Because the objective of investors is inevitably to create portfolios, expectations of risk and return can be viewed as signals to be used in achieving that end. Perhaps surprisingly, we don’t even need accurate expected returns versus future realized returns in order to generate value-add portfolios, those capable of outperforming a particular benchmark. We can demonstrate this in the context of a two-asset portfolio of US stocks and bonds. Restricting our case study to two assets is done for simplicity and to illustrate a point, not to imply that investors should ever restrict themselves simply to two assets.
A very common way to generate portfolio weights from risk and return expectations is through the use of mean-variance optimization (MVO), which aims to create the portfolios with the highest achievable return per unit of risk, also known as efficient frontier portfolios. Although the benefits of MVO are vast, the approach has a few important drawbacks, such as high sensitivity to our input expectations as well as difficulty in tying the resulting portfolio weights to the input expectations, especially when the number of assets grows. Thus, for our case study, let’s take a different, but very straightforward, approach.
Instead of comparing our risk and return expectations cross-sectionally among assets, à la MVO, let’s compare the current expected return for each asset against its own historical time series of expectations. In this way, we are attempting to neutralize some of the deficiencies (noise) in our models that we expect will be relatively constant over time. Through this comparison, we can derive a confidence score for each asset based on its expected return. For example, if an asset has a high expected return versus its expected return history, our model should show more confidence in the cheapness of that asset versus how the model has historically viewed it. It’s easy to understand why we would want to overweight that asset from its neutral position, or vice versa if the expected return is low. This approach is not new, and Asness, Ilmanen, and Maloney (2015) discuss a very similar approach.
The first step is to create a confidence score (i.e., raw weight) for each asset5 by comparing the current expected return to its historical median using a variant of standard min–max scaling. The confidence score then indicates the amount of the over- or underweight compared to the neutral position. The following equation shows that if the current expected return is higher than the historical median, the raw weight implies an overweight to the asset, or if less, an underweight: