MSc Thesis for the course Banking & Finance at U.S.E. - Analysis of different cryptos regressed one-by-one on the original, already well-diversified, benchmark portfolio, - Calculation of risk-adjusted reward performances and comparizon with mean-var. spanning/intersection test, - Portfolio optimization & weights final, combined, portfolio.

1. International portfolio
diversification with
cryptocurrencies
Federico GaravagliaBanking and finance
June 25th, 2018

2. Cryptocurrencies & Blockchain
Master

3. • Over 1500 different cryptocurrencies
• US$ 613.7 Bn. Market capitalization (January 1st, 2018)
Introduction
“Will the addition of decentralized digital currencies to an
already well-diversified portfolio of risky international assets
yield diversification gains for the period considered?”
Master
The impact that the introduction of additional risky assets
(cryptocurrencies), has on the mean-variance efficient frontier of an
investment opportunity set of traditional assets is positive and statistically
significant;
Some cryptocurrencies are not spanned.
The combined portfolio exhibits positive excess returns,
Jensen’s alphas are positive and statistically significant.
The combined portfolio exhibits a significant increase of
Sharpe ratio.
H1:
H2:
H3:

4. Dyhrberg, A. H. (2016) - Baur, D. G., Dimpfl, T., & Kuck, K. (2017)
Bitcoin, gold and the US dollar. Negative correlation, useful for risk averse investors, in anticipation of market downturns.
Zhu, Y., Dickinson, D., & Li, J. (2017)
Bitcoins and the CPI, Dow Jones Industrial Average, US dollar Index (high), Federal Funds Rate, and Gold price (low).
Wong, W. S., Saerback, D., & Delgado Silva, D. (2018)
Payoff CRIX. Low correlations, new investment class.
Allan, M. J. (2014)
Bitcoin and Litecoin. Low correlations with traditional assets. CoVaR increases but additional risk compensated by higher returns.
Pellegrini, C. (2017)
Effect on a well-diversified portfolio of Bitcoin addition. Viable diversification tool, but appeal reduced by high volatility.
Combination of approaches
Different testing procedure
Multiple currencies of different type
Indexes are not purchasable in practice
Best single cryptos for portfolio hedging
Literature
Kajtazi, A., & Moro, A. (2018)
Bitcoins and American, European and Chinese assets comparison.
Master

5. Time range: 01/01/2015 - 01/01/2018
Number of obs.: 158 each - 948 total
Type: Weekly and US$
Source: Thomson Reuters DataStream
Bitcoin, Cash and Gold (BTC, BTH, BTG)
Ethereum, Ethereum Classic (ETH, ETHc)
Private Instant Verified Transactions (PIVX)
New Economy Movement (NEM)
Litecoin (LTC)
Decred (DCRD)
ZCash (ZCH)
Dash (DSH)
Dogecoin (DGC)
Monero (XRM)
Vertcoin (VRTC)
Verge (VRG)
Digibyte (DGB)
Ripple (XRP)
Bletchley20 (index)
Time range: 01/01/2015 - 01/01/2018
Number of obs.: 158 each – 2,844 total
Type: Weekly and US$
Source: CoinMetrics
*Volume, Market capitalization,
Price, Exchange volume
and Generated coins.
Risk-free rate: Weekly T-Bill rate from Kenneth R. French data
library (Ibbotson & Associates Inc. database)
Database Benchmark portfolio
MSCI World Index
MSCI Emerging Markets Index
MSCI EAFE Currency Index
S&P Enhanced World Commodity Index
MSCI Global Developed Real Estate Index
UBS Global Hedge Fund Index
Test portfolio*
Master

