A Comparative Study of Bitcoin and Gold as Portfolio Diversifiers

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Anton Iribozov

8 min readNov 8, 2017

Why Bitcoin is better than Gold?

Despite the huge amount of research papers focusing on bitcoin as a technology there is a severe lack of research papers that serve to investigate the economic implications of holding bitcoin. Bitcoin and gold behave similarly as investments however no other research paper draws this comparison directly.

BitCoin

The term ‘bitcoin’ refers to the tradable and investable tokens that exist within the Bitcoin network, where ‘Bitcoin’ refers to the decentralised network that achieves global consensus over a shared public ledger, known formally as the Blockchain. This is the main premise of Bitcoin founder — Nakamoto’s idea: replacing the need for trusted intermediaries when participating in financial transactions (Nakamoto, 2009)

Gold

Throughout history, gold has been in the forefront of the world’s development and economy. Its first documented usage dates back to 4000 BC where it was used to fashion decorative objects. 1000 years later it came to be used as jewelry and decoration of Egyptian tombs. By 1500 BC, gold became the recognised standard medium for international exchange.

Portfolio Diversification

Portfolio diversification relates to the age-old saying of ‘Don’t keep all of your eggs in one basket’. Just as one would diversify the risk of dropping the basket containing all eggs by spreading the eggs between multiple baskets, so too should investors spread the downside risk of a single asset by holding multiple assets.

The approach of our study

The following approach will be adopted in order to meet the stated objectives:

Taking the stance of an investor with the ability to hold positions internationally in a variety of financial assets, an initial investment portfolio will be formed. The portfolio must be somewhat diversified therefore major indexes representing each asset class will be used. The asset classes will span equities, bonds, currencies, commodities and hedge funds.

This initial portfolio will form the basis of the investigation because it will act as a benchmark for the evaluation of diversification benefits.
The second portfolio will consist of the same assets as the initial portfolio, with gold added.
The third portfolio will consist of the same assets as the initial portfolio, with bitcoin added.

Coefficients

By using a linear regression and regressing the three portfolios against the market portfolio, which will be the S&P 500, this will enable a comparison of each portfolio’s correlation coefficients and portfolio beta’s. A linear regression takes two variables, a dependent variable and an independent variable and it is used to model the relationship between the two. In this case, the returns of each portfolio will be analysed for a dependency on the market portfolio. This dependency will be apparent the higher the correlation between the two variables. Pearson’s R is the measure of the linear correlation between two variables, ranging between 1 and -1. A measure of 1 means a perfect correlation and therefore when the market moves, the portfolio moves in exactly the same way. A measure of -1 would be a perfect negative correlation and therefore if the market moves upwards, the portfolio will move downwards. This is the equivalent of a hedge. Another measure is the R-square value, which describes how good a fit the regression line is with the data. The main premise for using the linear regression is to test the effects of adding bitcoin and gold to the initial portfolio, with focus on the R-values and R-square values.

The regression will be enabled using the IBM SPSS program and taking weekly closing price data from Bloomberg and Qaundl for bitcoin price data. The SPSS package is a statistics based package that is able to handle large amounts of data and provides key data analysis techniques that will be beneficial to the study.
The outputted results are generated in a clear and consistent manner that will enable straightforward analysis of the data.
The documentation and easy of use of this package makes it a solid choice for carrying out the linear regressions.

This approach allows for a comparison of the diversification benefits of bitcoin and gold, compared with the less diversified portfolio of solely traditional assets.

Capital Asset Pricing Model

Another measure that will be investigated is the beta of each portfolio. The beta is the measure of systematic risk of a portfolio in comparison with the market portfolio.
A beta lower than 1 indicates that either the portfolio is less volatile compared with the market portfolio or that the portfolio is more volatile yet not correlated with the market portfolio. Generally, a beta exceeding 1 means the portfolio is both volatile and moves in the same direction as the market portfolio. As theorised in the Capital Asset Pricing Model, beta is said to share a linear relationship with expected returns and therefore investor’s should favour higher beta portfolios. However, in terms of diversification benefits it is bad practice to chase a higher beta as this can lead to a stronger correlation to the market portfolio. Due to the criticisms of the model the beta of each portfolio will only serve as an illustration of the change in beta and not as an investment appraisal measure.

