Memoire Online - Global portfolio diversification with cryptocurrencies

As can be seen from the asset allocation weights graphs, portfolios of traditional assets under inverse volatility and maximum diversification strategies are more diversified. On the other hand, Conditional Value at Risk strategy sets extreme weight allocations to bonds indices followed by S&P 500 since they exhibit the least volatility. Therefore, the C-var optimizer omits weighting other indices, which performed really bad and were highly volatile during estimation periods. This results in the basis portfolio exhibiting the best performance under this strategy with a Sharpe of 1.07.

When cryptocurrencies are included, I notice that the weighting scheme of other asset classes fluctuates to compensate for the additional volatility. Equity indices weights change the most during the sample period. I observe a significant increase in S&P 500 proportion but also a small position taken in gold. In addition, through the whole investment period, optimal portfolios contain between 0 and 3% of cryptocurrencies with the higher allocation share during the years 2016-2017, the period of tremendous growth for cryptocurrencies. Indeed, cryptocurrencies are considered too risky for the parameters of the optimization problem.

It is also noticeable that Bitcoin dominates over alternative cryptocurrencies. In fact, none of the Altcoins is given more than 1% weight during the whole optimization process.

Regarding risk budgeting approaches, I observe that portfolio assets do not fluctuate that much when adding cryptocurrencies. Moreover, the weight allocated to cryptocurrencies is larger under those two strategies. Until 2017, there is an increasing allocation in cryptocurrencies. However, it decreases drastically after the Bitcoin boom.

Furthermore, the Maximum Diversification strategy, which boosted the performance of investments significantly, invests between 0 and 10% in cryptocurrencies. Thus, the higher cryptocurrency exposure had a huge impact on maximizing the portfolio performance.

5.5. Robustness check

To assess the robustness of the trading strategies results, tables 12, 13, 14 and 15 present performance results using weekly data and monthly rebalancing.

The results of the study are robust with regard to the asset allocations employed. I find that cryptocurrencies always add substantial value when included in the stocks-bonds-alternative investments portfolio. Sharpe ratio increases significantly under the different optimization frameworks. However, similar results regarding the downside risk of the basis portfolio are found when using weekly data. Alternative cryptocurrencies worsen of the maximum drawdown of the portfolio whereas Bitcoin increases slightly the maximum drawdown under Inverse volatility and minimum variance strategies.

Interestingly, Minimum conditional value at risk performs better than maximum diversification and yields the highest Sharpe Ratio when cryptocurrencies are added.

6. Conclusion

This study seeks to address the possible hedging and diversification benefits of cryptocurrencies as an alternative investment. From the perspective of a global investor, I investigate the market linkages between Cryptocurrencies and global asset indices as well as the benefits of their inclusion within these assets.

Using the dynamic conditional correlation model, I find that block-chain assets can act as effective diversifiers for the investment period analyzed. I also detect that the correlation of traditional assets against Bitcoin are closer to zero and more stable than against over crypto-tokens. Moreover, I find that Bitcoin, Dash and Litecoin do possess hedging properties against some assets' indices. However, none of the cryptocurrencies acts as hedge against European, American and emerging market equities.

The resulting diversification properties further endorse the cryptocurrencies use case in a diversified portfolio. These findings are useful for global investors seeking protection from markets downward movements. I examine the out of sample performance of portfolios with and without cryptocurrencies via risk-based investment strategies: minimum variance, minimum conditional value at risk, inverse volatility and maximum diversification.

The results are in line with previous research regarding the inclusion of Bitcoin in a global portfolio of equities, bonds and alternative assets. I find that the risk return efficiency is enhanced under all strategies. The small increase in volatility was compensated with proportionally greater returns.

Despite their extreme volatility, the addition of alternative cryptocurrencies to a global diversified portfolio, which already contains Bitcoin, enhances the risk return reward. However, these crypto-assets yield higher volatility and higher maximum drawdown under all strategies. Further, the performance of the portfolio is boosted significantly under inverse volatility and maximum diversification. In fact, these modern risk based strategies prompt higher risk return reward via greater cryptocurrency exposure and especially greater alternative cryptos exposure. On the other side, due to their volatility structure, Minimum variance and Minimum C-var strategies invested in cryptocurrencies and particularly in Bitcoin only in certain points of time.

