Wednesday, December 12, 2007


I'm now turning to looking at volatility of stock prices and seeing if it could be a useful addition to my trading model. More sophisticated investors and traders and familiar with measures of stock price volatility derived from the implicit volatility expressed in options prices according to the Black-Scholes options pricing model. The VIX and VXN are the best known of these and measure the volatility implied by options on the S&P 500 and NASDAQ 100 indices. But one can also measure volatility directly from stock prices. The most straightforward would be a standard deviation of changes in the index. The problem with this and the reason why the options based indicators are popular is there will be a different result depending on how many observations are used to compute the standard deviation. This indicator also doesn't address intraday volatility. A measure of intraday volatility is Average True Range. True range measures the range of prices from previous close to close (and therefore includes any gaps in the range). ATR is simply an exponential moving average of this. A problem with this indicator is it is dependent on the level of prices. Of course we can simply divide true range by average price over the day to get a unit free measure of the daily range as a percent of price. The chart tracks a five day exponential moving average of this latter indicator.

The late 1990s and early 2000s were far more volatile than today with volatility peaking with an average of a 9% daily price range over the a five day period. As the post 2002 bull market took off volatility declined to very low levels and has now begun to re-emerge but not to the extent seen several years ago.

Why might volatility be interesting?

1. While mainstream finance theory claims that it is not possible to forecast stock prices (this is true though direction of stock prices may be forecastable) it is believed to be possible to forecast volatility in the short term. Typically ARCH (autoregressive conditional heteroskedasticity) time series econometric models are used. Being able to forecast volatility is a big advantage obviously in option trading and a reason I mostly avoid option trading except using deep in the money options as proxies for margined stock or futures. Volatility is not a component of futures prices which makes trading them a lot easier.

2. Stock prices are far more volatile when declining than rising. Market tops are more commonly characterised by narrow trading ranges that finally fail than by volatile "blow-offs". Market bottoms typically show violent intra- and inter-day fluctuations. If one forecast rising volatility - declining prices might also be associated with that forecast. Of course it makes sense that volatility is higher with declining prices -a rise in volatility implies a rise in risk and higher risk implies that lower prices are optimal - investors should pay less for a given amount of earnings with higher volatility assuming risk aversion.

At least volatility might explain some things about stock price behavior that my current completely price based model does not. So I'm going to do a bit of research on this. My first problem though is deciding on an appropriate indicator of volatility.

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