6. Summary statistics
Weekly returns Obs. Mean Std. Dev. Min Max
MSCI World 158 .002 .018 -.092 .052
MSCI Emerging 158 .002 .024 -.07 .061
MSCI Currencies 158 0 .01 -.03 .024
MSCI Real Estate 158 .001 .02 -.09 .05
S&P Commodities 158 -.001 .026 -.065 .066
UBS Hedge Funds 158 0 .014 -.054 .034
T-Bills weekly rate 158 .007 .008 0 .024
Bitcoin 158 .027 .085 -.186 .299
Bitcoin (Cash) 158 .02 .134 -.362 .537
Bitcoin (Gold) 158 .094 .553 -.946 4.53
Litecoin 158 .005 .105 -.287 .606
Ethereum 158 .063 .195 -.361 .916
Ethereum Classic 158 .011 .063 -.222 .235
Monero 158 .043 .182 -.278 1.128
ZCash 158 .008 .082 -.216 .287
Dash 158 .016 .211 -.705 1.357
Vertcoin 158 .037 .223 -.963 1.8
Decred 158 .014 .146 -.935 .516
Verge 158 .443 4.424 -.995 55.392
Digibyte 158 .038 .288 -.982 2.208
Dogecoin 158 .01 .147 -.737 1.091
NEM 158 .128 .503 -.962 3.618
PIVX 158 .031 .183 -.985 .81
Ripple 158 .025 .188 -.969 1.638
Bletchley20 158 .013 .075 -.233 .213
Bitcoin
Ethereum
Ripple
Bitcoin Cash
Litecoin
Monero
Dash
NEM
Ethereum Classic
0
50
100
150
200
Jan/15 Jan/16 Jan/17 Jan/18
BTC ETH XRP
-20%
0%
20%
40%
60%
80%
100%
MSCIWorld BTC ETH
• Indexed prices and returns
• Share of total market capitalization
InfographicsBenchmark Test assets

7. Intersection (H2 , H3)  𝛼J = 0
Spanning (H1)  α = 0 and 𝑖=1
𝑛
βi= 1
Rt
TEST – rf = αJ+ βn(Rn
BENCH – rf) + 𝜖t
Rt =
(INDEX𝑡−INDEX𝑡−1)
INDEX𝑡−1
%
Rt
TEST = α + β1R1
BENCH +… + βnRn
BENCH + 𝜖t
5
4
2
3
1
Methodology Mean-variance spanning and intersection test
Expected more significance for (3) because driven by differences
in mean returns and correlations while (5) by differences in
variance. According to existing literature, the latter should be
rejected more easily due to extreme volatilities.
Master

8. Correlation matrix
(!) Could change in future, if
more institutional investors start
buying digital tokens but,
currently, cryptocurrencies
mostly move relatively
independently to the market.
Master
Low correlations with
traditional investments,
weak relationships with
established asset classes.

9. Test results
Spanning
Bitcoin***
BCash Already spanned
BGold*
Litecoin*
Ethereum***
Ethereum Classic**
NEM***
Decred Already spanned
ZCash Already spanned
Dash Already spanned
Dogecoin Already spanned
PIVX Already spanned
Monero***
Vertcoin*
Verge Already spanned
Digibyte Already spanned
Ripple Already spanned
Bletchley20**
Intersection
Bitcoin**
BCash Not significant
BGold Not significant
Litecoin Not significant
Ethereum***
Ethereum Classic Not significant
NEM*
Decred Not significant
ZCash Not significant
Dash Not significant
Dogecoin Not significant
PIVX Not significant
Monero*
Vertcoin Not significant
Verge Not significant
Digibyte Not significant
Ripple Not significant
Bletchley20 Not significant

10. Robustness check & Portfolio optimization
Weekly:
Monthly:
Optimal weights: Weekly Monthly
Days-Weeks : high volatility;
Months : to little data available (36
months).
• Decreased power of testing procedure;
• Inherently more stable series;
• In the end, expected more significance
due to low volatility but only 2 cryptos
resulted; Vertcoin added to the sample.
..same testing procedure
using monthly data..
24%
-
-
-
23%
-
24%
13%
10%
4%
3%
21%
-
-
-
-
-
29%
13%
12%
14%
11%
• Rp:
• SDp:
• Sharpe:
• Rp:
• SDp:
• Sharpe:
MSCI World
MSCI Emerging
MSCI Currencies
S&P Commodities
MSCI Real Estate
UBS Hedge Funds
+ Bitcoin
+ Ethereum
+ Monero
+ NEM
+ Vertcoin
2,43%
4,04%
0,599
0,19%
1,76%
0,094
3,32%
4,43%
0,747
0,39%
1,97%
0,181
Benchmark
Test
Benchmark
Benchmark + Test

