Weighted Historical Volatility

Weighted Historical Volatility

June 5th, 2014

Historical Volatility describes the magnitude of price changes and uses the resulting stats to forecast the probability of specific price changes tomorrow (in the future).  Weighted Historical Volatility uses a similar approach but makes analyzing the past more flexible and perhaps more useful for your needs.

Historical Volatility

Historical volatility can be calculated for a variety of time frames. 10 day, 20 day, 100 day, 200 day, etc. The chart will be a moving average of the volatility figure.  If you prefer to purchase your volatility data, you can use iVolatililty or LiveVol or VictorSecurities.  Each offer varying degrees of sophisitication.  If you prefer to calculate your own historical volatility data series, yahoo provides stock data for free.  One of the benefits of yahoo is they provide the time series inclusive of all splits (adjusted close) making it easier to calculate your volatility levels quickly.

If you are a short term trader, short term volatility may be of more interest to you. If you are a long term investor, long term volatility may be of interest to you. If you’re a market maker or arbitrageur, you are likely interested in all of the above.

The 10 day historical volatility chart will show a lot of noise with very high peaks and low valleys. The 100 day historical volatility chart will look relatively smooth by comparison.

Table 1 below shows the historical volatility of Apple Computer over the past 14 years. The difference between the high and the low or the range of 10 day historical volatility was 128.7% compared to a range of 59.08% for the 100 day historical volatility.

BLOGIMGTable1 WHVOL

A long time sample will result in less noise and a smoother chart.  However, a decision regarding the trade-off between noise and smoother data will be necessary.

5 day historical volatility each trading day represents 20% of the time frame. If one of those days was an “event” such as earnings, you may have too high a volatility estimate. On the other hand 5 day volatility does have the advantage of providing a glimpse into the most recent past. That is, it reflects current market conditions.

20 day historical volatility each trading day represents 5% of the time frame.  a One day event won’t create as much noise as with our 5 day Volatility figure, but a balance between current data and smoothness of data must still be weighed.

100 day historical volatility each trading day represents 1% of the time frame. While it has the advantage of smoothing out your data, it’s also taking into account what happened almost 5 months ago. 100 day historical volatility may take in too much dated history and not enough recent data for your purposes.

The 2 charts below compare 20 day historical volatility with 100 day historical volatility over a four month period.  You can see the 20 day chart has more “noise” than the 100 day volatility chart.

BLOGIMG_AAPL20v100DHVOL_WHVOL

Weighted Historical Volatility Calculation

There are many ways we can adjust our time series.  For this article, we’re going to make the most recent data more important in our final calculation. For example 100 day historical volatility can be weighted using five 20 day historical volatilty figures.

Table 2 shows the weighting applied to each 20 day bucket so that the most recent 20 day history is highly weighted and the furthest 20 day period has a lower weighting in our number.

BLOGIMG_Picture2_WHVOL

To calculate 100 day weighted historical volatility:

1) Calculate 20 day volatility (moving average) for the past 100 trading days

2) Multiply each 20 day average by the weightings desired (see above)

a. weighting the most recent data by the highest %, data reflects current market conditions more than the conditions from 100 trading days ago

3) Add the five weighted 20 day historical volatilities. The result is a weighted 100 day historical volatility.

Weighted Historical Volatility Results

Table 3: weighted 100 day historical volatility table, showing the steps above

BLOGIMG_Table3_WHVOL

Table 3 above shows the weighted 100 day historical volatility is 45.36% while the 100 day unweighted volatility is 38.54%.  Therefore, the conclusion is that the market has been more volatile in the more recent past (55.26%) than the 20 day period back in September 2012 (24.17%)

Summary & Conclusion

The way this analysis is used will vary from trader to trader.   But, to whet your whistle for future blogs of this sort, I’ll set forth a simple example.  Please do not consider this a viable trading system but rather an illustration of using different time frames of historical volatility.

Firstly, we might setup the weighted volatility chart to view the weighted volatility over time.

Then define a reasonable range (or ratio 45.36% / 38.54% = 1.177 ratio) between the weighted & unweighted volatility.

If the spread narrowed we could presume the market has become less volatile recently.

If the spread widened, we could presume the market has become more volatile recently .

Based on the reasonable range we defined above, we might use this movement to  decide how to trade our Gamma (short dated options) book.

At least that’s one way Weighted Historical Volatility could be used.    Any thoughts?  Feel free to share them in the comment section below.

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