Why Inverse Price Is a Weak Volatility Proxy

Summary

The document considers whether inverse stock price, 1/P, can serve as a volatility factor and asks how this might relate to market microstructure. One response argues that price levels are a poor volatility estimator because prices are nonstationary, making comparisons across time difficult, and do not generally behave like mean-reverting volatility measures. A steadily rising price can therefore make the inverse-price relationship misleading: the price path may change while returns have no variation under the example given.

A second response notes that high volatility often accompanies falling prices, since declines represent movement in the underlying. It emphasizes that volatility is generally not a property of the absolute price level and suggests normalization as a possible role for inverse price. Together, the answers distinguish using price as a direct volatility proxy from using it to normalize a measure. The discussion is conceptual and provides no empirical test, specified estimator, or microstructure mechanism. It does not establish that inverse price is useful as a factor; any such use would need a clear definition and validation on appropriately scaled return or volatility data.

Key ideas

• Absolute price levels are nonstationary, which complicates comparisons across periods.
• Inverse price can misrepresent volatility when price trends while return variation stays unchanged.
• Volatility is generally more meaningfully measured relative to price than inferred from price alone.
• The responses suggest inverse price may help with normalization, but provide no test of that use.

Tags

# inverse of stock price


# inverse of stock price












Is there any intuition to use 1/P (inverse of the stock price) as a factor of volatility?

$VOLT = \beta_1 * \frac{1}{P} + Res$

P.S: In a research paper, I found it's related to the market micro-structure, but I don't really know in which way they are related.

## Answer by Forgottenscience (score 1)

https://quant.stackexchange.com/a/36160

This is a poor estimator of volatility. Prices suffer from lack of stationarity (making different time periods hard to compare), and aren't mean reverting like we mostly believe volatility is. For example, if an asset increases in price by a constant amount each day the volatility will seem to be going up, even though the standard deviation of the returns is 0.

## Answer by Pavel (score 0)

https://quant.stackexchange.com/a/36174

Re: high prices $\Rightarrow$ lower volatility

It's pretty common for high volatility to arise when prices are lowering. This is because prices lowering is a movement in the underlying, and thus increases vol. Volatility is generally not related to the actual price of the underlying - you would ideally like to normalize. $\frac{1}{P}$ could potentially be used for normalization.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.