Cameron Luke Wilson

Preface This analysis has been conducted out of curiosity of the historic risk component of broad market indices, as well as cryptocurrency indeces and funds. My field of study has led me to interact with many individuals who have either sung the crypto praise high, or have condemned it as just another asset bubble backed by no real value. My interactions with such individuals as well as my research beyond course requirements at the University of Cape Town has allowed me to learn how to conduct quantitative risk analyses of various assets. 1. Introduction This curt and somewhat informal report will highlight the various tools and methods used to conduct a risk analysis on various assets and asset classes. The focus of this study is the comparative risk analysis of broad market indices vs. cryptocurrency funds and cryptocurrency indices. The study has utilised market data from sources including Bloomberg, Statistica, Trading Economics, and the World Bank to quantitatively explore risk components of various market indices and funds. 2. Data Collection Methodology 2.1. Price Data All price data has been captured via Bloomberg Terminal. Monthly market data were captured for all assets, with broad market indices data comprising over 10 years, and cryptocurrency data comprising over two years. A two year window of price data was chosen for cryptocurrencies as the crypto arena has only been relevant in the last two years, with most funds only being constructed in the last two or three years. 2.2. Risk Free Rates Risk free rates for single markets were easily obtained via 10-year government bond yields of respective countries in which the markets are situated. However, when requiring broader risk free rates such as the ‘global risk free rate’ or an ‘emerging market risk free rate’, a weight adjusted method was used. Data of relevant yields per market segment and market capitalisations of respective debt markets per relevant country were obtained. The sources of these data include; Bloomberg, Statistica, Trading Economics, Bis.org, and Investing.com for market quotes and market capitalisations. The global and emerging risk free rates are weight adjusted by market capitalisations of respective debt markets as seen in tables one and two below. COUNTRY Brazil China Mexico Malaysia Poland Turkey Indonesia South Africa Thailand Philippines Russia Czech Republic Hungary Chile Peru TOTAL MEAN WEIGHT ADJUSTED Rf RATE % COUNTRY United States Euro Area United Kingdom Australia Switzerland Canada China Singapore Japan Hong Kong New Zealand Norway Mexico India TOTAL MEAN WEIGHT ADJUSTED Rf RATE % Emerging Market Risk Free Rate 10 YR YIELD Mkt Cap 2018 US Weight Adjusted Weighting Rf % Bn 9,-,8000 0,3220 3,0875 3,-,0000 0,2044 0,7220 7,-,5000 0,0888 0,6639 4,-,3000 0,0500 0,2027 3,-,0000 0,0495 0,1517 12,-,2000 0,0478 0,5851 6,-,2000 0,0467 0,3150 8,-,9000 0,0448 0,3594 2,-,0000 0,0402 0,0982 6,2400 73,2000 0,0262 0,1638 7,3200 64,0000 0,0230 0,1680 1,7430 51,4000 0,0184 0,0321 2,5400 45,1000 0,0162 0,0411 4,3600 43,2000 0,0155 0,0675 4,7850 18,8000 0,0067 0,-,6000 1,0000 5,6120 6,6904 GLOBAL RF RATE 10 YR YIELD Mkt Cap 2018 US Weightin Weight Adjusted % Bn g Rf 2,-,0000 0,5583 1,6027 0,-,6000 0,3499 0,1991 1,4000 56,3000 0,0408 0,0571 2,7900 29,4000 0,0213 0,0595 0,0500 7,8000 0,0057 0,0003 2,2600 6,0000 0,0044 0,0098 3,5320 5,7000 0,0041 0,0146 2,4220 4,1000 0,0030 0,0072 0,0380 3,6000 0,0026 0,0001 2,1420 3,6000 0,0026 0,0056 2,8200 3,3000 0,0024 0,0067 1,8960 3,2000 0,0023 0,0044 7,3900 2,4000 0,0017 0,0129 7,6800 1,3000 0,0009 0,-,3000 1,0000 2,7043 1,9872 Tables 1 and 2. Emerging Market and Global Risk Free Rates. 