A while ago I posted an article titled “INVESTMENT PORTFOLIO OPTIMISATION WITH PYTHON – REVISITED” which dealt with the process of calculating the optimal asset weightings for a portfolio according to the classic Markowitz “mean-variance” approach. With this method we aim to maximise our level of return for any given level of risk, in doing so we develop the concept of an “efficient frontier” and usually seek to identify the point/portfolio on that frontier which represents the best trade-off between risk and return (i.e. the portfolio with the highest Sharpe Ratio).
As nicely as the model allows us to identify our supposed “optimal asset weightings”, there are several, rather severe problems we face when using mean-variance optimisation.
- The model assumes asset returns are normally distributed.
- It can generate unintuitive, highly-concentrated portfolios.
- The inputs to the model include each individual asset’s predicted/expected return and volatility, but we of course can never know those values for certain. Common practice is to calculate the assets’ historic returns and standard deviations and use them as proxies – this makes the massive presumption that all the assets will continue to behave and perform just as they have done in the past. Not only does it assume the returns and volatility will remain the same, it also assumes that correlations between all the assets in question will remain stable through time. We know these assumptions are just not realistic.
- To make matters worse, not only do we use inputs that are reliant on our own “best guess” or forecasts, the model happens to be extremely sensitive to variations in these input values (especially to the return inputs, less so the volatility inputs). If the input values are changed, even by relatively small amounts, the optimal portfolio weightings created by the model can swing and vary wildly. Ideally we would like our model to be as “robust” as possible in this regard and generate stable/slowly changing suggested asset weightings when faced with changing input values.
In this post I am going to take a look at the Black-Litterman model, which is an adaptation of the classic mean-variance framework which enables investors to combine their unique views regarding the performance of various assets with the market equilibrium in a manner that results in intuitive, diversified portfolios.