# Bitcoin and Portfolio Diversification: A Portfolio Optimization Approach

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Data Description and Research Methodology

#### 3.1. Mean-Variance Optimization

#### 3.1.1. Scenario 1: Equal-Weighted or Naïve Portfolio (${\omega}_{i}=\frac{1}{N}\forall \text{}i$)

#### 3.1.2. Scenario 2: Semi-Constrained Max-Long Portfolio (${\omega}_{i}\in \mathbb{R}:{\omega}_{i}\le 0.25;\sum {\omega}_{i}=1)$

#### 3.1.3. Scenario 3: Semi-Constrained Min-Long Portfolio (${\omega}_{i}\in \mathbb{R}:{\omega}_{i}\ge 0.10;\sum {\omega}_{i}=1)$

#### 3.1.4. Scenario 4: Constrained Portfolio 1 (${\omega}_{i}\in \mathbb{R}:-0.25\le {\omega}_{i}\le 0.25;\sum {\omega}_{i}=1)$

#### 3.1.5. Scenario 5: Risk Parity (Long Only) Portfolio (${\omega}_{i}\Sigma {\sigma}_{i}^{2}=\frac{1}{N};{\omega}_{i}\in \mathbb{R}:{\omega}_{i}\ge 0;$ $\sum {\omega}_{i}=1)$

#### 3.1.6. Scenario 6: Risk Parity Unconstrained Portfolio (${\omega}_{i}\Sigma {\sigma}_{i}^{2}=\frac{1}{N};{\omega}_{i}\in \mathbb{R}:\underset{\omega}{\mathrm{max}}{\phi}_{i};\sum {\omega}_{i}=1)$

#### 3.1.7. Scenario 7: Unconstrained Portfolio (${\omega}_{i}\in \mathbb{R}:\underset{\omega}{\mathrm{max}}{\phi}_{i}:\sum {\omega}_{i}=1)$

#### 3.1.8. Scenario 8: Long Only Portfolio (${\omega}_{i}\in \mathbb{R}:{\omega}_{i}\ge 0;\sum {\omega}_{i}=1$)

#### 3.1.9. Scenario 9: Minimum Variance (${\omega}_{i}\in \mathbb{R}:\underset{\omega}{\mathrm{min}}{\sigma}_{P}:\sum {\omega}_{i}=1$)

#### 3.1.10. Scenario 10: Semi-Constrained Portfolio 2 (${\omega}_{i}\in \mathbb{R}:\underset{\omega}{\mathrm{max}}{\phi}_{i}:-1\le {\omega}_{i}\le 1;\sum {\omega}_{i}=1)$

## 4. Results and Analysis

#### 4.1. Descriptive Statistics

#### 4.2. Portfolio Optimization and Monte Carlo Simulation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A. Supplemental Dynamic Conditional Correlation Graphs

**Figure A1.**Dynamic conditional correlation—Bitcoin with all assets (DCC-GARCH). Note: The graph in Figure A1 suggests that Bitcoin exhibits a negative conditional correlation with Forex and BDI, while it exhibits a very low correlation with other assets throughout the sample period. The conditional correlation appears to sharply fluctuate (dip) during the periods of financial crisis (for instance, the COVID-19 crisis in early 2020), thereby suggesting some potential of Bitcoin as a hedge or safe haven against those assets.

**Figure A2.**Dynamic conditional correlation—Bitcoin with all assets (DCC-GARCH). Note: The graph in Figure A2 suggests that Bitcoin exhibits negative dynamic conditional correlation at low confidence intervals (negative price development of the reference asset) with a considerably low to negative correlation with all assets during normal price evolution. This indicates that Bitcoin may serve as a potential diversifier, while it may also have some potential properties ranging between a hedge and a safe haven; however, this property appears to dissipate with a slight change in the market conditions.