Moreover, the hedging properties of Cryptocurrencies are analyzed via the portfolios maximum drawdown. When adding Bitcoin, I find that it slightly drops under minimum variance and inverse volatility strategy. However, when Dash, Ripple and Litecoin are further added, the maximum drawdown increases under the four optimization models.

As robustness checking, I apply the aforementioned allocation strategies using weekly data. Results persist robustly. Cryptocurrencies enhance the portfolio performance on risk-adjusted basis but do not really decrease the portfolio downside risk.

In a nutshell, the study evidence suggests that cryptocurrencies can act as outstanding diversifier tools on a global perspective but do not offer appealing hedging properties.

However, the results of this study should be interpreted with caution. This analysis employs only limited asset allocation strategies. The sample period is small due to the short history of cryptocurrencies and better alternative to the selected cryptocurrencies might exist.

Summary statistics of daily log returns for traditional assets from 31 July 2014 to 30 April 2019. (N=1238 observations). Results are reported on a percentage basis apart from skewness, kurtosis, Sharpe ratio, the JB and LJBox tests. In addition, Sharpe ratio is annualized.

	S&P 500 Eurostoxx 50		SSE A shares	Nikkei 225	MSCI _Markets EM	IBOXX LIG	S&P GSD	FTSE EPRA NAREIT	S&P GSCI GOLD
Mean	0.042	0.008	0.027	0.030	0.011	0.014	0.002	0.022	-0.002
Standard Deviation	0.833	1.117	1.507	1.136	0.897	0.295	0.354	0.792	0.815
Skewness	-0.448	-0.786	-1.190	-0.261	-0.311	-0.332	-0.002	-0.748	0.271
Kurtosis	7.068	12.335	10.063	7.079	4.721	3.926	5.312	9.167	6.036
Minimum	-4.184	-11.102	-8.869	-5.742	-5.101	-1.451	-1.922	-6.912	-3.418
1% percentile	-2.520	-3.037	-6.109	-3.460	-2.330	-0.741	-0.950	-2.271	-2.252
5% quantile	-1.427	-1.709	-2.221	-1.791	-1.501	-0.492	-0.580	-1.235	-1.353
25% quantile	-0.255	-0.574	-0.473	-0.486	-0.511	-0.157	-0.187	-0.373	-0.404
Median	0.029	0.039	0.032	0.063	0.060	0.015	0.000	0.052	0.000
75% percentile	0.445	0.577	0.606	0.614	0.540	0.198	0.197	0.464	0.411
99% percentile	2.103	2.925	4.183	3.003	2.172	0.685	0.939	1.977	2.176
Maximim	4.842	5.567	5.599	6.414	3.228	0.938	1.802	3.622	4.590
Sharpe Ratio	0.800	0.117	0.285	0.414	0.193	0.767	0.013	0.442	-0.044
Jarque Bera Test	894.984	4622.047	2865.479	872.227	172.802	66.976	275.770	2077.435	490.681
Ljung Box Test	18.779	40.143	69.939	105.296	69.638	39.657	24.314	43.257	20.791
Critical Value Jarque Bera Test		5.943
Critical Value Ljung Box Test		31.400

Summary statistics of daily log returns for cryptocurrencies from 31 July 2014 to 30 April 2019. (N=1238 observations).

	Bitcoin	Ripple	Dash	Litecoin
Mean	0.179	0.330	0.242	0.185
Standard Deviation	4.394	7.513	7.522	6.945
Skewness	-0.210	2.381	0.015	1.000
Kurtosis	8.206	20.257	27.050	15.789
Minimum	-23.874	-35.328	-86.020	-51.393
1% percentile	-13.533	-18.051	-19.343	-15.550
5% quantile	-7.056	-9.364	-9.759	-8.994
25% quantile	-1.423	-2.430	-2.845	-2.138
Median	0.222	-0.345	-0.276	0.000
75% percentile	1.890	2.089	2.990	1.822
99% percentile	13.828	27.293	23.589	26.831
Maximim	22.512	75.083	76.818	53.980
Sharpe Ratio	0.645	0.698	0.511	0.422
Jarque Bera Test	1406.84	16530.00	29834.76	8643.49
Ljung Box Test	31.76	91.30	26.56	36.60
Critical Value Jarque Bera Test		5.94
Critical Value Ljung Box Test		31.40

This table shows unconditional pairwise correlation coefficients between cryptocurrencies and traditional assets from 31 July 2014 to 30 April 2019.

