Measuring Intentional Position Size Changes
How do you know when a manager changes their conviction associated with a position versus the natural drift caused by inflows and market movements?
While position size is crucial to understanding a manager's conviction in a position, position size changes may not always reflect a change in conviction, as position sizes are also affected by market movements and rebalancing activities triggered by inflows and outflows. This paper outlines a methodology to isolate each of these entities, providing investors an actual way to measure the signal carried by position size changes.
Definitions and Assumptions
Here's a list of definitions and abbreviations used in this document:
We furthermore assume that these flows happen at the end of the day and therefore generate no return for the day.
First of all, we need to compute the difference between portfolio weights at different times.
We know that:
We can then express AUM for t+1 in the following way:
We define the return of the whole portfolio between t and t+1 in the following way:
And rewrite (1) as:
The component linked to the active position size change is circled above.
We can express it more clearly as:
The meaning of this last formula is that the dollar-difference between the actual position value and the one we would have observed if the weights had not changed is explained by the following three factors:
Only one last step is needed to obtain the result. We can rewrite (8) as :
What we see here is that the position weight variation can be decomposed in two terms with a clear interpretation.
The first piece is a passive effect originating from the different returns of the position we are examining and the average return of the portfolio. If a position outperforms the portfolio, its weight will increase and this is exactly what we observe here.
The second term, on the other hand, is more directly linked to the active decisions of the asset manager and its value is equal to the deviation from the re-balancing needed to compensate a cash flow.
The ability to measure intentional choices using this framework helps remove market and rebalancing noise that would otherwise obscure position size analysis. Exercises like this are central to our goals here at Novus—extracting clear insights in an unclear world, and giving investors the tools to succeed.