1 Black Litterman vs Markowitz, Gilles Desvilles, Cnam

Comparing BL and Markowitz

Input Summary

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

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 3

Monte Carlo Approach

On average Markowitz closer to the benchmark !

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 4

Monte Carlo Approach

On average Markowitz closer to the benchmark !

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 5

Monte Carlo Approach

Markowitz =

Black Litterman

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 6

Monte Carlo Approach

Markowitz sells short and borrows

less on average

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 7

Monte Carlo Approach

Markowitz sells short and borrows

less on average

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 8

Monte Carlo Approach

Markowitz =

Black Litterman

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 9

Monte Carlo Approach Return variance:

Markowitz dominates

Black-Litterman

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 10

Monte Carlo Approach Utility:

Markowitz dominates

Black-Litterman

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 11

Monte Carlo Approach Sharpe ratio:

Markowitz dominates

Black-Litterman

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 12

Monte Carlo Approach

Now with uncertainty in views:

Same dominance

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 13

Monte Carlo Approach

On average Markowitz closer to the benchmark !

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 14

Monte Carlo Approach

On average Markowitz closer to the benchmark !

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 15

Monte Carlo Approach

On average Black Litterman

closer to benchmark !

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 16

Monte Carlo Approach

Markowitz sells short and borrows

less on average

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 17

Monte Carlo Approach

Markowitz sells short and borrows

less on average

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 18

Monte Carlo Approach

Black Litterman sells short

and borrows less on average

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 19

Monte Carlo Approach

Now with uncertainty in views:

Same dominance

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 20

Monte Carlo Approach

Now with uncertainty in views:

Same dominance

Black Litterman vs Markowitz, Gilles Desvilles, Cnam 21

Monte Carlo Approach

Now with uncertainty in views:

Same dominance

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

23 Black Litterman vs Markowitz, Gilles Desvilles, Cnam

Further Research

Heuristic analysis of the performance of the risky component of BL solution portfolio