## Appendix B

Constraining Framework | Scenario 1Naïve Portfolio | Scenario 2Semi-Constrained Max-Long Portfolio | Scenario 3Semi-Constrained Min-Long Portfolio | Scenario 4Constrained Portfolio | ||||

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | |

${\mathit{\omega}}_{\mathit{i}}=\frac{1}{\mathit{N}}\forall \mathit{i}:$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:{\mathit{\omega}}_{\mathit{i}}\le 0.25;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:{\mathit{\omega}}_{\mathit{i}}\ge 0.10;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:-0.25\le {\mathit{\omega}}_{\mathit{i}}\le 0.25;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | |||||

Asset/Index | ||||||||

Forex | 16.67% | 14.29% | 25.00% | 25.00% | 10.00% | 10.00% | 25.00% | 25.00% |

Bitcoin | - | 14.29% | - | 2.95% | - | 10.00% | - | 2.95% |

Baltic Dry Index | 16.67% | 14.29% | 2.65% | 10.31% | 10.00% | 17.66% | 2.65% | 10.31% |

Equities | 16.67% | 14.29% | 25.00% | 25.00% | 50.00% | 32.34% | 25.00% | 25.00% |

Energy | 16.67% | 14.29% | 0.36% | −1.99% | 10.00% | 10.00% | 0.36% | −1.99% |

Corporate Bond | 16.67% | 14.29% | 25.00% | 25.00% | 10.00% | 10.00% | 25.00% | 25.00% |

Gold | 16.67% | 14.29% | 21.98% | 13.74% | 10.00% | 10.00% | 21.98% | 13.74% |

Average Returns (${\xi}_{P})$ | 0.071% | 0.292% | 0.087% | 0.255% | 0.146% | 0.386% | 0.087% | 0.255% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.97% | 2.58% | 0.90% | 1.64% | 1.76% | 2.81% | 0.90% | 1.64% |

Sharpe Ratio $\left(\phi \right)$ | 3.58% | 11.29% | 9.68% | 15.57% | 8.28% | 13.74% | 9.68% | 15.57% |

Constraining Framework | Scenario 5Risk Parity (Long Only) Portfolio | Scenario 6Risk Parity (Unconstrained) Portfolio | Scenario 7Long Only Portfolio | Scenario 8Unconstrained Portfolio | ||||

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | |

${\mathit{\sigma}}_{\mathit{i}}^{2}=\frac{1}{\mathit{N}};{\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:{\mathit{\omega}}_{\mathit{i}}\ge 0;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\sigma}}_{\mathit{i}}^{2}=\frac{1}{\mathit{N}};{\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:\underset{\mathit{\omega}}{\mathbf{max}}{\mathit{\phi}}_{\mathit{i}};$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:{\mathit{\omega}}_{\mathit{i}}\ge 0;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathbb{R}:\underset{\mathit{\omega}}{\mathbf{max}}{\mathit{\phi}}_{\mathit{i}};$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | |||||

Asset/Index | ||||||||

Forex | 0.00% | 6.04% | −118.94% | −28.69% | 66.64% | 66.60% | 67.08% | 67.18% |

Bitcoin | - | 4.90% | - | 8.84% | - | 0.29% | - | 0.44% |

Baltic Dry Index | 5.84% | 3.14% | 14.60% | 5.53% | 0.28% | 2.40% | 0.39% | 2.61% |

Equities | 19.76% | 22.75% | 43.20% | 23.08% | 20.59% | 20.25% | 22.62% | 22.96% |

Energy | 13.00% | 9.95% | 28.62% | 15.21% | 0.00% | 0.00% | −2.34% | −3.16% |

Corporate Bond | 37.00% | 27.22% | 79.94% | 48.96% | 5.05% | 5.60% | 4.56% | 4.99% |

Gold | 24.41% | 25.99% | 52.59% | 27.07% | 7.44% | 4.86% | 7.68% | 4.98% |

Average Returns (${\xi}_{P})$ | 0.064% | 0.123% | 0.084% | 0.155% | 0.087% | 0.125% | 0.093% | 0.137% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.37% | 1.36% | 3.61% | 2.06% | 0.48% | 0.60% | 0.51% | 0.65% |

Sharpe Ratio $\left(\phi \right)$ | 4.67% | 9.03% | 2.34% | 7.49% | 18.11% | 20.83% | 18.35% | 21.14% |

## Notes

1 | Data is available online: https://www.coindesk.com/price/Bitcoin (accessed on 10 June 2021). |

2 | Data is available online: https://www.coindesk.com/price/Bitcoin (accessed on 10 June 2021). |

3 | Data is available online: https://www.bloomberg.com/quote/BDIY:IND (accessed on 10 May 2020). |

4 | Data is available online: https://www.coindesk.com/price/Bitcoin (accessed on 10 June 2021). |

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Variable/Index/Asset | Mnemonics | Indices and Definition |
---|---|---|