2.3 Expected Market Returns Expected market returns were easily gathered via Bloomberg’s Equity Risk Premium function for respective markets. However, global and emerging market expected returns had to be estimated using a weight adjusted approach as used for the risk free rates seen above. Expected returns data per country from respective markets, global and emerging market, were obtained via Bloomberg. These expected returns were then weight-adjusted by the locally-listed equities market capitalisations of respective countries. Market capitalisation data were found via Trading Economics. The Weight-adjusted expected returns for the emerging markets and global market can be seen in tables three and four below. Market BOVESPA SZSE & SSE (China) NSE & BSE (India) MICEX-RTS JSE TOTAL MEAN EM WEIGHT ADJUSTED E(Rm) % Market NYSE NASDAQ LSE TSE SSE SEHK EURONEXT SZSE TSX FWB TOTAL Emerging Market Expected Return E(Rm) Market Cap US$ Weightin % Bn g 14,-,5600 5,9948% 12,-,2700 68,8438% 0 13,-,6800 12,3812% 0 16,382 622,0500 4,9160% 0 13,286 995,1200 7,8643% 0 12653,6800 13,901 2 12,947 6 Global Expected Return Market Cap E(Rm) % US​$​ Trn 10,0620 21,0000 10,0620 7,0000 11,6840 4,0000 10,9260 4,2000 12,5140 3,0000 14,4450 3,0000 9,5010 3,5000 12,5140 2,0000 11,8880 2,1000 10,3700 1,8000 51,6000 Weight Adjusted E(Rm) % 0,8455 8,6151 1,6368 0,8053 1,0448 1,0000 Weighting 40,6977% 13,5659% 7,7519% 8,1395% 5,8140% 5,8140% 6,7829% 3,8760% 4,0698% 3,4884% 1,0000 Weight Adjusted E(Rm) % 4,0950 1,3650 0,9057 0,8893 0,7276 0,8398 0,6444 0,4850 0,4838 0,3617 MEAN GLOBAL WEIGHT ADJUSTED E(Rm) % 11,3966 10,7975 Tables 3 and 4. Emerging Market and Global Expected Returns (Equities). 2.4 Beta Coefficients The beta coefficients are the correlation coefficients obtained when regressing an asset on its respective market. These data are either obtained via Bloomberg or can be calculated in Excel via the Data Regression function. All beta values used are adjusted betas, or adjusted correlation coefficients, as adjusted values are a better forward-looking approximation of an asset’s beta coefficient. 3. Risk Analysis 3.1. Assumptions This analysis assumes that the Capital Asset Pricing Model (CAPM) holds and will thus be utilised to calculate the expected returns of various assets using the CAPM formula: E(R​i​) = R​f​ + β(MRP) E(R​i​) = Expected asset return R​f = Respective Risk Free Rate Β = Correlation coefficient of regressing an asset on its respective market MRP = Market Risk Premium (Expected Market return less the Rf) 3.2. Measures of Risk Risk is defined by the level or amount of uncertainty of an asset’s future price movement. Risk can be measured historically by considering historical risk and can potentially be extrapolated to get an estimate of future risk, however, forward risk is out of the scope of this project. Five measures of risk have been used to determine the historic risk of each asset under consideration. These are: The standard deviation of returns (SD), the semi-standard deviation of returns (SSD) or downside risk beneath a given benchmark, Treynor Index (market risk premium per unit of Beta risk), Sharpe Ratio (market risk premium per unit of SD risk), Sortino Ratio (market risk premium per SSD unit of risk), and the Risk Adjusted Performance (RAP). An example of a risk analysis of the JALSH (Johannesburg All Share Index) has been provided below. Note that all data are ​monthly​figures. JALSH Max Returns 12,2875% AM 0,6985% JALSH E(R​i​) Min Returns -13,9560% GM SD SSD 0,6084% 4,2567% 3,0547% EM E(R​m​) TREYNOR INDEX SHARPE RATIO SORTINO RATIO RSA R​f ADJUSTED BETA 0,7268% 0,5477 RAP 0,9197 % 1,0790 % 0,0035 0,0453 0,0632 1,0201 % Table 5. Risk Analysis on JALSH Where ​AM is the arithmetic mean, ​GM the geometric mean, ​JALSH E(R​i​) the expected return of the JALSH index, and ​EM E(R​m​)​the emerging market expected return. 