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kaveh
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Joined: November 28th, 2007, 9:00 pm

Black-Litterman optimization doesn't work

November 27th, 2013, 7:58 pm

Hi everyone,Hope someone can help me on this topic. I am trying to build a simple black-litterman module for fixed income asset allocation (Canadian bonds, High yield, etc.) and I just can't get reasonable results out of optimizer.Here is the setup: I have 7 assets for which I calculate the implied returns (RiskAversion*Cov*Weq). Equilibrium weights (Weq) come from an arbitrary index which I have to follow, Risk aversion of such portfolio is around 28 (does it make sense?). When I express my views through P and Q matrices I get reasonable new expected returns (returns are tilted according to my views). I also calculate the new Cov matrix and feed these results to a simple optimizaerr with constraints on sum of weights (equal to 1) and lower and upper bands (no shortselling, max weight 1). This gives me a concentrated portfolio in one asset only which is exactly what BL model is promising yo avoid. My main question is, has anybody encountered such a thing? Is there any trick there that I ma not applying? Am I not supposed to get stable weights out of an optimizer?When I use the data of He and Litterman and use the closed form formula for optimal weights (inv(Cov)* Ret)/RiskAversion) in my program, I get the same results that they have in their paper. So it seems that my calculation of new returns and Cov are correct, but still no result.Any insight or recommendation is most welcome and appreciated. If you need to check my program and data I can send them to you upon request. Thanks in advance.
 
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Rufus
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Joined: January 18th, 2002, 5:24 pm

Black-Litterman optimization doesn't work

December 18th, 2013, 1:42 pm

I think once you have calculated the equilibrium portfolio you then apply the B-L formula with your view matrices (P & Q) to get the adjusted portfolio weights then solve the unconstrained optimisation problem [$]w = ( \lambda \Sigma)^{-1}\mu[$].This should adjust the equilibrium weights of the assets that have a view expressed although the others may also change due to [$]\Sigma[$].Do you have this paper: Step by Step Guide to Black Litterman ?
Last edited by Rufus on December 17th, 2013, 11:00 pm, edited 1 time in total.
 
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kaveh
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Joined: November 28th, 2007, 9:00 pm

Black-Litterman optimization doesn't work

December 18th, 2013, 2:21 pm

Hey all, and thanks Rufus for taking the time to reply. I wanted to delete this thread as I have found the problem with my method, but have decided to keep it in case somebody has the same problem. So, turns out my mistake was that I was maximizing the Sharpe ratio where I should have maximized the utility function. In markowitz framework these two are basically the same but not in BL.