Written by Adrian L.

## Overview

The Mean-Variance approach is a common portfolio optimisation method which is based on the assumption that all investors make rational investment decisions if they are given access to complete market information. On the other hand, the Black-Litterman model is a more advanced method of portfolio optimisation. The primary reason for developing this model was that it aimed to overcome fundamental issues such as errors in estimation, portfolios that are too concentrated, and technical issues such as input sensitivity. The two approaches have their own strengths and weaknesses (Idzorek, 2007). This paper aims to discuss these features and make a comparison that can be of value to investors.

## Analysis of Strengths and Weaknesses

The mean-variance and the Black-Litterman portfolio optimisation models are among the most commonly used techniques when it comes to managing portfolios. The primary strength of the Black-Litterman model compared to the mean-variance approach is that the former requires the portfolio manager to provide inputs in the form of investor or analyst views (Opus Finance, 2008). The model converts these views into forecasted returns for the securities in the portfolio. Another advantage is that the number of views is not restricted in any way and is flexible. Additionally, since the Black-Litterman model makes use of market data as well as the portfolio manager’s views, it is a much more holistic approach compared to the Mean-Variance theory (Cheung, 2010). On the other hand, the mean-variance model is regarded as one of the foundational theories of finance. The main strength of the mean-variance model is that it is based on just two factors to optimise a portfolio. The investor needs to know the mean return (profit) and variance (risk) of securities. The model simply attempts to strike the right balance between profits and the subsequent risks involved in a portfolio. Another strength of the model is that this approach is fundamental in nature in the sense that it simply assumes that rational decision making will be made if the information provided to the portfolio manager is comprehensive (Lai et al., 2011).

The Black-Litterman approach has another strength as it can be altered to accommodate for inverse optimisation. Scholars have managed to make use of this technique to attain better returns without increasing the amount of risk involved. Although the mean-variance approach is a fundamental theory, it is not open to inverse optimisation. In this regard, the model is much more rigid compared to the Black-Litterman approach. Flexibility can be the crucial deciding factor for portfolio managers who are looking for a risk-averse method to maximise their returns. Furthermore, it has been noted that the risk cohesion factor in the Black-Litterman approach is better when compared with the mean-variance model (Bertsimas et al., 2012).

The Black-Litterman model does face certain inherent weaknesses. Firstly, the model faces certain practicality issues. In theory, the portfolio manager is expected to provide his or her views, and it is synchronised with market data to provide the output. However, there are times when alternative views of the portfolio manager may result in indifferent results. This is because the model does not account for stock-specific or factor views. Further, the model can suffer from non-linearity. Additionally, it is widely believed that the model needs further explanation and research in order for it to become more practical. In its current state, the model is not perceived to be too practical because of its inherent weaknesses. It is widely presumed that further research on the model will be able to overcome its weaknesses (Cheung, 2010). Conversely, one of the most widely noted criticisms of the mean-variance approach is that at times the model proves to be counterintuitive. This is due to the fact that minor changes in the expected returns of the portfolio can lead to widespread changes in the portfolio mix (Robeco, 2014). This can often result in extreme weights being given to certain assets. This can be a very dangerous situation for a portfolio manager since ultimately the risk factor also rises. Although some portfolio managers have attempted to devise ad-hoc solutions for this weakness, it continues to prevail (Da Silva et al., 2009). Another limitation of the mean-variance approach is that it makes an assumption that covariance between assets’ returns will persist in the future, which is not the case in the real world.

The Black-Litterman approach is often seen as a much more complicated approach compared to the mean-variance model. Although fundamentally it is related to the mean-variance approach, it has been widely noted that portfolios which had been optimised using the Black-Litterman method did not perform so well in practice when compared to the theoretical predictions (Martellini and Ziemann, 2007). Additionally, making constant changes in the portfolio in order to optimise it according to the model may result in extremely high transaction costs. These aspects of transaction costs are not considered either in the mean-variance model or the Black-Litterman model and thus the practical application can be difficult at times. The applicability of the Black-Litterman model in the real world has been often criticised (Fabozzi, Focardi, and Kolm, 2006). On the other hand, the mean-variance approach has also been questioned by various scholars around the world. It has been noted that the approach leads to portfolios which are highly concentrated. Further, the approach has been questioned on its ability to take into account the uncertainty of parameters. All of these factors result in the mean-variance model being less popular compared to the Black-Litterman approach in the modern era. Portfolio managers give precedence to the Black-Litterman approach since its results in terms of portfolio returns are more reliable and have lower risk attached compared to the mean-variance approach (Kooli and Selam, 2010).

## Conclusion

To sum up, it is evident that the two portfolio optimisation approaches have their own set of strengths and weaknesses. After comparing the key features of both models, it can be concluded that the Black-Litterman model is a more comprehensive model and it may turn out to be more useful for portfolio managers if sufficient research is conducted in this field. Nevertheless, the mean-variance approach continues to be one of the most important models in portfolio management in spite of its assumptions and limitations. Both approaches continue to be used extensively by portfolio managers in the real world.

## References

Bertsimas, D., Gupta, V. and Paschalidis, I.C. (2012) Inverse optimization: A new perspective on the Black-Litterman model, *Operations Research*, *60*(6), pp.1389-1403.

Cheung, W. (2010) The Black–Litterman model explained, *Journal of Asset Management*, *11*(4), pp.229-243.

Da Silva, A.S., Lee, W. and Pornrojnangkool, B. (2009) The Black-Litterman model for active portfolio management, *The Journal of Portfolio Management*, *35*(2), pp.61-70.

Fabozzi, F.J., Focardi, S.M. and Kolm, P.N. (2006) Incorporating trading strategies in the Black-Litterman framework, *The Journal of Trading*, *1*(2), pp.28-37.

Idzorek, T. (2007) A step-by-step guide to the Black-Litterman model: Incorporating user-specified confidence levels, *Forecasting expected returns in the financial markets,1,* pp. 17-38.

Kooli, M. and Selam, M. (2010) Revisiting the Black–Litterman model: The case of hedge funds, *Journal of Derivatives & Hedge Funds*, *16*(1), pp.70-81.

Lai, T.L., Xing, H. and Chen, Z. (2011) Mean–variance portfolio optimization when means and covariances are unknown, *The Annals of Applied Statistics*, *5*(2A), pp.798-823.

Martellini, L. and Ziemann, V. (2007) Extending Black-Litterman analysis beyond the mean-variance framework, *Journal of Portfolio Management*, *33*(4), p.33.

Opus Finance (2008) The Black-Litterman approach: Original model and extensions, available at http://www.opus-finance.com/sites/default/files/Fichier_Site_Opus/Article_recherche/Articles_externes/2013/The_BlackLitterman_Approach/The_BlackLitterman_Approach.pdf [Accessed on 13 December 2018].

Robeco (2014) 'The best of two worlds' - alternating between mean variance and risk parity, available at https://www.robeco.com/en/insights/2014/07/the-best-of-two-worlds-alternating-between-mean-variance-and-risk-parity.html [Accessed on 13 December 2018].