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How can equilibrium weights be found for momentum factor in Black-Litterman model?

I have a momentum factor which consists of going long in three rising ETFs and going short in three falling ETFs. I want to use this factor as part of my portfolio for Black-Litterman model, however I ...
Karina's user avatar
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Black Litterman Model: can Market Weights be replaced?

I'm new to applying the Black Litterman model. One point that is troubling me, from a multi asset point of view, is the market portfolio as the starting point for the model. Correct me if I'm wrong ...
Farrep7's user avatar
2 votes
2 answers
280 views

Portfolio construction for almost identical assets

The problem I am looking at concerns the treatment of almost identical assets in portfolio construction. Let us assume that we have two assets, both with a standard deviation $\sigma=0.2$ and a ...
Hans-Peter Schrei's user avatar
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116 views

For mean-variance portfolio optimization, shouldn't all the allocations sum to 1?

Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns. In Table III, the authors show two portfolios ...
Arthur Santana's user avatar
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1 answer
396 views

Black-Litterman and Implied Market Returns

The first step in the Black-Litterman method is to find the "implied market returns" (the prior). Usually this is calculated as: $\Pi = \lambda \Sigma w$, where $\Pi$ is the vector of ...
randomwalker's user avatar
2 votes
1 answer
105 views

relation between risk averson coefficient and maximum Sharp ratio in Black-Litterman context

BL model compute the implied returns based on the reverse optimization where the objective is: $${\underbrace U_{{\rm{investor's \ risk \ utility}}} \buildrel \Delta \over = {\bf{w}}_M^T{\bf{\Pi }} - \...
sci9's user avatar
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229 views

Black-Litterman Weights Don't Change for Assets Without Views

I am using Idzorek 2002 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Idzorek_onBL.pdf) as a reference to implement the BL model in R. I have specified the model in its standard form, ...
Leo Hsia's user avatar
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188 views

Black-Litterman for quant portfolio

I have seen a lot of research around the Black-Litterman approach and I think theoretically, it is a nice framework. However, it appears that its main strength is from a practitioner's point of view, ...
Jim's user avatar
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2 votes
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71 views

Black-Litterman Weights for Intersecting Asset Classes

I'm trying to implement Black-Litterman for an arbitrary selection of assets some of which might be subsets or intersect with others. For example, one portfolio might be US Equities (VTI) A global ...
jtanman's user avatar
  • 121
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1 answer
705 views

Black-Litterman model with only positive weights

I'm trying to realize Black-Litterman Model for my stocks portfolio, but under optimization, I get a subset of weights with negative values. I want to get only positive weights. IS it possible to add ...
Dmitriy's user avatar
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Index to track my portfolio of all ETFs

I have the following portfolio of all ETFs: I am attempting to apply Black Litterman and on the step of calculating market weights. I have the following questions: How can I define what index to use ...
Erdos_x's user avatar
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180 views

Calculating portfolio weights for Black-Litterman model

I am attempting to construct a portfolio using the step by step Black-Litterman model. My idea is to have a portfolio of, say 10 ETF's (equity based) in one sector and then add some uncorrelated asset ...
Ali khan's user avatar
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2 answers
152 views

Black-Litterman model - Unable to obtain correct implied weight from implied returns

I'm using Excel 2016 to analyse the ASX200 at June 2012. Out of the ASX200 index, I've found 136 stocks with 5-yr of monthly stock close price data (01 July 2007 - 30 June 2012). I generated monthly ...
Scorpion Haven's user avatar
0 votes
1 answer
368 views

Covariance Shrinkage in Black-Litterman Framework

Good evening guys I am looking into the effects of covariance shrinkage on the diversification of asset weights for different portfolio optimisations. Initially, I was interested to see how it affects ...
Riskay's user avatar
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1 answer
500 views

Market Capitalisation Weights for Black-Litterman portfolio

I am implementing the Black Litterman model for a few assets, in particular I am using five ETF: EFA (EAFE stock index: developed markets outside US and Canada) EEM (stocks from Emerging Markets) ...
Matteo's user avatar
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Black litterman's formula

Hi just curious where can I find the proofs of Black litterman's first term and second term formula? I don't quite know how exactly they derive the entire formula using inverses of matrix. Thanks!
Leopardl's user avatar
3 votes
1 answer
835 views

Black-Litterman computation in R - where am I going wrong?

