comparing bl and...
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![Page 1: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/1.jpg)
1 Black Litterman vs Markowitz, Gilles Desvilles, Cnam
Comparing BL and Markowitz
Input Summary
![Page 2: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/2.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 2
Monte Carlo Approach
500 000 views are generated through random draws from normal distributions
of mean 1% (Π) and volatilities 4.4%, 3.3% and 3.7% (Σ)
for A, B and C, pairs (A,B), (B,C) and (A,C), and triplet (A,B,C) with and without uncertainty
![Page 3: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/3.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 3
Monte Carlo Approach
On average Markowitz closer to the benchmark !
![Page 4: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/4.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 4
Monte Carlo Approach
On average Markowitz closer to the benchmark !
![Page 5: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/5.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 5
Monte Carlo Approach
Markowitz =
Black Litterman
![Page 6: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/6.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 6
Monte Carlo Approach
Markowitz sells short and borrows
less on average
![Page 7: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/7.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 7
Monte Carlo Approach
Markowitz sells short and borrows
less on average
![Page 8: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/8.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 8
Monte Carlo Approach
Markowitz =
Black Litterman
![Page 9: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/9.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 9
Monte Carlo Approach Return variance:
Markowitz dominates
Black-Litterman
![Page 10: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/10.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 10
Monte Carlo Approach Utility:
Markowitz dominates
Black-Litterman
![Page 11: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/11.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 11
Monte Carlo Approach Sharpe ratio:
Markowitz dominates
Black-Litterman
![Page 12: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/12.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 12
Monte Carlo Approach
Now with uncertainty in views:
Same dominance
![Page 13: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/13.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 13
Monte Carlo Approach
On average Markowitz closer to the benchmark !
![Page 14: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/14.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 14
Monte Carlo Approach
On average Markowitz closer to the benchmark !
![Page 15: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/15.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 15
Monte Carlo Approach
On average Black Litterman
closer to benchmark !
![Page 16: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/16.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 16
Monte Carlo Approach
Markowitz sells short and borrows
less on average
![Page 17: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/17.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 17
Monte Carlo Approach
Markowitz sells short and borrows
less on average
![Page 18: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/18.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 18
Monte Carlo Approach
Black Litterman sells short
and borrows less on average
![Page 19: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/19.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 19
Monte Carlo Approach
Now with uncertainty in views:
Same dominance
![Page 20: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/20.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 20
Monte Carlo Approach
Now with uncertainty in views:
Same dominance
![Page 21: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/21.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 21
Monte Carlo Approach
Now with uncertainty in views:
Same dominance
![Page 22: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/22.jpg)
Black Litterman vs Markowitz, Gilles Desvilles, Cnam 22
Conclusion • Big surprise: on average Black Litterman
beaten by Markowitz from weigthing stability standpoint !
• despite favorable δ (= 15)
• Has only average modest advantage when all assets are forecasted
• In all cases risk, Sharpe and utility deterministic dominance by Markowitz
![Page 23: Comparing BL and Markowitzrationnel-finance.com/Files/black_litterman_vs_markowitz_site_rationnel.pdfComparing BL and Markowitz Input Summary . Black Litterman vs Markowitz, Gilles](https://reader031.vdocuments.net/reader031/viewer/2022011900/5f03b82a7e708231d40a6f92/html5/thumbnails/23.jpg)
23 Black Litterman vs Markowitz, Gilles Desvilles, Cnam
Further Research
Heuristic analysis of the performance of the risky component of BL solution portfolio