11. Conclusion
Master
H1: H2: H3:
• Young age, sparse data on price activity + only 3 years of analysis;
• Value function of utility  unclear which: as currency, remittance platform or distributed
network? (Unquantifiable variables affecting prices);
• Tested mean-variance properties but also sustainability issues has to be considered (high
carbon footprint of mining, regulations).
• Periods of even worse price corrections but DB estimate for 2030 10% GDP regulated through
blockchain technology, natural selection best cryptos;
• Important to develop “official” databases with financial variables to use in further researches to
shed light on long-term attractiveness for portfolio management.

12. THANK YOU!
Any Questions?

13. Variables BTC BCH LTC ETH ETHc XRM ZEC BCG DSH VRTC DCRD
MSCIW 0.110 0.012 -0.203 -0.065 0.020 -0.040 0.134 0.048 0.035 -0.014 0.080
MSCIE 0.149 0.059 -0.077 -0.116 0.080 0.005 0.132 -0.003 0.015 -0.008 0.106
MSCIEAFE 0.089 -0.004 0.012 -0.101 -0.042 -0.067 -0.006 -0.079 -0.040 0.010 -0.011
MSCIREAL 0.050 -0.031 -0.098 -0.139 -0.047 0.032 0.003 -0.022 0.108 0.005 0.078
S&PGSCI 0.064 0.032 -0.179 -0.023 0.043 -0.093 0.095 0.027 -0.050 0.110 0.038
UBSHF 0.091 -0.006 -0.082 -0.005 -0.033 -0.014 0.025 0.039 -0.045 0.062 0.006
Variables VRG DGB DGC NEM PIVX XRP Bletch20
MSCIW 0.037 0.109 -0.022 -0.037 0.009 0.062 -0.011
MSCIE 0.016 0.137 -0.056 -0.091 0.068 0.082 0.036
MSCIEAFE -0.031 0.058 -0.043 -0.025 0.070 0.016 -0.042
MSCIREAL -0.011 0.071 0.000 -0.091 0.053 0.122 -0.036
S&PGSCI -0.074 0.062 -0.023 -0.084 -0.025 0.006 -0.053
UBSHF -0.016 0.067 -0.022 0.033 0.047 0.067 -0.054
Table 3. Pairwise correlation matrix coefficients
In this table are reported the coefficients of pairwise correlation between the 18 test assets and 6 benchmark assets for
the period January 1, 2015 - January 1, 2018
Variables BTC BCH LTC ETH ETHc XRM ZEC BCG DSH VRTC DCRD
MSCIW 0.110 0.012 -0.203 -0.065 0.020 -0.040 0.134 0.048 0.035 -0.014 0.080
MSCIE 0.149 0.059 -0.077 -0.116 0.080 0.005 0.132 -0.003 0.015 -0.008 0.106
MSCIEAFE 0.089 -0.004 0.012 -0.101 -0.042 -0.067 -0.006 -0.079 -0.040 0.010 -0.011
MSCIREAL 0.050 -0.031 -0.098 -0.139 -0.047 0.032 0.003 -0.022 0.108 0.005 0.078
S&PGSCI 0.064 0.032 -0.179 -0.023 0.043 -0.093 0.095 0.027 -0.050 0.110 0.038
UBSHF 0.091 -0.006 -0.082 -0.005 -0.033 -0.014 0.025 0.039 -0.045 0.062 0.006
Appendix
Master