	Bitcoin	Ripple	Dash	Litecoin	S&P500	Eurostoxx 50	SSE A Shares	Nikkei 225	MSCI EM	IBOXX LIG	S&P GSD	FTSE EPRA	S&P GSCI GOLD
Bitcoin	1.000	0.330	0.485	0.592	0.039	0.036	0.012	-0.037	0.016	-0.023	0.010	-0.019	0.023
Ripple		1.000	0.254	0.332	0.053	0.030	-0.007	0.020	0.063	0.035	0.033	0.010	0.026
Dash			1.000	0.431	0.080	0.068	0.030	-0.013	0.049	-0.073	-0.037	-0.017	-0.006
Litecoin				1.000	0.026	0.004	-0.015	-0.026	0.007	-0.006	0.009	-0.015	-0.016
S&P500					1.000	0.493	0.162	0.065	0.441	-0.193	-0.214	0.515	-0.138
Eurostoxx 50						1.000	0.127	0.160	0.578	-0.125	-0.026	0.256	-0.099
SSE A Shares							1.000	0.211	0.413	0.013	-0.101	0.230	-0.058
Nikkei 225								1.000	0.416	0.203	0.124	0.181	0.102
MSCI EM									1.000	0.022	-0.032	0.435	0.018
IBOXX LIG										1.000	0.446	0.108	0.280
S&P GSD											1.000	-0.373	0.558
FTSE EPRA
NAREIT												1.000	-0.177
S&P GSCI
GOLD													1.000

The following figure illustrates Gaussian kernel density estimators of cryptocurrencies against fitted normal distribution.

The subsequent tables summarize the dynamic conditional correlations between daily returns of the four cryptocurrencies and traditional asset class. Standard deviations are expressed in percentage.

	Mean	Std.deviation	Minimum	Median	Maximum	25% quantile	75% quantile
S&P 500	0.0146	2.2501%	-0.1343	0.0147	0.2738	0.0099	0.0194
Eurostoxx 50	0.0648	0.0022%	0.0648	0.0648	0.0649	0.0648	0.0648
SSE_A shares	-0.0056	0.0038%	-0.0061	-0.0056	-0.0052	-0.0056	-0.0056
Nikkei 225	-0.0374	3.2494%	-0.0977	-0.0317	0.0194	-0.0693	-0.0102
MSCI EM	0.0196	0.0002%	0.0196	0.0196	0.0196	0.0196	0.0196
IBOXX LIG	-0.0149	0.0002%	-0.0150	-0.0149	-0.0149	-0.0149	-0.0149
S&P GSD	0.0112	0.2561%	-0.0252	0.0112	0.0243	0.0106	0.0118
FTSE EPRA
NAREIT	-0.0320	0.2980%	-0.0541	-0.0321	-0.0029	-0.0331	-0.0310
S&P GSCI gold	0.0166	0.0002%	0.0165	0.0166	0.0166	0.0166	0.0166

	Mean	Std.deviation	Minimum	Median	Maximum	25% quantile	75% quantile
S&P 500	0.064	3.12%	-0.009	0.064	0.173	0.040	0.082
Eurostoxx 50	0.044	0.00%	0.044	0.044	0.044	0.044	0.044
SSE_A shares	0.004	7.65%	-0.255	-0.002	0.337	-0.040	0.048
Nikkei 225	0.013	2.13%	-0.049	0.011	0.094	0.000	0.025
MSCI EM	0.073	2.56%	-0.010	0.071	0.200	0.059	0.084
IBOXX LIG	0.018	0.13%	0.007	0.018	0.026	0.018	0.018
S&P GSD	0.034	0.00%	0.034	0.034	0.034	0.034	0.034
FTSE EPRA
NAREIT	0.020	4.48%	-0.312	0.019	0.338	0.002	0.037
S&P GSCI gold	0.026	0.00%	0.026	0.026	0.026	0.026	0.026

