Over the years, numerous studies have shown how complex investment strategies fail to outperform simple asset allocation methods. Other studies emphasise the amount of sheer luck that goes into the favourable performance of the investment strategies; it has been repeatedly shown that in many instances, an attempt to deviate from the market portfolio has odds no better than a coin flip. These findings seem to point towards one cold fact - the optimal portfolio weights are impossible to find. Or are they? 

To answer this question, we go back to the basics of portfolio construction. Financial markets have a random nature making it impossible to estimate future returns correctly. To put it plainly; we cannot predict the future.  

Since most investment strategies are based on estimations, this simple fact threatens to hinder the performance of the portfolio allocations (in terms of the classical trade-off between risk and return) that we meticulously worked out. We decided to find out how sensitive the performance of various portfolio construction strategies is to estimation errors by conducting a small study backtesting different portfolio allocation frameworks. Please note that in this case, we mainly discuss financial data predictability within the monthly frequency. This becomes a notable aspect as high-frequency strategies may be exploiting stationary aspects of order matching or market connectivity that could enable fast players to extract rent in return for providing liquidity. 

First of all, it is common practice to define a drift term when modelling financial returns. It is done to estimate the expected return in a more realistic way. The randomness of the market is represented by a volatility term, which reflects the uncertainty of the return on investments. Since ideally, the portfolios consist of more than one asset, it is reasonable to assume a dependence structure between assets. Setting the estimated mean log-returns as the drift, and assuming that the estimated covariance defines our volatility and dependence structure, we now have all the necessary elements for constructing a simple multivariate normal simulation model for our assets. 

Having done all of the above, we estimated an optimal portfolio using some arbitrary investment strategy. What happens if we slightly change the estimates of the mean or covariance? 

Driven by curiosity, we attempted to answer this question within the scope of the study mentioned above. As it turns out, a change in mean as small as 0.6% changed the optimal portfolio weight up to 80% (!). Adding to our distress, most asset returns varied considerably over time. That is, a change of 0.6% doesn’t even begin to cover it. 

Could this imply that estimation-based investment strategies are not that reliable? Unfortunately, it could. It is commonly hypothesised that non-stationary processes govern financial markets because of the feedback mechanisms (MalkielFama, 1970). – created by market participants analysing the market information and trading accordingly, thus destroying any temporary stationarity. It is also notable that modelling non-stationary environments is challenging because the dynamics of the process may be affected by the unknown and not directly perceptible causes, which forces the reinforcement learning methods to re-learn the policies from scratch (Da Silva, Basso et al., 2006). 

However, there is still some light at the end of the tunnel. First of all, although our investment strategy doesn’t give us a robust optimal portfolio allocation (otherwise we would all be extremely wealthy), it can provide us with a general idea of an approximate optimal portfolio. Secondly, there are quite easy ways to improve the performance of an estimation-based investment 

Back to the question at hand – can we find the optimal investment strategy? The short answer is no. The more elaborate answer is also no, but we can find a sufficiently close approach.  Using a measured combination of well-thought-out models and common sense, you might get a reasonably good approximation.  We explore how it could be done within the following article series:  

  1. Part I – Portfolio Construction - Parameter & Model Uncertainty; 

  2. Part II – Portfolio Construction - Sampling & Optimisation; 

  3. Part III – Portfolio Construction - The Real World Analysis 

References 

  1. Malkiel, B. G., & Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The journal of Finance25(2), 383-417.
  2. Da Silva, B. C., Basso, E. W., Bazzan, A. L., & Engel, P. M. (2006). Dealing with non-stationary environments using context detection. In Proceedings of the 23rd international conference on Machine learning (pp. 217-224). ACM.