14. Test assets Bitcoin
Bitcoin
(Cash) Litecoin Ethereum
Ethereum
Classic Monero ZCash
Bitcoin
(Gold) Dash
Benchmark
MSCIW 0.542 -0.061 -2.162** 0.765 -0.014 -2.662 1.211 3.063 -0.599
(0.804) (1.276) (0.971) (1.829) (0.593) (1.716) (0.769) (5.221) (1.997)
MSCIE 0.740 1.132 1.117* -0.800 0.748* 0.922 0.624 -1.146 -0.652
(0.525) (0.833) (0.634) (1.194) (0.387) (1.120) (0.502) (3.408) (1.304)
MSCIEAFE 0.848 0.236 0.668 -4.712* -0.127 -4.621* 0.341 -14.405* -0.987
(1.223) (1.943) (1.478) (2.784) (0.902) (2.612) (1.170) (7.946) (3.039)
SPGSCI -0.130 0.028 -0.506 0.079 0.018 -0.768 -0.003 -0.140 -0.503
(0.324) (0.514) (0.391) (0.737) (0.239) (0.691) (0.310) (2.103) (0.805)
MSCIREAL -0.825 -1.163 0.263 -1.359 -0.776* 1.658 -1.367** -2.054 2.549*
(0.611) (0.970) (0.738) (1.391) (0.451) (1.305) (0.585) (3.970) (1.518)
UBSHF -0.196 -0.473 -0.665 3.186 -0.277 2.615 -0.394 9.836* -0.166
(0.878) (1.394) (1.060) (1.997) (0.647) (1.874) (0.840) (5.702) (2.181)
Constant 0.025*** 0.020* 0.007 0.066*** 0.010** 0.043*** 0.006 0.094** 0.015
F( 2, 151)
Prob > F
(0.007)
6.83***
0.0014
(0.011)
2.06
0.1305
(0.008)
2.70*
0.0707
(0.016)
10.42***
0.0001
(0.005)
4.44**
0.0133
(0.015)
6.36***
0.0022
(0.007)
0.69
0.5007
(0.045)
2.66*
0.0732
(0.017)
0.55
0.5754
Table 4. Regression results – Spanning test
This table reports the results of the mean-variance spanning test, when test assets returns are regressed on benchmark
returns. The benchmark is composed of: (1) MSCI world, (2) MSCI emerging markets, (3) MSCI EAFE Global
Currency index, (4) MSCI World Real Estate index, (5) Standard & Poor’s Goldman Sachs Commodity index and (6)
UBS Global Hedge Fund index. 17 single cryptocurrencies and one index, the Bletchley20, represents the test assets.
Coefficients are shown with standard errors between brackets; moreover, stars indicate statistical significance. Below,
the results and p-values of the F-test are reported. Recalling the methodology section, the following hypotheses are
tested (1) α = 0 and (2) β = 1.

15. F( 2, 151)
Prob > F
6.83***
0.0014
2.06
0.1305
2.70*
0.0707
10.42***
0.0001
4.44**
0.0133
6.36***
0.0022
0.69
0.5007
2.66*
0.0732
0.55
0.5754
Table 4 (continued)
Test assets Vertcoin Decred Verge Digibyte Dogecoin NEM PIVX Ripple Bl20
Benchmark
MSCIW -2.161 -0.184 43.363 1.269 -0.156 4.369 -1.245 -1.583 -0.033
(2.109) (1.396) (42.086) (2.735) (1.402) (4.752) (1.743) (1.780) (0.708)
MSCIE -0.612 0.852 9.205 1.931 -0.770 -2.370 1.133 0.351 0.679
(1.377) (0.911) (27.477) (1.786) (0.916) (3.102) (1.138) (1.162) (0.462)
MSCIEAFE -3.057 -0.578 -4.679 1.574 -1.265 -5.517 0.817 -2.905 -0.015
(3.210) (2.124) (64.060) (4.163) (2.135) (7.233) (2.654) (2.710) (1.078)
SPGSCI 1.424* -0.096 -24.152 -0.281 0.035 -1.952 -0.469 -0.321 -0.259
(0.850) (0.562) (16.957) (1.102) (0.565) (1.915) (0.702) (0.717) (0.285)
MSCIREAL 1.263 0.040 -29.073 -1.558 0.797 -2.912 0.467 1.957 -0.546
(1.604) (1.061) (32.001) (2.080) (1.066) (3.613) (1.326) (1.354) (0.538)
UBSHF 2.603 -0.057 -0.396 -0.442 0.694 6.285 0.037 2.350 -0.354
(2.304) (1.524) (45.968) (2.987) (1.532) (5.190) (1.904) (1.945) (0.774)
Constant 0.041** 0.013 0.367 0.034 0.010 0.128*** 0.030** 0.024 0.012**
(0.018) (0.012) (0.360) (0.023) (0.012) (0.041) (0.015) (0.015) (0.006)
Constant 0.041** 0.013 0.367 0.034 0.010 0.128*** 0.030** 0.024 0.012**
F( 2, 151)
Prob > F
(0.018)
2.79*
0.0648
(0.012)
0.79
0.4575
(0.360)
0.53
0.5916
(0.023)
1.20
0.3055
(0.012)
0.96
0.3846
(0.041)
5.08***
0.0073
(0.015)
2.03
0.1350
(0.015)
1.40
0.2505
(0.006)
3.86**
0.0231
Standard errors are in parenthesis
Table 4 (continued)
Master