Exchange Rate/Forex | US $CWBN | US Nominal Dollar Broad Index, representing the number of US dollars for 1 Euro. The USD–Euro exchange rate is considered the most important indicator of Forex markets in the world. The importance of the USD–Euro exchange rate is due to the investment and trade of these two large economic areas with one another. The trade and investment among the two regions is such that the prices in these economic regions are arbitraged against the exchange rate (Brian 2008). |

Economic Activity | BALTICF | Baltic Exchange Dry Index (BDI). The BDI provides insights into global supply and demand trends and is considered an indicator of global economic activity. The Index was first started in January 1985 by the London-based Baltic Exchange. The BDI is a composite of the Capesize, Panamax, Handysize, and Supramax subindices.3 It measures the changes in the cost of transporting raw materials across more than 20 different sea routes. |

Bitcoin | BTCTOU$ | USD to Bitcoin (Bitstamp). Bitcoin is a special kind of asset called cryptocurrency and has the highest market capitalization of all cryptocurrencies. The market capitalization of Bitcoin currently sits at USD 690 billion as of 10 June 2021.4 |

Stock Market | SBBUSD$ | Standard and Poor’s United States Broad Market Index (BMI). The S&P 500 is considered the best representation of the US stock market. The S&P 500 Index is one of the most used proxies for the stock market and captures the performance of 500 large companies listed on the US stock exchanges. |

Energy Market | DJUBENS | Formerly known as the Dow Jones–UBS Energy Spot Subindex (DJUBENS), this index measures the price movements of energy included in the Bloomberg CI and select subindexes. |

Corporate Bond | U:IGLB | iShares Long-Term Corporate Bond ETF. The iShares Long-Term Corporate Bond ETF seeks to track the investment results of an index composed of US dollar-denominated, investment-grade corporate bonds with remaining maturities greater than ten years. |

Gold | NGCC.01 | CMX-Gold 100 Ounce TRC1. This index quotes the price of 100 ounces of 0.995 fine (24-karat) gold in US dollars. |

BDI | Bitcoin | Bonds | Energy | Equity | Forex | Gold | |
---|---|---|---|---|---|---|---|

Mean | 0.001248 | 0.016187 | 0.000290 | −0.000354 | 0.002588 | 0.000483 | −0.000022 |

Median | 0.001340 | 0.009284 | 0.001238 | 0.000430 | 0.003559 | 0.000300 | 0.000526 |

Maximum | 0.470774 | 0.665419 | 0.083595 | 0.158034 | 0.160962 | 0.042156 | 0.061457 |

Minimum | −0.335448 | −0.919529 | −0.110510 | −0.236569 | −0.153451 | −0.022924 | −0.144423 |

Std. Dev. | 0.099 | 0.127 | 0.014 | 0.038 | 0.023 | 0.007 | 0.022 |

Sharpe Ratio | 1.26% | 12.71% | 2.05% | −0.91% | 10.88% | 6.62% | −0.10% |

Skewness | 0.138 | −0.426 | −1.079 | −0.558 | −0.550 | 0.634 | −1.071 |

Kurtosis | 4.491 | 11.502 | 15.517 | 6.341 | 12.781 | 6.194 | 8.567 |

Jarque–Bera | 48.674 | 1545.651 | 3415.117 | 262.738 | 2050.655 | 250.075 | 753.402 |

Probability | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Forex | BDI | Bitcoin | Equity | Energy | Bonds | Gold | |
---|---|---|---|---|---|---|---|

Forex | 1.000 | ||||||

BDI | 0.000 | 1.000 | |||||

Bitcoin | −0.029 | −0.004 | 1.000 | ||||

Equity | −0.447 | 0.044 | 0.107 | 1.000 | |||

Energy | −0.287 | 0.129 | 0.082 | 0.367 | 1.000 | ||

Bonds | −0.325 | −0.050 | 0.058 | 0.177 | −0.006 | 1.000 | |

Gold | −0.410 | −0.076 | 0.179 | 0.018 | 0.023 | 0.335 | 1.000 |

Constraining Framework | Scenario 1 Naïve Portfolio | Scenario 2 Semi-Constrained Max-Long Portfolio | Scenario 3 Semi-Constrained Min-Long Portfolio | Scenario 4 Constrained Portfolio | ||||
---|---|---|---|---|---|---|---|---|

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | |

${\mathit{\omega}}_{\mathit{i}}=\frac{1}{\mathit{N}}\forall \mathit{i};$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:{\mathit{\omega}}_{\mathit{i}}\le 0.25;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:{\mathit{\omega}}_{\mathit{i}}\ge 0.10;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:-0.25\le {\mathit{\omega}}_{\mathit{i}}\le 0.25;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | |||||