I am trying to compute a small Black Litterman model in R. I am following a Youtube video and translating the excel implementation in R. I have a var cov S matrix ...
user113156's user avatar
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67 views

Labeling Returns in 5 categories based on BL view approach

I have to label a time series of returns into 5 categories based on the Black Litterman view approach. The categories should look as follows: very bullish: + 2 std. dev. bullish: + 1 std. dev. ...
smartquant's user avatar
1 vote
1 answer
74 views

Rationale for likelihood function parameter choice in Black-Litterman model?

So we are interested in a PDF for equilibrium returns given the views. Why do we choose our view means as the mean parameter and observed market covariance as the covariance parameter? Seems a bit ...
A.L. Verminburger's user avatar
0 votes
1 answer
157 views

Black-Litterman risk aversion

I'm trying to better understand how BL works and what I would like to know if there is a way to adjust the portfolio created based on a risk aversion variable determined by the user. I can't really ...
fraccaman's user avatar
2 votes
0 answers
194 views

Black-Litterman proof with P=I and Omega=tau*Sigma

Elsewhere on this site (link), Richard notes that \begin{equation} \Pi_{BL} = \frac{1}{2} \Pi + \frac{1}{2}Q, \end{equation} so long as we set $ P = I $ (where $I$ is the identity matrix) and $\Omega ...
user221772's user avatar
2 votes
1 answer
240 views

How to calculate market capitalization weights for a currency portfolio?

I am implementing Black-Litterman optimization on a currency portfolio and I could not calculate market capitalization weights for currencies. Please give me some suggestion.
bhavesh wadibhasme's user avatar
2 votes
0 answers
186 views

Black-Litterman implied returns using rolling window

I am building an active risk-based Portfolio with a risk-based Portfolio such as the minimum variance Portfolio as the neutral starting point. Therefore, I calculate the rolling 36 month covariance ...
MANGo 92's user avatar
4 votes
1 answer
2k views

Implied Equilibrium Returns Example

I've been trying to work through a simple example using A Step-by-Step Guide to the Black Litterman Model, but I'm having trouble understanding implied risk aversion. Say I have two uncorrelated ...
rhaskett's user avatar
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Black Litterman - numerical instability

I am trying to work out the formula for the posterior mean in Black Litterman's model assuming 100% confidence : Ref: https://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/...
natt010's user avatar
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4 votes
1 answer
2k views

Struggling with tau in Black-Litterman

According to the omega formula in B-L tau is used in the Omega estimation to determine the degree of uncertainty given to views of the investor: So, if tau is given a low value then the inverse of ...
JamesHudson81's user avatar
1 vote
0 answers
521 views

Problems with Black-Litterman: negative portfolio weights, and very poor returns

I am trying to implement the Black-Litterman model using own-defined views matrix (from consensus analysts). However, I have encountered the problems of negative portfolio weights in some periods, and ...
Mataunited17's user avatar
1 vote
1 answer
974 views

Can Black-Litterman-type expected return estimation be used for regional ETFs?

The Black-Litterman approach to return estimation overcomes the problems associated with estimating expected returns via historical averages by determining the equilibrium returns implied by the ...
Constantin's user avatar
3 votes
1 answer
571 views

black litterman for rebalancing

I've noticed in my backtests that "shrinking" the expected returns vector towards zero tends to improve the performance. This has led me to investigate shrinkage methods for the forecasts/expected ...
Michael's user avatar
  • 500
0 votes
1 answer
969 views

CVXPY 's constrains doesn't work

I am trying to implement a max return optimization with a large number of assets. I am not sure why this problem won't work. ...
Bowen's user avatar
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1 vote
1 answer
2k views

How to generate the views in Black-Litterman model?