16. Test assets
Bitcoin Bitcoin
(Cash)
Litecoin Ethereum Ethereum
Classic
Monero ZCash Bitcoin
(Gold)
Dash
Jensen’s Alpha 0.018** 0.014 -0.005 0.049*** 0.002 0.035* 0.005 0.068 0.004
F( 1, 151)
Prob > F
(0.008)
5.17**
0.0244
(0.013)
1.14
0.2881
(0.010)
0.23
0.6294
(0.019)
6.97***
0.0091
(0.006)
0.12
0.7281
(0.018)
3.86*
0.0513
(0.008)
0.46
0.4992
(0.053)
1.67
0.1984
(0.020)
0.04
0.8405
Table 5 (continued)
Test assets Vertcoin Decred Verge Digibyte Dogecoin NEM PIVX Ripple Bletchley20
Jensen’s Alpha 0.034 0.002 0.109 0.008 -0.012 0.089* 0.024 0.001 0.006
F( 1, 151)
Prob > F
(0.021)
2.46
0.1185
(0.014)
0.02
0.8911
(0.425)
0.07
0.7982
(0.027)
0.09
0.7616
(0.014)
0.73
0.3950
(0.048)
3.42*
0.0664
(0.018)
1.82
0.1798
(0.018)
0.00
0.9452
(0.007)
0.72
0.3965
Standard errors are in parenthesis
*** p<0.01, ** p<0.05, * p<0.1
Table 5. Regression results – Intersection test
This table reports the results of the mean-variance intersection test, when test assets returns are regressed on
benchmark returns. Coefficients are shown with standard errors between brackets and stars indicate statistical
significance. Results and p-values of the test are shown below, where the hypothesis tested is (1) α = 0
Master
Test assets
Bitcoin Bitcoin
(Cash)
Litecoin Ethereum Ethereum
Classic
Monero ZCash Bitcoin
(Gold)
Dash
Jensen’s Alpha 0.018** 0.014 -0.005 0.049*** 0.002 0.035* 0.005 0.068 0.004
F( 1, 151)
Prob > F
(0.008)
5.17**
0.0244
(0.013)
1.14
0.2881
(0.010)
0.23
0.6294
(0.019)
6.97***
0.0091
(0.006)
0.12
0.7281
(0.018)
3.86*
0.0513
(0.008)
0.46
0.4992
(0.053)
1.67
0.1984
(0.020)
0.04
0.8405
Table 5 (continued)
Test assets Vertcoin Decred Verge Digibyte Dogecoin NEM PIVX Ripple Bletchley20
Jensen’s Alpha 0.034 0.002 0.109 0.008 -0.012 0.089* 0.024 0.001 0.006
F( 1, 151)
Prob > F
(0.021)
2.46
0.1185
(0.014)
0.02
0.8911
(0.425)
0.07
0.7982
(0.027)
0.09
0.7616
(0.014)
0.73
0.3950
(0.048)
3.42*
0.0664
(0.018)
1.82
0.1798
(0.018)
0.00
0.9452
(0.007)
0.72
0.3965
Standard errors are in parenthesis
*** p<0.01, ** p<0.05, * p<0.1

17. Master
Figure A. Country weights
Graphs below show geographical diversification in the benchmark portfolio index: MSCI World and Emerging.