Bitcoin Weight | - | 14.29% | - | 2.95% | - | 10.00% | - | 2.95% |

Average Returns (${\xi}_{P})$ | 0.071% | 0.292% | 0.087% | 0.255% | 0.146% | 0.386% | 0.087% | 0.255% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.97% | 2.58% | 0.90% | 1.64% | 1.76% | 2.81% | 0.90% | 1.64% |

Sharpe Ratio $\left(\phi \right)$ | 3.58% | 11.29% | 9.68% | 15.57% | 8.28% | 13.74% | 9.68% | 15.57% |

HS VaR (95%) | 3.03% | 3.77% | 1.12% | 2.09% | 2.70% | 3.93% | 1.12% | 2.09% |

HS VaR (99%) | 4.69% | 6.71% | 2.39% | 4.23% | 4.69% | 7.07% | 2.39% | 4.23% |

VCV VaR (95%) | 3.17% | 3.96% | 1.39% | 2.44% | 2.75% | 4.23% | 1.39% | 2.44% |

VCV VaR (99%) | 4.51% | 5.72% | 2.00% | 3.55% | 3.95% | 6.15% | 2.00% | 3.55% |

HS CVaR (95%) | 4.25% | 5.88% | 1.98% | 3.66% | 3.97% | 6.37% | 1.98% | 3.66% |

HS CVaR (99%) | 5.61% | 10.22% | 3.89% | 7.85% | 6.91% | 12.28% | 3.89% | 7.85% |

VCV CVaR (95%) | 3.96% | 4.99% | 1.74% | 3.09% | 3.45% | 5.35% | 1.74% | 3.09% |

VCV CVaR (99%) | 5.06% | 6.43% | 2.24% | 4.00% | 4.44% | 6.92% | 2.24% | 4.00% |

Probability of Loss (HS) | 48.82% | 41.34% | 41.93% | 39.37% | 43.31% | 39.76% | 41.93% | 39.37% |

Portfolio Framework | Scenario 1 Naïve Portfolio | Scenario 2 Semi-Constrained Max-Long Portfolio | Scenario 3 Semi-Constrained Min-Long Portfolio | Scenario 4 Constrained Portfolio | ||||
---|---|---|---|---|---|---|---|---|

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | |

Average Returns (${\xi}_{P})$ | 0.065% | 0.28% | 0.083% | 0.23% | 0.138% | 0.37% | 0.087% | 0.26% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.98% | 2.57% | 0.89% | 1.64% | 1.77% | 2.82% | 0.90% | 1.65% |

Sharpe Ratio $\left(\phi \right)$ | 3.28% | 10.90% | 9.30% | 13.94% | 7.79% | 13.29% | 9.67% | 15.52% |

MC CVaR (95%) | 3.97% | 4.97% | 1.74% | 3.12% | 3.48% | 5.38% | 1.75% | 3.12% |

MC CVaR (99%) | 5.08% | 6.41% | 2.24% | 4.03% | 4.47% | 6.95% | 2.26% | 4.04% |

Probability of Loss (MC) | 48.72% | 45.45% | 46.06% | 44.21% | 47.26% | 44.26% | 46.17% | 43.68% |

Constraining Framework | Scenario 5 Risk Parity (Long Only) Portfolio | Scenario 6 Risk Parity (Unconstrained) Portfolio | Scenario 7 Long Only Portfolio | Scenario 8 Unconstrained Portfolio | ||||
---|---|---|---|---|---|---|---|---|

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | |

${\mathit{\omega}}_{\mathit{i}}\Sigma {\mathit{\sigma}}_{\mathit{i}}^{2}=\frac{1}{\mathit{N}};{\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:{\mathit{\omega}}_{\mathit{i}}\ge 0;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\Sigma {\mathit{\sigma}}_{\mathit{i}}^{2}=\frac{1}{\mathit{N}};{\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:\underset{\mathit{\omega}}{\mathit{m}\mathit{a}\mathit{x}}{\mathit{\phi}}_{\mathit{i}};$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:{\mathit{\omega}}_{\mathit{i}}\ge 0;$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | ${\mathit{\omega}}_{\mathit{i}}\in \mathit{\mathbb{R}}:\underset{\mathit{\omega}}{\mathit{m}\mathit{a}\mathit{x}}{\mathit{\phi}}_{\mathit{i}};$$\sum {\mathit{\omega}}_{\mathit{i}}=1$ | |||||

