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Global portfolio diversification with cryptocurrencies


par Salma Ouali
Université de Neuchâtel  - Master of science in finance 2019
  

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Bitcoin is a swarm of cyber hornets serving the goddess of wisdom, feeding on the fire of truth, exponentially growing ever smarter, faster, and stronger behind a wall of encrypted energy

3. Data

To conduct the analysis, I retrieve data from two different sources. I retrieve daily closing prices for traditional assets in form of indices from DataStream. While the data for cryptocurrencies are extracted from coinmarketcap.

According to Abidin et Al. (2004), international diversification is proven to yield higher returns and reduce risks and since cryptocurrencies are global in nature, I decide to adopt the perspective of a global investor. Therefore, I create a well-diversified international portfolio composed of cryptocurrencies and traditional assets.

Emphasis lies on the largest cryptocurrency assets. Therefore, I select four cryptocurrencies from the ten largest cryptocurrencies by market capitalization. Bitcoin and three major alternative cryptocurrencies: Litecoin, Ripple and Dash. These cryptocurrencies are portrayed as more suitable than other major altcoins like Bitcoin cash and Ethereum, which were only introduced in 2015 and 2017, respectively, and would not provide enough set of data to conduct the research. Additionally, the selection is made based on the underlying correlation of the alternative cryptocurrencies with Bitcoin. Ripple and Dash are moderately correlated with Bitcoin while Litecoin is relatively highly correlated with the latter.

Traditional and alternative assets comprise equity, fixed income, real estate and gold. Each asset class is embodied by liquid financial indices.

Equity indices are selected based on the four most important markets of cryptocurrencies trading. I use four regional indices S&P 500, Euro Stoxx 50, Nikkei 225, SSE (Shanghai Stock Exchange) as well as MSCI Emerging Markets Index. Considering the global bond universe of fixed income, I adopt the following indices: S&P Global Developed Sovereign Bond Index and

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IBOXX Liquid Investment Corporate Grade Index. Gold is added in consonance with Dyhrberg et al. (2015) since the latter is typically depicted as hedge. As of real estate, I use as a reference FTSE EPRA NAREIT global.

The sample contains daily price information from 30 July 2014 to 31 April 2019. I remove the daily data of cryptocurrencies during the weekends in order to match the number of observations with traditional assets.

Furthermore, I compute daily log returns since they are deemed more convenient for time series analysis and provide a better fit for statistical models. Therefore, daily log returns are obtained using the following formula:

Pi,t

rit = log Pi,t-1

4. Methodology

Modern portfolio theory states that correlation is the basis of diversification in a portfolio. Accordingly, investing in low correlated or negatively correlated assets can achieve efficient diversification (Bodie et Al, 2014). Following this, I examine diversification capabilities of cryptocurrencies as well as their ability to enhance the risk-return reward of a global investor.

4.1. Correlation analysis

I perform a correlation analysis in order to assess if cryptocurrencies can be a diversifier or a hedge. At first, I estimate correlation coefficients of cryptocurrencies and other assets via a pairwise correlation. However, the latter is only the average estimation and correlation in general is known to display time varying properties.

Hence, I conduct the multivariate dynamic conditional correlation (DCC) model by Engle (2002). The advantage of the model lies in its limited number of estimated parameters, univariate GARCH flexibility and its direct parameterization of conditional correlation.

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The estimation of the DCC model is performed in three steps:

I estimate an ARMA (1, 1)2 mean equation to model the conditional mean and deal with the autocorrelation in the time series returns.

The conditional mean equation for each asset is presented in the equation below:

?? ??

???? = ?? + E??+ ? ????????-?? + ? ???? E??-??

??=1 ??=1

Where c is a constant term, E?? is the white noise, p is the autoregressive term, q the moving average term and ö, è are the model parameters.

After deeming the conditional mean for each asset, the ARMA residuals are used to estimate the GARCH (1, 1) variance model.

Therefore, conditional variances are implemented one by one using the following formula:

????2= ??+ ?? E??2 + ??????-1

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Where ??t is the conditional variance, ?? is the intercept, ?? is the coefficient displaying the impact of previous shocks, E??2 is the squared residual and ?? is a coefficient that transmits the GARCH (1, 1) effect.

Afterward, I model conditional covariance of standardized returns using computed variances from first step.

With ????,??,??+1 = ????????(????+1

?? , ????+1

?? ) and ????,?? = ??

1-??-??

The dynamic conditional correlation is computed as follows:

??

????,??,??+1 = ????,?? + ?? (????+1??????+1- ??????) + ?? (????,??,?? - ??????)

2 Autoregressive moving average (1,1) model

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Once the auxiliary variable gi,j,t+i is forecasted, I compute the dynamic conditional correlation

as follows:

Pi,j,t+i =

gi,j,t+i

.gi,i,t+i.gj,j,t+i

After studying the co-movement between the selected asset classes and cryptocurrencies, I investigate the usefulness of cryptocurrencies as a diversification tool from a portfolio perspective.

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Bitcoin is a swarm of cyber hornets serving the goddess of wisdom, feeding on the fire of truth, exponentially growing ever smarter, faster, and stronger behind a wall of encrypted energy








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