Exponential Weighted Moving Average (EWMA) Volatility Measure

Exponential Weighted Moving Average (EWMA) Volatility Measure

One of the drawbacks with the historical approach of forecasting volatility of asset prices is that all observations during the sampling period (the squared periodic returns) are assigned equal weights. This does not make much sense since recent returns in the market tend to have a higher influence in forecasting volatility than past returns.

EWMA approach helps to overcome this shortcoming in the historical approach by introducing exponentially decreasing weighting factors. A smoothing factor (λ), also termed as the decay factor is used for this purpose. For instance, the variance (square of volatility σ) at time-i is given by,

We see that under this method, as observations get older they are assigned exponentially decreasing weights thus giving more importance to recent data than the older ones. The above equation can be written as,

Also variance at time (i-1) can be written as,

Hence σ _i² can be written in terms of σ _i-1²,

To give a better understanding of the approach, we employed both the EWMA and the historical method to predict the volatility of GE’ stock on 04/13/2008 using the daily adjusted closing price of the stock over the past two years (Source: http://www.finance.yahoo.com).

The Excel spreadsheet can be downloaded here.

Predicted Variance (04/13/2008)

EWMA: 0.1441% (Volatility: 3.8%)
Historical (Equal weight): 0.0084% (Volatility: 0.92%)