Bitcoin Weight | - | 4.90% | - | 8.84% | - | 0.29% | - | 0.44% |

Average Returns (${\xi}_{P})$ | 0.064% | 0.123% | 0.084% | 0.155% | 0.087% | 0.125% | 0.093% | 0.137% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.37% | 1.36% | 3.61% | 2.06% | 0.48% | 0.60% | 0.51% | 0.65% |

Sharpe Ratio $\left(\phi \right)$ | 4.67% | 9.03% | 2.34% | 7.49% | 18.11% | 20.83% | 18.35% | 21.14% |

HS VaR (95%) | 1.89% | 1.68% | 5.37% | 2.90% | 0.58% | 0.76% | 0.65% | 0.48% |

HS VaR (99%) | 3.44% | 3.78% | 8.39% | 5.31% | 1.52% | 2.14% | 1.48% | 1.75% |

VCV VaR (95%) | 2.19% | 2.11% | 5.85% | 3.24% | 0.70% | 0.86% | 0.74% | 0.93% |

VCV VaR (99%) | 3.12% | 3.04% | 8.31% | 4.65% | 1.03% | 1.27% | 1.09% | 1.37% |

HS CVaR (95%) | 3.10% | 3.09% | 8.13% | 4.62% | 1.03% | 1.33% | 1.07% | 1.39% |

HS CVaR (99%) | 5.23% | 6.08% | 14.10% | 8.63% | 1.93% | 2.79% | 1.86% | 2.82% |

VCV CVaR (95%) | 2.74% | 2.65% | 7.28% | 4.06% | 0.90% | 1.10% | 0.95% | 1.19% |

VCV CVaR (99%) | 3.50% | 3.41% | 9.30% | 5.21% | 1.16% | 1.44% | 1.23% | 1.55% |

Probability of Loss (HS) | 48.82% | 43.11% | 48.03% | 45.87% | 41.54% | 39.37% | 41.73% | 37.99% |

Portfolio Framework | Scenario 5 Risk Parity (Long Only) Portfolio | Scenario 6 Risk Parity (Unconstrained) Portfolio | Scenario 7 Long Only Portfolio | Scenario 8 Unconstrained Portfolio | ||||
---|---|---|---|---|---|---|---|---|

Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | Without Bitcoin | With Bitcoin | |

Average Returns (${\xi}_{P})$ | 0.043% | 0.12% | 0.070% | 0.14% | 0.084% | 0.13% | 0.094% | 0.15% |

Standard Deviation $\left(\mathcal{R}\right)$ | 1.35% | 1.33% | 3.65% | 2.06% | 0.48% | 0.60% | 0.51% | 0.65% |

Sharpe Ratio $\left(\phi \right)$ | 3.21% | 9.33% | 1.92% | 7.02% | 17.53% | 20.99% | 18.60% | 22.38% |

MC CVaR (95%) | 2.72% | 2.60% | 7.38% | 4.07% | 0.89% | 1.10% | 0.94% | 1.19% |

MC CVaR (99%) | 3.48% | 3.34% | 9.42% | 5.22% | 1.16% | 1.44% | 1.22% | 1.55% |

Probability of Loss (MC) | 48.82% | 46.18% | 49.99% | 47.43% | 42.67% | 44.27% | 42.31% | 41.62% |

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## Share and Cite

**MDPI and ACS Style**

Bakry, W.; Rashid, A.; Al-Mohamad, S.; El-Kanj, N.
Bitcoin and Portfolio Diversification: A Portfolio Optimization Approach. *J. Risk Financial Manag.* **2021**, *14*, 282.
https://doi.org/10.3390/jrfm14070282

**AMA Style**

Bakry W, Rashid A, Al-Mohamad S, El-Kanj N.
Bitcoin and Portfolio Diversification: A Portfolio Optimization Approach. *Journal of Risk and Financial Management*. 2021; 14(7):282.
https://doi.org/10.3390/jrfm14070282

**Chicago/Turabian Style**

Bakry, Walid, Audil Rashid, Somar Al-Mohamad, and Nasser El-Kanj.
2021. "Bitcoin and Portfolio Diversification: A Portfolio Optimization Approach" *Journal of Risk and Financial Management* 14, no. 7: 282.
https://doi.org/10.3390/jrfm14070282