NLV2: Capturing the 3rd Derivative
In the previous post, I introduced the concept of a non-linear filter that combines volatility and acceleration. However, this is just one configuration to leverage the concept of a non-linear filter. Using a traditional volatility calculation assigns each data point an equal weight, when in practice some data points should logically have more weight than others. To capture different weighting functions, one could use multiple indicators to weight data points in the volatility calculation to make it more responsive to incoming market data. Using acceleration was an interesting idea to reduce lag and quickly capture changes in volatility. Preliminary analysis showed some promise in this regard. Acceleration is the 2nd derivative, so an interesting question is whether the 3rd derivative- or the velocity of acceleration-can produce even better results. I created a new framework to capture the non-linear weighting that is much simpler to understand and implement:
A) Calculate the rolling series of the square of the daily log returns minus their average return
B) Calculate the rolling series of the absolute value of the first difference in log returns (acceleration/error)
C) Calculate the rolling series of the absolute value of the first difference in B (the absolute acceleration/error log returns) this is the 3rd derivative or velocity of acceleration.
D) Weight each daily value in A by the current day’s C value divided by the sum of C values over the last 10 days-
F) Find the sum of the values in D- this is NLV2
Here is how NLV2 performs on the S&P500 (SPY) versus the other methods previously presented:
The profile of this method is very different than the others, and while it hasn’t performed as well comparatively in recent years it has been the best performer over the entire period that was tested. While other people may dismiss things that have underperformed recently, my own research suggests that this is a mistake- many systems and methods mean-revert around some long-term average. Since this method has fewer moving parts than NLV, that makes it inherently more desirable and perhaps more durable. In either case the point of presenting this method is not to evaluate performance or suggest that it is a superior weighting scheme. It is to present an alternative way to look at the data- clearly different derivatives of log returns carry different pieces of information, and combining these into a calibrated forecast model or a non-linear filter may add value above and beyond the standard volatility formulation.