Apr 23

Volatility Decay

by David Harper, CFA, FRM, CIPM

FRM | Risk |

Vol_decay1

We previously discussed three approaches to the estimation of volatility: implied, non-parametric and parametric. Among parametric approaches, we contrasted a simple unweighted approach (i.e., the simple average variance over some history) with weighted approaches where history is not democratic. Specifically, in weighted approaches we assign greater weight to more recent observations. Among weighted approaches, keep in mind that the exponentially weighted moving average (EWMA) is just a particular form of the more flexible GARCH(1,1):

Vol_decay_paramOverview

The EWMA is given by an elegant, recursive formula:

Emwa

It says, today's (estimated) variance is a function of yesterday's variance and yesterday's squared return. Lambda is the smoothing or persistence parameter. RiskMetrics says the average lambda is about 94%. If lambda is 94%, then the remaining weight of 6% is assigned to yesterday's (or the most recent) squared return.

Here is a spreadsheet where you can change the lambda parameter and see the impact on the series of historical weights assigned to the squared returns. For a high lambda, the weights are "smoother" in the sense that more distant returns are included. When lambda is high (nearer to one), sudden volatility shocks do not abruptly adjust the estimate: the series "remembers" history. It is more smooth or more persistent.

EditGrid Spreadsheet by user/davidharper.

Conversely, as you lower the lambda, higher weights are assigned to more recent observations. Shocks will have a greater impact on the volatility estimate. In summary:

  • High lambda implies high persistence and slower (less) decay. Shocks are less quickly absorbed due to a smoother series with greater "recollection:" more history is included.
  • Low lambda implies low persistence and faster (more) decay. Shocks abruptly adjust the series. The series does not "remember" a longer history; it relies on a smaller sample.

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