This report is produced by Huobi Research; please cite “Huobi Quant Academy” for reference. Abstract As one of the finance classics, Modern Portfolio Theory is one of the most important and influential economic theories dealing with finance and investment. The theory provides a mathematical framework to build a portfolio of assets that maximizes expected return for a given level of risk taken. This article applies the theory to cryptocurrency trading and evaluates its effectiveness in risk diversification and investment return improvement. Full Report We built mathematical models to backtest the risk diversification effectiveness of Modern Portfolio Theory by using historic data of the top 10 cryptocurrencies (BTC, ETH, XRP, BCH, EOS, LTC, ADA, XLM, TRX, IOTA). The result demonstrated that a well-proportioned portfolio diversification within Cryptocurrency investing can indeed reduce idiosyncratic risk effectively. Data Preparation We used the historical pricing data of the top 10 cryptocurrencies (by market cap) captured from Coinmarketcap from Nov 30th 2017 to May 21st 2018. Data Processing Daily ROI of Top 10 Cryptocurrencies Standard Deviation of Daily ROI and Sharpe Ratio of Top 10 Cryptocurrencies Covariance Matrix between the price of top 10 Cryptocurrencies Pearson Correlation Matrix between the price of top 10 Cryptocurrencies Mathematical Modeling We built the portfolio based on Modern Portfolio Theory and assigned each top 10 Cryptocurrency with different weight, with a total weight adding up to 1. By doing so, we should be able to achieve higher returns for a given risk level. Here, we used standard deviation of daily return to evaluate risk and used Sharpe ratio to evaluate effectiveness of portfolio diversification. According to Modern Portfolio Theory, adding assets to a diversified portfolio that have correlations of less than 1 with each other can decrease portfolio risk without sacrificing return. Such diversification will serve to increase the Sharpe ratio of a portfolio. Sharpe ratio = (Expected Portfolio Return − Risk-free Rate)/Standard Deviation of Portfolio Return Under two conditions (all weights are greater than 0, and all weights add up to 1), we built a stochastic model by calculating the standard deviation of portfolio return, expected portfolio return and sharpe ratio respectively based on 500,000 random values. As a result, we were able to find a set of optimal investment portfolios. Results Below is the scatter plot created from 500,000 stochastic simulations, with x-axis representing expected volatility (standard deviation of portfolio return) and y-axis representing expected portfolio return. The size of sharpe ratio is represented by different colors of the dots, with deeper color representing a larger sharpe ratio. From the plot, we can see that dots close to the bottom-right corner of the graph have larger sharpe ratios that represent better portfolio diversifications. Dots in the upper left corner are bounded by “efficient frontier” — a set of optimal portfolios that offers the highest expected return for a defined level or risk or the lowest risk for a given level of expected return. We can then draw the efficient boundary and find the best portfolio with largest sharpe ratio, marked by the red star in the figure below. We can then connect the red star to the the origin (since we assume Risk free return to be 0), and draw the capital market line — the best portfolio composed of risk and risk-free assets along the efficient boundary line. We then plotted efficient boundary, expected returns of optimal portfolio and single currency, standard deviations on the same graph in order to compare risk diversification. Conclusion Based on the evaluation above, we can see it is indeed possible to use Modern Portfolio Theory to construct an efficient frontier of optimal portfolios offering the maximum possible expected return for a given level of risk. However, we do realize that there are many other finance theories and models worth studying, and we will continue to explore these theories and models in our future reports. References Zvi Bodie, Investments 10th edition; Jonathan Berk, Peter DeMarzo, Corporate Finance 3th edition; Harry Markowitz, Portfolio Selection; Wes McKinney, Python for Data Analysis Huobi Research About us: Huobi Research of Blockchain Application (Huobi Research) was founded in April 2016 and started research and explorations in various aspects in blockchain area since March 2018. We cover blockchain technology research, industry analysis, application innovation and economic model explorations etc. We aim to establish a research platform and to offer theoretical foundations as well as judgements of trends in blockchain to the public, ultimately promoting the development of the entire industry. Contact us: E-mail： huobiresearch@huobi.com Twitter: @ Huobi_Research Medium: Huobi Research Facebook: Huobi Research Website: http://research.huobi.com/ Disclaimer: 1. Huobi Research does not have any form of association with blockchain projects or other third-parties mentioned in this report that could jeopardize the objectivity, independence and fairness of this report. 2. All outside information, data referenced in this report is from compliant and legitimate sources that we deem as reliable, and Huobi Research have conducted the due diligence concerning its authenticity, accuracy and completeness, but such due diligence does not provide any guarantee. 3. This report is only for reference purposes. Conclusions and viewpoints in the report do not constitute any form of investment advice on crypto assets. Huobi Research is not responsible for any losses resulting from the use of this report, unless stipulated by law. Under no circumstances should the readers give up their own investment analysis and judgements. 4. This report only reflects the opinions from Huobi Research on the day it was finalized. Future market condition changes may lead to updates of such judgements. 5. The report is copyrighted by Huobi Research, please cite the source when quote, and get approval from us when large amount of contents is referenced. Under no circumstances is reference, abridgment and modification contrary to original intention permitted.
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