can someone explain to me why the BLM will always end up a more diversified portfolio than traditional mean-variance approach? i understand that when we back out from a well diversified index (1st step of BLM), we have a fairly diversified portfolio. but, the 2nd step of BLM allows manager to express his/her own views on assets (return expectation, risk, etc) in the portfolio. with changed views (say, manager is very bullish on international stocks), an optimizer can easily spit out an undiversified portfolio (a 100% international portfolio). if so, why bother?
What’s this “always” thing?
this seems to be the most important reason why the industry widely adopts BLM versus the straight forward MV, especially in managing global macro’s. if you plan to have an interview at GSAM where Bob Litterman is the head of the division, you better know the answer.
I doubt that Litterman ould say something like “you always end up with a more diversified portfolio than using MV optimization”. I don’t even know what that would mean - I can think of about 20 different definitions of “diversified” and none of them are robust enough to ensure that Black-Litterman + some analyst’s wacky views results in something more diversified. If I talked to Litterman (which I have never done), I also doubt that he would expect me to think that Black-Litterman was very special. It’s a pretty routine Bayesianesque calculation which he would expect me to know. The world of computational finance is about 5 quantum leaps tougher than B-L.
i dont disagree with you at all. but, the review of asset allocations indeed highlighted the advantage of BL over MV as “yields more diversified portfolios”, which is where I got lost. i dont know 20 different definitions of “diversified” except the one given by cfai. my question is purely confined in this very context as well. as to if routine bayesian plus mv is leaps behind the itos lemma, i dont really care. i just hope i could manage my L3 exam on the basics of this subject. appreciated if you dont mind sharing your view on the B-L!
I don’t think B-L is even related to Ito’s lemma in any way that I know.
BLM is not really well explained in the CFAI text but I think that they say it “generally” results in a more diversified portfolio. I wouldn’t read it as “always”. Reason is that it uses “equilibrium returns” which temper investor views that potentially lead to greater weighting in fewer asset classes under MVO method. The part I don’t really understand is where the equilibrium returns comes from – I know you assume that the market portfolio is on the EF and backsolve, but the text doesn’t really demonstrate how this is done or even the theory behind why it works. Anybody have ideas on this last part?
I think you just have to remember the two advantages of Black-Litterman: A) More diversified portfolio. B) Includes the view of the investor related to the assets class performance and the strength of this view. Ponpon
TooOld4This Wrote: ------------------------------------------------------- > BLM is not really well explained in the CFAI text > but I think that they say it “generally” results > in a more diversified portfolio. I wouldn’t read > it as “always”. > > Reason is that it uses “equilibrium returns” which > temper investor views that potentially lead to > greater weighting in fewer asset classes under MVO > method. > > The part I don’t really understand is where the > equilibrium returns comes from – I know you > assume that the market portfolio is on the EF and > backsolve, but the text doesn’t really demonstrate > how this is done or even the theory behind why it > works. Anybody have ideas on this last part? When in doubt, google… http://www.styleadvisor.com/resources/conference/2004/AllocationADVISOR%202004.pdf
ahaha, that was an interesting link, thanks. my feeble understanding is that with a mechanical MVO approach one can end up with a simplistic portfolio. rough example: small cap stocks have outperformed other stocks, high yield bonds have outperformed other bonds. Let’s put all our money in small cap stocks and high yield bonds! Great idea! Oh wait, now we’re concentrated in two asset classes that are poised to underperform over the next multi year period. Enter the Black Litterman model. BL takes into consideration the relative current valuation of the asset classes and models the portfolio based on future expectations rather than historical results. BL is almost a tactical overlay of the traditional MVO process. This is imho, and based on reading nothing more than a paragraph or two about BL.
I think the problem is that your allocation is based on a forward looking correlation matrix, where the process takes the “oh sure, just use the correlation matrix”:position. In general, I think figuring out n correlations to base your portfolio on is a lot easier said than done; however, this is really a JoeyD question and not an ahahah question…
JoeyDVivre I really want to know those 20+ definitions of “diversified”, I suppose you mean definitions with certain level of mathematical rigour. A survay study of them would be interesting. Do you know of any?
Hmm. 1) # of securities 2) maximum variance attributable to 1 security/portfolio variance 3) eigenvalue of first principal component 4) percentage of variability attributable to first k principal components 5) The intraportfolio correlation (Q) 6) The number of risk factors from some factor model (e.g., RiskMetrics) and just keep listing crap like that…
If I met Litterman I would punch him right in the face.