I want to apply a Black-Litterman approach for portfolio optimization. My question is how to select investor views? I need to base the choice on a model. I would be thankful if you could give me some ...
Nourhaine Nefzi's user avatar
2 votes
0 answers
54 views

Black Litterman with strongly skewed/leptokurtic variables

I am trying to apply a BL-like model to a random variable which is strongly skewed and leptokurtic. The random variable is actually the change through time of GARCH conditional variance $\sigma_{t+1}^...
Petreius's user avatar
1 vote
1 answer
291 views

Can I formulate a general relative view in Black-Litterman?

We have often discussed the Black-Litterman approach/model in the forum. What I was wondering is: is it possible to formulate relative views in the model. Relative in the sense $$ \mu_1 > \mu_2 $$ ...
Richi Wa's user avatar
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3 votes
1 answer
453 views

Black Litterman: Is it possible to have multiple views (from different sources) on the same asset?

From the basics of Black Litterman I understand that each view on a stock is implemented via the pick matrix P with the expected value of the views in Q. I have read several papers where each stock ...
user20862's user avatar
4 votes
2 answers
1k views

Is it possible to deal with non-normal distribution in Black-Litterman model?

Suppose that I know that the normality assumption about my data is unrealistic (as it is very frequently): is it possible to apply any distribution that I judge the right one to the Black-Litterman ...
simmy's user avatar
  • 585
3 votes
1 answer
362 views

Systematic Views in Black-Litterman?

Are there any literature on selecting systematic views for Black-Litterman along with methods to specify the uncertainty parameter? For example, rather than specifying a portfolio manager's subective ...
Kevin  Pei's user avatar
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5 votes
2 answers
1k views

Black-Litterman: Why should the views be independent of each other?

This question relates to this question. In the Black-Litterman framework views of inverstors on the market are modelled. These views have a covariance-matrix $\Omega$. I always found it quite ...
Richi Wa's user avatar
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5 votes
2 answers
3k views

Black-Litterman, how to choose the uncertainty in the views $\Omega$ for smooth transitions from prior to posterior

In Black-Litterman we get a new vector of expected returns of the form: \begin{align} \Pi_{BL} = \Pi + \underbrace{\tau \Sigma P^T[P\tau\Sigma P^T+\Omega]^{-1}}_{\text{correction}}[Q-P\Pi] \end{align} ...
Richi Wa's user avatar
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0 votes
0 answers
903 views

Black-Litterman with simple portfolio

In an attempt to learn Black-Litterman I have come across this "simple" example. Suppose that you analyze market data using CAPM $$r_i-r_f=\beta_i(r_m-r_f)+\epsilon_i$$ Suppose there are 2 assets in ...
Wintermute's user avatar
2 votes
1 answer
659 views

Is an arbitrary prior for Black-Litterman valid? Or do we need a market implied one?

I went through The Black-Litterman Approach: Original Model and Extensions - see also. The BL approeach starts with a prior on the expected returns vector derived from the hypothesis that the market ...
Richi Wa's user avatar
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5 votes
3 answers
2k views

What is the tau parameter in the Black-Litterman model?

Could someone please provide me with a clear and concise definition of the $\tau$ parameter in the Black-Litterman model? It seems one is rather hard to come by. I understand it to be the 'weight on ...
Ryan's user avatar
  • 53
10 votes
2 answers
3k views

Market weights for Black-Litterman

I'm trying to implement Black-Litterman for an arbitrary selection of assets. One of the input for BL is the "Equilibrium market capitalization weights for each asset". In most examples I've seen, ...
Bjorn's user avatar
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