	Mean	Std.deviation	Minimum	Median	Maximum 25% quantile 75% quantile
S&P 500	0.11	1.4%	0.03	0.10	0.18	0.10	0.11
Eurostoxx 50	0.10	3.1%	-0.08	0.10	0.27	0.09	0.11
SSE_A shares	0.04	0.0%	0.04	0.04	0.04	0.04	0.04
Nikkei 225	0.02	0.7%	-0.03	0.02	0.11	0.02	0.03
MSCI EM	0.08	2.5%	0.00	0.08	0.18	0.07	0.10
IBOXX LIG	-0.07	0.0%	-0.07	-0.07	-0.07	-0.07	-0.07
S&P GSD	-0.04	0.0%	-0.04	-0.04	-0.04	-0.04	-0.04
FTSE EPRA
NAREIT	-0.01	8.2%	-0.45	-0.01	0.49	-0.05	0.03
S&P GSCI gold	-0.02	2.1%	-0.26	-0.02	0.10	-0.02	-0.01

	Mean	Std.deviation Minimum		Median	Maximum	25% quantile 75% quantile
S&P 500	0.018	4.89%	-0.164	0.011	0.192	-0.010	0.040
Eurostoxx 50	0.035	1.88%	-0.036	0.035	0.120	0.027	0.043
SSE_A shares	-0.027	2.90%	-0.099	-0.029	0.042	-0.044	-0.014
Nikkei 225	-0.021	0.00%	-0.021	-0.021	-0.021	-0.021	-0.021
MSCI EM	0.020	2.47%	-0.086	0.020	0.110	0.006	0.033
IBOXX LIG	-0.010	4.31%	-0.129	-0.009	0.181	-0.031	0.012
S&P GSD	0.001	0.00%	0.001	0.001	0.001	0.001	0.001
FTSE EPRA
NAREIT	-0.016	0.00%	-0.017	-0.016	-0.016	-0.016	-0.016
S&P GSCI gold	-0.016	5.46%	-0.207	-0.009	0.154	-0.046	0.018

Figure 2 : Dynamic conditional correlation plot of S&P 500 against cryptocurrencies and gold.

The following tables present the performance of the three optimal portfolios: Portfolio I: a portfolio of traditional assets, which encompasses equities, bonds and alternative investments. Portfolio II: a portfolio of traditional assets and Bitcoin. Portfolio III: a portfolio of traditional assets, Bitcoin and alternative cryptocurrencies. Four different optimization frameworks are performed subsequently: Minimum variance, Minimum Conditional Value at Risk, Inverse Volatility and Maximum Diversification frameworks. I use a 200 days moving window and the out of sample period ranges from May-08-2015 to April-30-2019. Sharpe ratio, mean daily return and standard deviation are annualized.

The following graphs display the weight allocation for traditional assets and cryptocurrencies from 8 May 2015 until 30 April 2019 under the following strategies: minimum conditional value at risk, inverse volatility, and maximum diversification.

08.05.2015 08.07.2015 08.09.2015 08.11.2015 08.01.2016 08.03.2016 08.05.2016 08.07.2016 08.09.2016 08.11.2016 08.01.2017 08.03.2017 08.05.2017 08.07.2017 08.09.2017 08.11.2017 08.01.2018 08.03.2018 08.05.2018 08.07.2018 08.09.2018 08.11.2018 08.01.2019 08.03.2019

Minimum Conditional Value at Risk Portfolio of tradtional assets and cryptocurrencies

The subsequent tables present the results obtained from the robustness check. It reports the performance of the optimal portfolios when using weekly data. I use 40 weeks (Equivalent of 200 trading days) moving window and the out of sample period ranges from May-08-2015 to April-30-2019. Sharpe ratio, mean daily return and standard deviation are annualized.

		Table 14: Inverse volatility strategy
		Portfolio I		Portfolio II	Portfolio III
Mean (%)		3.00%		4.59%	8.16%
Standard deviation (%)		6.15%		6.23%	6.85%
Skewness		-0.78		-0.83	-0.66
Kurtosis		5.75		5.81	4.73
Maximum drawdown (%)		10.83%		9.83%	11.0%
Cumulative wealth		1.11		1.18	1.32
Sharpe ratio		0.49		0.74	1.19
	Table 15: Maximum diversification strategy
	Portfolio I		Portfolio II			Portfolio III
Mean (%)	3.11%		6.55%			11.64%
Standard deviation (%)	5.76%		6.52%			8.83%
Skewness	-1.24		-1.20			0.36
Kurtosis	9.39		8.25			7.40
Maximum drawdown (%)	8.69%		10.02%			9.57%
Cumulative wealth	1.12		1.26			1.45
Sharpe ratio	0.54		1.00			1.31

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Global portfolio diversification with cryptocurrencies

5.4. Portfolio weights analysis

5.5. Robustness check

6. Conclusion