# Good old Black Litterman

Hey guys/gals… I kinda get the BL, but one thing I dont seem to understand. What is meant by the following phrase…“Back out the equilibrium returns implied by these inputs using a reverse optimization process”, I mostly have a hard time with the “backing out the equilibrium returns & reverse optimization process” I understand the global index port part of the BL process, and the fact that an analyst will us the inputs formt he global index, and because these inputs are from a diversified global port they should represent average mkt expectations, but the 2 statements confuse me. Can any of you guys re-explain it in a different manner? Once this is done, the analyst will incorporate his views (ie tweak what he sees is necessary) and adjusts the returns accordingly. Does he adjust the other inputs as well (stdev, corr etc…) or only the returns, and if its only the returns, does he then work backwards to find out what the other variables are? Thanks!

sbmfj, Let me take a stab at this - though I’m no expert. Also, I’m using the CFAI materials which seem a little different than what you’re using given what’s in quotes. With reverse optimization what you are doing is reverse engineering the historical return of each individual product implied by the current weights within the market portfolio (or the index that’s under consideration) and the portfolio’s historical return. In the CFAI readings they actually build an efficient frontier using the standard deviations of each individual product and the implied returns. I think they reference using the covariance matrix because you would need correlation coefficients (and individual product variances) to determine the portfolio’s (or index’s) variance. In the next step you adjust only return, not std. dev., correlations, etc. These variables are determined computaionally on a historical basis. I think it’d be pretty tough to alter anything other than expected return.

I read this online and this is what i understand… Mean variance approach suffers from a serious problem: although the covariances of a assets can be adequately estimated, it is difficult to come up with reasonable estimates of expected returns.B-L bypasses this problem by not requiring the user to input estimates of expected return. So by using current market weights, S.D and covariance, one can backout equilibrium expected return. Next step is to adjust these expected returns depending how managers expectation differs from the market.

Here is my summary of BL: 1) Esimate covariance matrix (B) 2) Use market weights (w) to come up with expected excess returns (er): er = B*w 3) Come up with some opinions p with corresponding covariance matrix Omega (reflects confidence in opinions and there relationships). 4) Use GMM to find portfolio weights.

This is the LOS - discuss the strengths and limitations of the following approaches to asset allocation: mean–variance, resampled efficient frontier, Black–Litterman, Monte Carlo simulation, ALM, and experience based; (CFA Institute. Level 3 Volume 3 - Portfolio Management—Study Sessions 6-8, 3rd Edition. Pearson Custom Publishing 225). Pretty much all you have to know is that UBL allows for short sales and gives you portfolio that make more sense than regular MVO because of the shorting constraint. And that BL, while constrained, allows investors to use market data to pull out expected returns and then adjust them with their own views - this is easier than coming up with CMEs on your own from zero. I’m pretty sure that is all you have to know. This curriculum has so much info that it is very important to read the LOS’s and not over do it. This exam is about a general understanding of CFAI’s investment process, it is not financial trivial pursuit like LI and LII.

thanks, the tips were helpful. Ill re-read them after work, as its hard to concentrate now…

sebrock Wrote: ------------------------------------------------------- > This is the LOS - > > discuss the strengths and limitations of the > following approaches to asset allocation: > mean–variance, resampled efficient frontier, > Black–Litterman, Monte Carlo simulation, ALM, and > experience based; (CFA Institute. Level 3 Volume 3 > - Portfolio Management—Study Sessions 6-8, 3rd > Edition. Pearson Custom Publishing 225). > > Pretty much all you have to know is that UBL > allows for short sales and gives you portfolio > that make more sense than regular MVO because of > the shorting constraint. And that BL, while > constrained, allows investors to use market data > to pull out expected returns and then adjust them > with their own views - this is easier than coming > up with CMEs on your own from zero. > > I’m pretty sure that is all you have to know. This > curriculum has so much info that it is very > important to read the LOS’s and not over do it. > This exam is about a general understanding of > CFAI’s investment process, it is not financial > trivial pursuit like LI and LII. Well said and good advice to keep in mind when deciding what to “ignore” when going through the CFA text in general.

Lots of language but its simpler. I think of it more as the opposite of Mean Variance. For average risk you end up with the Global Portfolio.

It has been a while since I reviewed this but I am remembering the following related to BL: >Regular mean variance framework suffers from estimation bias of the expected return (uses historical standard deviation, correlations, and estimated expected returns) >overcome estimation bias by using BL, which uses the weights of the assets in a global index to back out their implied expected returns using a reverse optimization process >adjust this implied expected return based on your expectations >use this adjusted expected return to run a traditional mean variance framework to construct an efficient frontier Let me know if you all agree with this and if I am missing anything.

