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Shannon’s Demon

Author: 小小梦, Created: 2017-11-09 18:33:25, Updated:

Shannon’s Demon

via. https://blog.enigma.co/is-there-a-free-lunch-in-the-crypto-markets-c4aa331443f1

An in-depth look at one quantitative trading strategy Hello to all! This is Enigma’s first article focusing on cryptocurrency trading strategies tested with our Catalyst platform, submitted by a member of the Catalyst community. We intend to create many more of these articles as our community and platform grow and evolve. Please leave your feedback and remember to try our alpha and join our Slack community! Introduction Claude Shannon, often called the father of the Digital Age, is known primarily for his major contribution to information theory. However, he also made significant contributions to the fields of cryptography and finance. Since cryptocurrencies are the intersection between these three fields, I imagine that he would’ve found them particularly interesting. For this article, Shannon is important for his financial experiment known as Shannon’s Demon, whose findings could be applied to an investment strategy for cryptocurrencies. Fortunately, there is now a platform designed specifically for testing algorithmic trading strategies on crypto-assets. This platform is Enigma Catalyst. Interestingly, Shannon was an MIT student and professor, Catalyst was developed by MIT alumni, and I am an MIT student. Naturally, when I found about Catalyst, I was eager to test the trading strategy that Shannon himself developed during his time at MIT. Shannon’s Demon Shannon’s Demon was an experiment designed by Claude Shannon that proved that it is possible to make profits of an asset, even if it doesn’t have a positive expected return. The experiment’s asset was a hypothetical stock with a “random walk” behavior. It had a 50% chance of doubling its price and a 50% chance of halving it every day. The investment scheme was simple: invest 50% in the asset and the remaining 50% in cash, and rebalance daily. William Poundstone provides an example of the way this investment scheme generates returns in his “Fortune’s Formula” book: “Imagine you start with $1,000, $500 in stock and $500 in cash. Suppose the stock halves in price the first day. This gives you a $750 portfolio with $250 in stock and $500 in cash. This is now lopsided in favor of cash. You rebalance by withdrawing $125 from the cash account to buy stock. This leaves you with a newly balanced mix of $375 in stock and $375 in cash. Now repeat. The next day, let’s say the stock doubles in price. The $375 in stock jumps to $750. With the $375 in the cash account, you have $1,125… … After a dramatic plunge, the stock’s price is back to where it began. A buy-and-hold investor would have no profit at all. Shannon’s investor has made $125.” This way, Shannon’s Demon makes money of the fluctuations of the asset’s price (i.e. volatility harvesting) instead of through the appreciation of the asset. The rebalanced portfolio is also much less volatile than a buy-and-hold investment scheme for the same asset. These findings provided insight into the benefits of diversification and portfolio rebalancing. However, Shannon never put this strategy into practice because of the limitations of the financial markets at the time. In practice, the costs of the transactions required to rebalance the portfolio would’ve had a significantly negative effect on its performance. However, the main limitation was that this strategy required an extremely volatile asset to make significant profits (recall that the stock in the experiment had either 100% gains or 50% losses every day). No asset at that time had enough volatility to compensate for the transaction costs. However, financial markets have changed significantly since that time, so it’s worth putting the strategy to the test once again. Are cryptocurrencies the right asset to apply Shannon’s Demon? At first glance, it seems like cryptocurrencies are excellent candidates for this investment scheme: they are known to be very volatile, are extremely difficult to value, and their prices seem to be driven mostly by speculative trading. However, a deeper analysis is needed to reach a conclusion. Algorithm backtest findings with Catalyst I performed Shannon’s Demon’s first test on the most popular token: Bitcoin (BTC). However, instead of rebalancing the portfolio daily (as was done in the original experiment) I programmed the algorithm to wait for the asset price to either double or half relative to the last rebalancing price. I used all the available historical prices from Catalyst, which uses data from the Poloniex exchange. The time frame for the test was from February 21, 2015 to August 7, 2017, which adds up to 899 days. In this test, the trading algorithm rebalanced the portfolio 3 times after the initial portfolio construction. This implies a rebalancing rate of 1.21 times per year. This rate is not enough to generate attractive returns from volatility harvesting. Moreover, the price of the Bitcoin surged 1,266% during this time, and the general trend was upwards. Thus, it doesn’t seem to have followed a “random walk” pattern. Not surprisingly, the trading algorithm underperformed the buy-and-hold strategy by a whopping 901%. The following graphs provide a timeline of the algorithm’s performance:

