A Practical Approach to the Black and Litterman Model: An Example on European Sectors

In this section, we reflect upon the limits of mean-variance model that the Black- Litterman model seeks to solve. A description of them can help practitioners to understand both the reasons on B-L model analysis and the motivations of the surprisingly little impact of M-V portfolio selection in the investment industry. He and Litterman (1999) focus on the limits of M-V approach and identify two reasons of this unsatisfactory implementation in practice: first, instead of attributing estimated expected returns on all the assets as M-V requires, asset managers usually select small segments and analyze fundamental ratios, momentum and characteristics to find undervalued stocks; second, M-V optimization considers expected returns as inputs of the model and portfolio weights as result of the process while practitioners operate directly in terms of portfolio weights. Furthermore, the extreme and unintuitive weights returned by M-V optimizer appear unsuitable for a client’s portfolio. The need to avoid extreme and unrealistic portfolios was the stimulus for Black and Litterman to re-define the traditional M-V model adding subjective views in order to obtain more intuitive and less extreme and unstable portfolio weights. In detail, the problems regarding M-V approach are discussed to support the unsatisfactory use among investors.
One of the requirements of mean-variance model is represented by the estimation of the expected returns and the variance-covariance matrix for all assets in the investment universe considered. Typically, practitioners can obtain return forecasts only for a selected set of securities and the estimation of the variance-covariance matrix is even more harder to calculate.
It is impossible for an investor to produce good estimates for a large set of assets and, probably, it represents one of the reasons of M-V poor use in practice. Therefore, a first deficiency concerns the large amount of inputs required by the model.
The estimation process concerns both expected returns and variance-covariance matrix.
Some arguments involve how to estimate the inputs of the model and which approach should be adopted to limit the estimation error. Merton (1980) claims that especially the choice of the vector of expected returns influences significantly the ex-post performance of the portfolios.
Markowitz’s model requires that both inputs of mean-variance optimization must be forwardlooking.
Some practitioners use past information to estimate both variables. The choice of historical data needs to accept a certain framework (e.g. the frequency, the sample size and the dataset) that influences the estimation results. Unfortunately, Merton demonstrates how this method generates poor proxies for future expected returns. In addition, according to Michaud (1989), Markowitz’s optimizers maximize errors. The impossibility to use exact estimates of both expected returns and variances leads to estimation errors. In particular, the model tends to overweight (underweight) securities with high (low) expected returns, negative (positive) correlations and small (large) variances. Such assets result most likely to contain high estimation errors. A way to reduce this problem can be the Bayes-Stein shrinkage estimator suggested by Jorion19 (1986).
Mean-variance approach does not consider the level of confidence in the inputs and assumes that inputs are deterministic and known with certainty. The uncertainty associated with them should influence the optimizer results. Even if it makes sense for the uncertainty of inputs to be part of the optimization process, thus making the model more realistic, unfortunately optimizers completely ignore this problem. Therefore, there could not be a relation between the optimal weights and the investor’s actual view. In particular, often the differences in estimated means may not be statistically significant and, therefore, every point on the efficient frontier may
have a neighbourhood in which an infinite number of portfolios is statistically equivalent.