BL was tested in the Essay part of the exam in 2007 and I would guess it is prime material for 2010. Can anyone describe what is the difference between Unconstrained (short sales allowed) and BL model? I am reading from CFAI Text. The only thing I can come up with is the short sale issue, is there anything else.

I agree with the observation that you need to understant the key characteristics and strengths/weaknesses of each of the asset allocation approaches, so be careful not to “overanalyze” the minute details. Here’s how I understand the Black-Litterman (BL) approach to asset allocation. 1. We are using the mean-variance optimization to derive the efficient frontier. 2. We are combining the efficient frontier with a risk free asset (Rf) 3. The tangent line from Rf to the efficient frontier (also known as the CML) dominates any portfolio on the efficient frontier in terms of risk and return and “touches” the efficient frontier at global market portfolio (M). 4. Each investor/portfolio manager will have his/her own views on the global market portfolio return expectations and his/her own risk tolerance. 5. If the return expectations are “average” this implies “average” risk tolerance, and the investor/PM should simply choose to invest in the global market portfolio (M). If the return expectations are “below average” this implies a “below average” risk tolerance, and the investor/PM should select a mix of Rf and M on the CML, with the allocation lying somewhere between Rf and M on the CML depending on the standard deviation threshold of the investor. If the return expectations are “above average” this implies an “above average” risk tolerance, and the investor/PM should leverage up by selling short Rf (borrowing) and investing that additional amount in the global market portflio, with the allocation lying somewhere above M on the CML (assuming no short sale restrictions), depending on the standard deviation threshold of the investor. 6. The result is that you have a highly diversified portfolio (given the use of the global market portfolio) – Strength, while the use of historical volatility (which may not be appropriate in the future) and the complexity of mean-variance optimization are the main weaknesses. Hope the above is clear. Inptut/corrections/suggestions welcome!

askajan Wrote: ------------------------------------------------------- > It has been a while since I reviewed this but I am > remembering the following related to BL: > > >Regular mean variance framework suffers from > estimation bias of the expected return (uses > historical standard deviation, correlations, and > estimated expected returns) > >overcome estimation bias by using BL, which uses > the weights of the assets in a global index to > back out their implied expected returns using a > reverse optimization process > >adjust this implied expected return based on your > expectations > >use this adjusted expected return to run a > traditional mean variance framework to construct > an efficient frontier > > Let me know if you all agree with this and if I am > missing anything. Thanks! This is exactly what I have “memorized”.

ylager Wrote: ------------------------------------------------------- > I agree with the observation that you need to > understant the key characteristics and > strengths/weaknesses of each of the asset > allocation approaches, so be careful not to > “overanalyze” the minute details. > > Here’s how I understand the Black-Litterman (BL) > approach to asset allocation. > > 1. We are using the mean-variance optimization to > derive the efficient frontier. > 2. We are combining the efficient frontier with a > risk free asset (Rf) > 3. The tangent line from Rf to the efficient > frontier (also known as the CML) dominates any > portfolio on the efficient frontier in terms of > risk and return and “touches” the efficient > frontier at global market portfolio (M). > 4. Each investor/portfolio manager will have > his/her own views on the global market portfolio > return expectations and his/her own risk > tolerance. > 5. If the return expectations are “average” this > implies “average” risk tolerance, and the > investor/PM should simply choose to invest in the > global market portfolio (M). If the return > expectations are “below average” this implies a > “below average” risk tolerance, and the > investor/PM should select a mix of Rf and M on the > CML, with the allocation lying somewhere between > Rf and M on the CML depending on the standard > deviation threshold of the investor. If the return > expectations are “above average” this implies an > “above average” risk tolerance, and the > investor/PM should leverage up by selling short Rf > (borrowing) and investing that additional amount > in the global market portflio, with the allocation > lying somewhere above M on the CML (assuming no > short sale restrictions), depending on the > standard deviation threshold of the investor. > 6. The result is that you have a highly > diversified portfolio (given the use of the global > market portfolio) – Strength, while the use of > historical volatility (which may not be > appropriate in the future) and the complexity of > mean-variance optimization are the main > weaknesses. > > Hope the above is clear. > Inptut/corrections/suggestions welcome! ylager: Not sure where did you get the idea of risk free asset in BL? I think that the most important thing to note about BL is this: 1. BL Model reverse engineers the expected returns implicit in a diversified portfolio (reverse optimization) and combines with an investor’s own views on expected returns. 2. Ensures strategic allocation is well diversified 3. Improvement on MVO - no large positions which is a common result in unconstrained MVO 4. Combining inv views with equil returns helps dampen the effect of any extreme views the inv holds which could otherwise dominate the optimization