The final measure will be the risk-reward profile of the portfolios. This will consist of a comparison of the volatilities of each portfolio. Next there will be a comparison of the returns of each portfolio.

Next the Sharpe ratio will be calculated of each portfolio. The Sharpe ratio measures the performance of an investment by adjusting for its risk, taking the excess returns of the portfolio over the market portfolio, divided by the standard deviation of the portfolio. A higher Sharpe ratio indicates a greater risk-reward ratio of an investment. An asset that improves the Sharpe ratio by decreasing risk and increasing returns is a good diversifier.

The final measure that will be calculated is the Sortino ratio. This is a modification of the Sharpe ratio that instead measures the downside volatility below a specific target return rather than penalising both the upside and downside as the Sharpe ratio does. By incorporating both of these industry standard measures this will serve to convey the performance of each portfolio.

Therefore, the main assumptions regarding portfolio diversification benefits for this study are:

The portfolio which has the lowest correlation coefficient — when regressed against the market — is the best diversified
The portfolio with a beta below 1 is more favorable for an investor in terms of diversification
The portfolio with the best risk-reward ratio will be more attractive to the investor

Data

The data used to form the portfolios is in line with similar studies by (Brière et al. 2013), (Pandey et al. 2014) and (Eisl et al. 2015). A base portfolio was created encompassing traditional asset classes that included equities, bonds, currencies, commodities and hedge funds. This portfolio was constructed using an index for each asset class that represented their price movements. This approach is in contrast to individual stock picking however by using indices this grants the most accurate representation and ensures diversification is achieved throughout each asset class. The MSCI ACWI index was chosen to represent equities — this is the All Country World Index that captures large and mid cap companies across 23 developed markets and 23 emerging market. This covers approximately 85% of the global investable equity opportunity set (MSCI, 2016). The BCOR index was chosen to represent bonds — this is the Bloomberg Global Investment Grade Corporate Bond Index that measures the investment-grade, fixed rate, global corporate bond market. The BBDXY index was chosen to represent currencies — this is Dollar Spot Index and it tracks a basket of leading global currencies against the dollar. The SPGSCI index was chosen to represent commodities — this is the S&P Goldman Sachs Commodity Index and it is the most widely recognised global benchmark for investment in the commodity market. The HFRXGL index was chosen to represent hedge funds — this is the Global Hedge Fund Research Index that is designed to encompass all eligible hedge fund strategies. For the portfolio inclusive of bitcoin, data was sourced from www.qaundl.com for the Bitstamp exchange — this is one of the longest running bitcoin exchanges and the second largest by volume denominated in USD.
For the portfolio inclusive of gold, the XAUUSD spot exchange rate was used — this is the dollar rate per ounce of gold.
The market portfolio in this study was the S&P 500 Index — this is one of the most commonly followed equity indices and the best representation of the US stock market.

Results

The weekly returns of each asset were analysed to give the following correlations.

Beta

From the above chart it can be concluded that each of the three portfolios have a relatively low beta value compared with the market portfolio (S&P 500). By definition the market portfolio has a beta of 1 because its covariance with itself equals its variance, and its variance divided by its variance is equal to 1.

Return and Volatility

The equally weighted portfolios above highlight the effect adding bitcoin and gold has on each portfolio.

Portfolio A has average annual returns of 3.54% with an average volatility of 7.18%.
Portfolio B has average annual returns of 2.01% with an average volatility of 7.69%.
Portfolio C has average annual returns of 28.66% with an average volatility of 28.14%.

It is therefore apparent that the inclusion of gold has a detrimental effect on the average annual returns and also increases portfolio volatility, in comparison to Portfolio A. The inclusion of bitcoin in Portfolio C increases the average annual returns drastically by 25.12 percentage points however the portfolio volatility increases hugely too.

Cumulative Returns

The below chart describes the returns a $10,000 investment in each portfolio would have yielded over the investment period that the study has examined.