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
2
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
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as follows:
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Pi,j,t+i =
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gi,j,t+i
.gi,i,t+i.gj,j,t+i
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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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