3.3. Risk Comparisons A risk analysis is not very helpful when conducted on one asset alone. In order to obtain an idea about how risky and asset is, a comparison to another asset or a basket of assets (index) is required. Once an analyst is satisfied with his/her measures of risk can they then begin to compare and rank these measures per asset. For all measures selected, a higher value of each is preferable. For the Treynor Index, higher market risk premium (MRP) per beta unit of risk is preferable to a lower value. The same goes for the Sharpe ratio, but instead measures MRP per unit of standard deviation risk, and the Sortino Ratio which measures MRP per unit of semi-standard deviation risk. Finally, a higher risk adjusted performance is also intuitively desirable. 3.4. Results The results of the rankings of each measure of risk can be evaluated in tables below. Each measure has been ranked from best to worst. RANKED TRAYNOR INDEXES ASSET VALUE MVIS LC 86,1988 HFRCI 86,1988 BTC 86,1988 ECHFI 86,1988 INDXX C10 86,1988 MSCI WORLD 7,3419 S&P 500 6,8767 DJIA 6,8767 JALSH 3,5222 MSCI EM 3,4226 RANKED SHARPE RATIOS ASSET VALUE INDXX C10 0,2919 HFRCI 0,2677 MSCI WORLD 0,1612 S&P 500 0,1527 DJIA 0,1467 ECHFI 0,1377 BTC 0,1018 JALSH 0,0453 MSCI EM 0,0397 MVIS LC 0,0148 RANKED SORTINO RATIOS ASSET VALUE HFRCI 0,9491 INDXX C10 0,8877 ECHFI 0,8137 BTC 0,5629 S&P 500 0,2116 MVIS LC 0,2116 DJIA 0,2070 MSCI WORLD 0,1409 JALSH 0,0632 MSCI EM 0,0532 RANKED RAPs ASSET VALUE INDXX C10 9,3466% HFRCI 8,6316% ECHFI 4,7914% BTC 3,7320% MVIS LC 1,1624% JALSH 1,0201% MSCI WORLD 0,8998% S&P 500 0,8463% DJIA 0,8188% MSCI EM 0,7381% Table 6. Ranked Measures of Risk from Least Risky to Most Risky. It appears as per the data collected over the given periods of time that cryptocurrency indices and funds outperform equities on a risk adjusted measure. This goes against popular belief and rightly so. The data collected on cryptocurrencies do not stretch back far enough for accurate risk analyses to be conducted in this manner. There has approximately been 2 years of volatile price data in the crypto space, with half of the price data showing insane initial gains which offset major losses occurred over the last few months. This suggests that the data are heavily skewed to the right. 4. Recommendations and Conclusions The above analysis is not representative of cryptocurrency volatility and appears to have been the incorrect method to measure price volatility over the last two years. It is recommended that logged price data be used for an update of this analysis on cryptocurrency prices. However, not all is lost. This analysis is a great indication of relative risk amongst cryptocurrencies alone or equity indices alone. It is further suggested that comparisons of similar assets be compared in this manner. Also, an analyst should wait for more crypto price data to be available and possibly exclude the initial “bubble-rally”, witnessed in 2016 and 2017, from their analysis. Once crypto price data has been observed for a long enough period of time, comparable to that of equities markets, can a meaningful comparison be made between equities and cryptocurrencies. This informal study set out to compare and rank risk measures of various equity and cryptocurrency assets. The study compared these assets on the assumption of CAPM, allowing expected returns to be calculated from risk free rates, beta coefficients and market risk premiums. Data were gathered from various sources including Bloomberg, Statistica, Trading Economics and The World Bank amongst other reputable sources including Bis.org and Investing.com. The study came up inconclusive with respect to the comparison of risk measures between equities and cryptocurrencies. This is attributable to the irregularities of cryptocurrency price data over the last two to three years, resulting in positively skewed data. However, this analysis proves useful when comparing equities only or cryptocurrencies only.