May be an alternative understanding of the Black-Litterman (BL) model (and its utility) could be something like this: 1- Black-Litterman (and more generally Bayesian inference) is about combining two distinctive Sources of information (S1 and S2) to produce an ‘as good as possible’ guest (Forecast). 2- The degree to which S1 and S2 are respectively represented in the output (the distribution of the forecast) is controlled by the reliability the information (eg as measured by the covariance matrices Cov1 and Cov2 of S1 and S2). If Cov2 is rather large compared to Cov2, the forecast will be made predominantly from S1 because S1 is the most reliable source of information, and vice versa. 3- BL suggested to combine the Views held by the Analysts with the information publicly available (eg derived from the observed historics of stock returns). 4- BL suggested to mix Analyst Views with the ‘Implied Returns’ rather than with the ‘Historical Returns’ because their ultimate goal is Portfolio Allocation. The reason for using ‘Implied Returns’ derives from the fact that Historical Returns are known to be very poor quality input for Markowitz-type Portfolio optimisation (they produce corner type solution, see related message). 5- ‘Implied return’ are obtained by reverse optimisation, ie assuming the covariance matrix known (and therefore of good quality), find the set of Returns that when imputed in Markowitz-type optimisation reproduces the (known) market capitalisation (the relative weight of each position making the market). In practical application of BL, the market capitalisation is limited to a restricted number of assets. 6- BL tends to produce well-balanced portfolio because in its practical use the Implied Returns are gently updated/modified with the Analysts Views (rather than the opposite). Thus, the Implied Returns are very much represented in the final output (the final Forecast) so when used as input in the Markowitz-tpye optimisation they naturally tend to produce a well diversified portfolio. 7- They could be two main reasons for which the ‘Implied Returns’ dominate the final Forecast. 7i- this might be a choice of the user of the BL procedure, that has decided that Implied Returns are more reliable than the Analyst Views (and therefore has chosen to use a comparatively large Cov matrix for the Analysts Views). 7ii- they might be only a few positions for which Analyst Forecast are available, therefore many positions won’t be much affected by the BL procedure and the vector of final Forecasts will be overall very similar to the vector of Implied Returns.
Allocating a porfolio following MarkowitwPortfolioTheory (eg via mean-variance optimisation) results in underdiversified portfolio. Intuitively, this could perhaps be seen as a too great sensitivity of the Markowtiz-type optimisation to intrinsically unreliable data. Alternatively stated: the optimisation procedure assumes that the input data are hard numbers (ie 100% reliable), when in reality, input data are not hard numbers. Example: Let us take two positions (P1 & P2) whose returns are identical (and can remain unspecified) and whose risk (Risk1 and Risk2) are ‘quasi’ identical. Let us further consider that P1 & P2 are fully correlated (linear correlation coef ->1) so that there is no benefit in diversification. In such condition the best portfolio suggested by Markowitz Portfolio theory will be made by the single position whose risk in the smallest. Eg: if Risk1 = 10.001% (10.000%) and Risk2 = 10.000% (10.001%) then the investor will end up in a corner solution, ie holding of 100% of P2 (P1). This is a corner solution. Such result makes total sense from a calculus point of view. The result would also make sense from an investment point of view if two conditions could be *strictly* satisfied: c1- the investment horizon is distant enough (in the long run, the converge in probability of the sample moments towards the true population parameters will make sure that the position will the smallest risk is indeed the position will the smallest risk). c2- the exact value of the Returns, Risks… parameters are known without uncertainty. In real life, c1 is probably not too realistic but c2 is just impossible to satisfy: Even in the ideal situation where Returns, Risks… (or their log) could be exactly described by a given (normal, student…) distribution, the moments of the true distribution (Returns, Risks…) will still have to be estimated from a sample (the observed historics). Now, it is easy to imagine that by including one more day in our Historics Times Series of Returns, we could go from a situation where Risk1 = 10.001% and Risk2= 10.000% to a situation where Risk1 = 10.000% and Risk2 = 10.001% and *therefore* radically changed the nature of the portfolio held (of the output of the optimisation). Naturally, in real optimisation, assets will be correlated to each other and the numerics might not be so close either. Nevertheless, it will remain than rather small variation in the input could result in rather big variation in the output of the optimisation procedure. Robust optimisation techniques (eg bootstrap) have been developed to address this data sensitivity issue.