5.3. Portfolio performance
In this section, I discuss the results of the different
optimization frameworks performed for the three optimal portfolios: a portfolio
of traditional assets, a portfolio of traditional assets and
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Bitcoin and finally, a portfolio of traditional assets,
Bitcoin and the three alternative cryptocurrencies: Ripple, Dash and
Litecoin.
Table 8 reports the performance of the optimal portfolios
under the Minimum Variance optimization. I find that allocating Bitcoin to the
basic portfolio slightly increases the annualized returns. Interestingly, the
volatility of the optimal portfolio remains unchanged and maximum drawdown is
even lower.
Likewise, the inclusion of alternative cryptocurrencies
increases a bit more the returns but at the cost of a slightly higher
volatility and a higher maximum drawdown. In fact, allocating even an
insignificant share into altcoins does not compensate for their very high
volatility. However, the higher returns seem to offset the evident increase in
risk and the risk return reward of 1.26 vindicates the importance of adding
Cryptocurrencies to the basic portfolio.
Due to the fat tail problem of cryptocurrencies, Conditional
Value at Risk emerges as more coherent risk measure than variance. Table 9
presents the performance of Minimum Conditional Value at Risk optimization. It
is important to note that the strategy's ability to focus on the expected
shortfall only brought higher returns for the portfolios with
cryptocurrencies.
When including Bitcoin in the basic portfolio, the strategy
shows a slight increase in the returns from 3.8% to 4.51%. The inclusion of
alternative cryptocurrencies improved more the returns with an annualized mean
of 5.08%. Once again, the high returns of cryptocurrencies offset their excess
volatilities. Despite the increase in standard deviation, annualized Sharpe
ratio increases from 1.05 to 1.17 when adding Bitcoin and to 1.29 when Altcoins
are included.
Skewness and kurtosis of the second and third portfolios are
slightly improved. Cumulative wealth increases as well. However, I observe a
higher maximum drawdown when including Bitcoin and the effect is more prominent
for the third portfolio.
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Optimal portfolio weights is the main scope of the two
aforementioned risk strategies. Now, I switch to risk budgeting strategies
which impose constraints on the volatility contribution of each asset to the
total portfolio volatility.
Table 10 summarizes the results of the inverse volatility
strategy. I observe that diversification effects of this framework worsen off
the performance of the basic portfolio. In fact, all the indices in the
portfolio have positive weights in spite of their level of risk while the two
first strategies omit weight allocations for the riskiest assets. The basic
portfolio gives mean return of 2.9%, a standard deviation of 5.17% and a Sharpe
ratio of only 0.56. The effect of cryptocurrencies is more prominent here. When
adding Bitcoin, Sharpe ratio increased by 0.28 from 0.56 up to 0.85 that is
driven by a significant improve in returns and an insignificant increase in
volatility of 0.03%. The contribution of alternative cryptocurrencies is even
more significant. Portfolio III displays a risk return efficiency of 1.30 and a
cumulative wealth of 1.30. Contrariwise, maximum drawdown is again higher than
first and second portfolios. Lastly, table 11 illustrates the performance of
the maximum diversification strategy, which aims to maximize diversification
effects by creating a portfolio with minimally correlated assets. Effective
diversification benefits of cryptocurrencies are the most pronounced under this
strategy. In fact, adding cryptocurrencies increases drastically the
performance of the basic portfolio as Sharpe ratio increases from 0.73 to 1.22
with Bitcoin and up to 1.54 when adding Ripple, Dash and Litecoin. The strategy
displays the highest returns for the second and third portfolio as well as the
highest standard deviation. Once more, the skyrocket returns of
cryptocurrencies seem to outweigh their high volatility.
Portfolio III shows higher maximum drawdown of 9.46% and more
leptokurtic returns. However, it is important to pinpoint that this is the only
portfolio to display positive skewness, which means that the probability of
positive returns was higher than negative ones. Moreover, portfolio III hits
the highest level of cumulative wealth with 1$ turning into 1.37$.
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So far, this study revealed crucial portfolio benefits when
adding cryptocurrencies to a traditional assets' portfolio independently of the
optimization strategy employed.
For further insights, a detailed analysis of portfolios weight
allocation is presented in the following section.
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