black liderman model the black litterman model is a traditional asset allocation model developed in 1990 by Fisher black and Robert litterman at Goldman Sachs. It expands on traditional portfolio Theory by addressing some of its criticisms and allowing it to be used with active strategies critically the model provides a tool for investors to calculate the optimal portfolio weights under specified parameters and avoid the issues of unintuitive results from mvo.

Problems with mean variance optimization that are addressed are first the outputs or asset allocations are highly sensitive to small changes in the inputs. Although the covariances of a few assets can be adequately estimated in the minds of many. It is difficult to come up with reasonable estimates of expected returns.

For example, when expressing a relative view on us equities versus Europe equities the general intuition. Is that only the allocation to these assets should change overweight one and underweight the other however with traditional mvo the allocation to other assets would change as well creating less stable portfolios.

Secondly with mean variance optimization investors would often find that efficient portfolios are highly concentrated in a subset of the available asset classes and lastly not reflective of unique investment views.

In the end BL combines both a passive input for expected returns using equilibriums and allows investors to also incorporate their active views expected returns is the yield the investor is looking forward to making on the investment. It is all of the actual income from dividends and/or interest plus any actual appreciation or minus any loss that occurred divided by the original investment the black liderman model attempts to create more stable and efficient portfolios based on an investors unique insights, which overcome the problem of input sensitivity.

Mvo solves for optimal asset weights based on expected returns correlations and a risk aversion coefficient based on predetermined inputs in Optimizer solves for the optimal asset allocation weights as the name implies reverse optimization works in the opposite direction reverse optimization takes as its inputs a set of asset allocation weights that are assumed to be optimal and with the additional inputs of correlations and the risk of version coefficient solves for expected returns. These are returns that would be expected. If all assets were priced by the cap M. They can also be called equilibrium implied or imputed returns equilibrium is an idealized state in which Supply equals demand. The equilibrium returns can be interpreted as the long run returns provided by the global Capital markets BL does not require an input estimate of expected return instead. It assumes that the initial expected returns are whatever is required. So that the equilibrium asset allocation is equal to what we observe in the markets.

When using reverse optimization to estimate a set of expected returns for use and forward-looking optimization the most common set of starting weights is the observed market capitalization value of the assets or asset classes that form the entire investment Universe in a lot of cases. This is seen as the World Market portfolio. This is considered a market neutral asset allocation because the asset weight equals that of the entire Market The Insight that black and litterman provided was as follows. Why don't we simply use the relative fractions of the value of each firm stock market capitalization also called the market weights and see what means in the mean variance optimization framework. We would need to get to those fractions as the outcome.

In other words, we back out what the means must have been for a mean variance optimal investor to get the portfolio weights consistent with the market weights. Why is this useful for you? If you run your own mean variance optimization scheme? Well, it provides a good starting point for the means that you can use you can then yourself decide whether you want to take these initial values and update them with either backward looking information, like historical return data or forward-looking measures that follow from your own analysis.

We start with an all-inclusive Market portfolio based on the constituents of the opportunity set in this example. We are assuming the entire world has only four asset classes for Simplicity next. We calculate the relative Market weights that we see in the market portfolios with betas for each asset class and Global Market risk premium assumption. We can calculate the expected return for each asset class based upon the capital asset pricing model or capm. But why are we using global market cap percentages is weights.

The main Insight of the BL model is that if the global Capital markets are in equilibrium, then the prevailing Market capitalizations of these asset classes suggest the investment weights of an efficient portfolio with the highest sharp ratio IE risk premium per unit of risk possible.

The reverse optimization process leads to a nice starting point in the next step is adding our specific investment views for each asset class with the equilibrium returns as an anchor. The next stop is an active management process of creating alternative forecasts or views regarding the expected return of one or more of the asset classes that differ from the returns implied by reverse optimization based on market capitalization rates.

The resulting expected returns and therefore the ultimate asset allocations are based upon market and economic reality via the market capitalization of the assets typically used in the reverse optimization process, but still reflect the information contained in the Investor's unique forecasts or views of expected return.

An efficient Frontier asset allocation area graph is then created based on these new BL returns to determine an optimal portfolio. This optimization process is complex as the model computes the weights to put on the portfolio representing each view according to the strength of the view which demands action judgments and estimations by an investor or an investment manager behavioral Finance research has shown that behavioral biases and psychological pitfalls can have a major impact on investment decision making the covariance between the view and the equilibrium and the covariances among the views.