4.3. Performance measurement
In order to measure the portfolios performance, I rely on
Sharpe ratio, which is a performance criteria widely used by practitioners and
in literature.
u,,
=
^ - Rf
o-^,,
Sharpe ratio is defined as follow:
^ SR,,
With û,, the portfolio sample mean returns and
o-^,, its sample standard deviation.
In addition, I compute the cumulative returns and the maximum
drawdown of the investment strategies for each of the optimal portfolios.
5. Empirical results
5.1. Sample Characteristics
Table 1 and table 2 display summary statistics of daily log
returns for cryptocurrencies and traditional assets.
Regarding traditional assets, equity indices exhibit slightly
positive mean returns with S&P 500 showing the highest average daily
returns and the lowest standard deviation. As expected, corporate and
government bonds indices have low mean returns and showcase the lowest standard
deviation among all financial assets. Commodities depicted by S&P GSCI gold
provide the worst reward to volatility with negative mean return and an
annualized Sharpe ratio of -0.04. On the other hand, real estate exhibit
promising performance with a favorable annualized Sharpe ratio of 0.44.
Meanwhile, in line with Chuen et Al. (2017), I find that
cryptocurrencies outperform traditional financial assets in terms of average
daily returns and have the highest standard deviation by far.
14
As can be noticed, the 1% and 99 % percentiles show that
extreme price movements are more severe for cryptocurrencies than for
traditional assets. Albeit, the higher magnitude of positive returns is
emphasized for cryptocurrencies when compared with negative ones.
In the case of skewness and kurtosis, I find Ripple, Dash and
Litecoin to be positively skewed, a significant characteristic rational
investors look for. In contrast, Bitcoin, equities, bonds and real estate
display a negative skewness that indicates a higher tail risk. Additionally, I
find that all-time series are leptokurtic. Eurostoxx 50 and Shanghai stock
exchange present high excess kurtosis but to a lesser extent than altcoins.
Apart from Bitcoin, cryptocurrencies have very high excess
kurtosis as the market for altcoins is still developing.
Therefore, the Jarque-Bera test supports the latter findings
by rejecting the normality for all assets at 1% significance level. All the
conventional assets and cryptocurrencies are not normally distributed.
Moreover, I conduct Ljung box test to check for serial correlation. Hence, I
find most conventional assets as well as Ripple to show significant
autocorrelation. Nevertheless, Bitcoin, Dash, S&P500, Sovereign bonds and
Gold display a low autocorrelation of daily returns, which suggests a lack of
predictability.
Cryptocurrencies pronounced deviation from normality is
visualized in Figure 1. The black line depicts a theoretical normal
distribution of Bitcoin. I observe that the latter is the least volatile with
more observations around the mean and a less pronounced tail than altcoins.
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