*The green triangles on the first graph indicate that the algorithm rebalanced the portfolio by buying Bitcoins, while the red ones indicate the opposite. Now, the fact that Shannon’s Demon didn’t outperform the buy-and-hold strategy during this period doesn’t mean that we should discard it, at least not yet. In fact, the very reason why Bitcoin is the most popular token has a lot to do with its appreciation, so an upwards trend was expected. Moreover, volatility is usually higher in the early-life of assets. Since Bitcoin has been trading for more than 7 years, it is likely that its volatility isn’t as high as it used to be. For this reason, I decided to perform my second test on a newer and less-known token: Augur (REP). Once again, I ran the test for all dates with available historical prices: from October 4, 2016 to August 7, 2017 (total of 308 days). During this time, the trading algorithm rebalanced the portfolio 5 times after the portfolio construction. This implies a rebalancing ratio of 5.93 times per year. This should be enough to generate decent volatility harvesting returns. From a return perspective, Shannon’s Demon still underperformed the buy-and-hold strategy. It generated cumulative returns of 103% compared to 126% for the buy-and-hold strategy. However, return alone is not the most important measure of a portfolio’s performance. This strategy incurred in much less risk than the buy-and-hold strategy. At its worst point, the buy-and-hold portfolio was loosing 68% of its initial value. Many investors would panic at that point. In contrast, Shannon’s Demon’s largest loss over the period was 35%. In terms of risk adjusted returns, I compared the Sharpe Ratio (SR) of both strategies. This measure tells us the return premium (above risk-free treasury notes) generated by each unit of risk. The annualized SR for the buy-and-hold strategy was 1.15 while Shannon’s Demon was 1.21. This means that the latter generated 6 basis points of additional return per unit of volatility (i.e. standard deviation) of the asset.

Suggestions for investors based on findings Based on these initial findings, we can derive two conclusions about Shannon’s Demon: it will generate less returns than a buy-and-hold strategy on an asset with a strong upward trend on its price. Second, it reduces the portfolio’s risk significantly. If I were to invest a significant amount of money in a crypto currency today, I would choose Shannon’s Demon investment scheme over buy-and-hold without question. There’s no way to tell where prices are going, and they are likely to vary a lot. However, there are many other trading algorithms worth testing. With Catalyst, you have the opportunity to be one of the first investors to write your own trading algorithms and backtest their performance. Data-driven investing can give you an edge over the market. This article was written by Rodrigo Gomez-Grassi, an MBA candidate at the MIT Sloan School of Management. Get Involved If after reading this article you’d like to test your own strategies, you’re in luck! Enigma has recently announced Catalyst Competitions and will be adding new strategies every week. Enigma will be rewarding 5,000 ENG tokens every week until the end of August to winning crypto-investment strategies built on the platform. The concept is straightforward: Winner gets 1,500 ENG 2nd place gets 1,000 ENG 3rd place gets 500 ENG Remaining 2,000 ENG is distributed equally to everyone who beats the weekly strategy To participate in the competitions, you can build on the weekly strategies provided by Enigma team or you can create new algorithms of your choosing. We do not accept buy and hold strategies. In order to get the reward, Enigma requires the top 3 places to write a quick blog post about their strategy. Ready to participate? Try our alpha and join our Slack community. Best of luck, and happy trading! Disclaimer — The material in this article is provided for informational purposes only. It is not a recommendation to buy or sell any security or implement any investment strategy.