer. It achieved this, however, with substantially less risk, its growth path almost looking like a straight line on the graph above. Only a few of the participants followed the optimal betting strategy, a finding made all the more terrifying by the fact that the sample consisted of students in economics and professional financial analysts. Armed with the Kelly capital growth investment criterion, we can now square that circle and distinguish between good and bad uses of leverage. As I wrote about in an earlier post on leverage , when looking at the stock market, those stocks that have had the least volatile returns in recent periods tend to perform about just as well as the overall market, but with obviously less volatility, implying they support a higher Kelly leverage ratio. In real life we can only estimate these parameters with great uncertainty. With the help of software engineers, he developed our proprietary investment management software. High-risk-high-reward seeking investors must be patient! But it turns out that simply assuming the volatility the market has experienced in the recent past will continue into the near future actually does a pretty good job in formulating forward-looking risk estimates. Armed with his system of card counting and the Kelly criterion for optimal bet sizing, Ed Thorp spent the next handful of years winning a small fortune in Nevada casinos and published the bestselling book Beat the Dealer about his strategy, much to the chagrin of casinos everywhere. Plugging in the numbers, that means the Kelly leverage ratio was 2. Not bad. And thus we see how the Kelly criterion can tell us how much leverage is too much and how aggressive investors can seek to maximize their returns without losing their shirts. An index is a hypothetical portfolio of securities representing a particular market or a segment of it used as indicator of the change in the securities market. Due to data availability I begin at the start of This is because by estimating volatility in real-time, the forward-looking Kelly investor is able to mitigate some of the worst drawdowns that the constant-leverage investor dealt with. There had to be an optimal amount of money to put at stake. Please contact us at your earliest convenience with any questions regarding the content of this post. That optimal strategy, known as the Kelly Criterion, is an underappreciated gem of applied mathematics. The Kelly criterion merely tells us the maximum amount of risk an investor can take to increase return, not whether that level is desirable or not. Not surprisingly, the half Kelly investor does better than the unlevered SPY but with more risk but worse than the full Kelly investor but with less risk. We have now entered the stratosphere. Related Posts.{/INSERTKEYS}{/PARAGRAPH} On the other hand, of course, if the gambler were too conservative and bet too little he would give up a tremendous amount of profit. Still, this illustrates my point about the Kelly formula and optimal leverage, which we can throw into greater relief by considering other leverage ratios over the same period. Past performance is no guarantee of future returns. Investing involves risk and possible loss of principal capital. {PARAGRAPH}{INSERTKEYS}Suppose I offer you a bet. But how much money should you be betting? The 2x Kelly bettor loses so much on each bad flip that he is never able to get off the ground, and ends up exactly where he started. In this particular case the true optimal ex-post leverage ratio is 2. In fact, its daily volatility was 0. I will ignore the effects of higher moments throughout the rest of the post. In particular, the Kelly criterion can be adapted to the continuously varying mathematics of the market to tell us how much leverage to use. From the perspective of an equity investor, the most diversifying asset class is government bonds, which tend to rally during recessions when investors rush to safety and lag during stock bull markets. Again, the Kelly investor would have had to endure incredible amounts of volatility to get there, especially during the financial crisis, and again this backtest is unrealistic for several reasons, but we see the principle at work behind rational levered investing. And after accounting for the hefty transactions costs and management fees these ETFs charge, even 2x might be suboptimal especially if you believe returns will be lower in the future than they have in recent decades. Where f is the fraction of her bankroll a gambler should bet, b is the betting odds or payout in the case of a win, p is the probability of winning and q is the probability of losing. Doing so would have looked like this:. In reality, investors have to try to estimate what future returns and risks will be using only information that is available at the present moment. This was no faint praise, as Shannon was one of the key contributors to the development of the digital computer, and the father of information theory. From this we start to see the problem with levered ETFs as they are currently constructed: they generally use too much leverage applied to too volatile of assets. Shannon was fascinated and immediately became a close friend and collaborator with Thorp. While we can prove this maximizes the growth rate of your bankroll with some calculus, a Monte Carlo simulation illustrates the point a little more intuitively.