When a style analysis is performed with exponential weighting, all input series to the analysis (i.e., manager and index series) are multiplied by an exponential function. Thus, if the original series was r1, ..., rn, the analysis will now use the series
where h is the chosen half-life. Although this can be done with both a positive and negative half-life, the most useful choice for style analysis is a positive half-life. In this case, the style analysis will place more emphasis on more recent returns. The smaller the half-life, the stronger this effect will be. For example, a half-life of 12 month means that the returns that lie one year in the past count half as much as the most recent ones, the returns that lie two years in the past count one fourth as much as the most recent ones, and so on. A shorter half-life allows the optimizer to pick up shifts in style more quickly, but also adds more noise to the optimization.
Dynamic Exponential Weighting
When a style analysis is performed with exponential weighting, the rolling window analysis employs exponential weighting with dynamically changing half-life. The half-lives for the individual windows are chosen according to a rather complex heuristic that aims at maximizing the overall R2. Dynamic exponential weighting helps strike a balance between capturing changes in style and creating a stable Style Benchmark.