English Portfolio Management

Subjective investing with Black-Litterman

Instead of following blindly historical data, investors can integrate subjective views. This is mostly justified in case of market anomalies, but dangerous in panic situations.

The heart of the Black-Litterman model is to abandon blindly following historical data by incorporating the investor’s subjective views. Less reliance on past data allows for more forward-looking portfolios and provides a structured approach to include subjective views.

Black-Litterman is not a revolution and builds on the classic mean-variance optimization (MVO) model – first introduced by Markowitz – and on the CAPM. It incorporates the investor’s own views as inputs into the portfolio optimization process. If an investor has no opinion about the market and considers the market to be efficient, the portfolio will have to match the market equilibrium. Therefore, an investor with no market view should follow the market and adopt a passive strategy: expected returns will be equal to market returns.

It is impossible to anticipate unpredictable events such as the stock market crash resulting from the coronavirus pandemic based on past data. When these events occur, real-time adjustment of portfolio positioning based on the investor’s view is essential to deal with unforeseen events. If there is an adjustment or if the investor has his or her own views, the portfolio will deviate from the market portfolio. If investors have little confidence in their views, the deviation will be minor and the resulting expected returns will be close to the market. When investors are more confident in their views, the resulting expected returns will deviate significantly from the market’s implied returns. 

In practice, investors generate opinions by applying various techniques. They can simply make a valuation with the information available to them; as of 1991, many of the early applications of Goldman Sachs economists Black and Litterman (hence BL) were human-generated. Investors can also use more sophisticated frameworks (quantitative techniques based on econometric or Machine Learning models) to generate opinions.  

 In conclusion, the BL model provides a structured approach to expressing subjective opinions and avoiding a mechanical dependence on historical back data. Ad hoc adjustments based on subjective opinions are dangerous in panic situations but mostly justified in market anomalies. Investors will avoid selling in a market crash and shall wait for an exit; they will try to take a contrarian view and use the market sell-off as an entry point if their own financial liquidity allows. In general, a good way to apply the model for an individual investor is to look at the current global market (significant weight in the U.S.) as a starting point and compare it to the expected long-term situation (e.g. more weight expected in Asia in 20-30 years). The result of this analysis will allow you to add subjective views across geographies or currencies to determine a target asset allocation.

Other thoughts for interested readers:

The inclusion of Bayesian statistics in the portfolio optimization process led to three main shortcomings of the original Black-Litterman model:

  • The normality assumption: Extreme events (positive and negative) such as black swans are not accounted for by the normality assumption, as they appear more often than implied by the Black-Litterman model;
  • Linearity is also assumed, but many investment strategies, for example with options, express non-linear views;
  • The basis of the BL model (MVO and CAPM) applies to a well-diversified portfolio. As such, the model is less useful beyond widely diversified portfolios. 

To address the shortcomings of the original BL model, various improvements have been made to align the BL model with actual investment processes:

  • Black-Litterman-Bayes (BLB) and multi-period models focus on the expected post-cost utility of portfolio value through multi-period forecasts: Increased forecast uncertainty is balanced against the costs of excessive trading;
  • In the basic BL model, investors’ views are expressed as a portfolio of securities and are not directly applicable to the views of factors. Based on arbitrage pricing theory (APT), the factor variant of the BL model considers securities with returns above the risk-free rate and focuses on the factors that explain security returns;
  • The robust Black-Litterman (rBL) model explicitly incorporates investor uncertainty. The investor-determined confidence level is based on prior error-dependent distributions. With lower confidence in the quality of the estimates, the ex ante distribution widens.

Black–Litterman and Beyond: The Bayesian Paradigm in Investment Management, The Journal of Portfolio Management, Volume 47, Issue 5, 2021, Petter N. Kolm, Gordon Ritter, and Joseph Simonian