Choosing Volatility Measures for Different Return Dynamics
Summary
The document explains why analysts use multiple historical volatility measures, including realized variance, realized absolute variation, and bipower variation. Its central point is that these measures describe different aspects of observed price behavior rather than serving as interchangeable estimates of one universal quantity. Other examples mentioned include intraday range-based measures and beta, which captures an asset’s variability relative to a benchmark.
This distinction affects how a researcher compares models that use different volatility measures as inputs. A measure suited to one dynamic, such as intraday price movement or signed upside and downside variation, may not answer the same question as another. The response gives a conceptual rationale, not a head-to-head empirical comparison or a rule for selecting a measure. Model fit statistics alone would assess predictive performance for the chosen target, so interpretation still depends on defining the volatility feature and research objective clearly.
Key ideas
- Different volatility measures capture different features of price and return behavior.
- Realized variance, absolute variation, and bipower variation summarize historical returns in distinct ways.
- Intraday range measures and beta address other aspects of price variability.
- Model fit statistics compare predictive performance for a specified target, not the conceptual meaning of measures.
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Full text
# Why are there different estimators for stock volatility? (realized variance, RAV, etc) # Why are there different estimators for stock volatility? (realized variance, RAV, etc) I am very confused about why different volatility estimators (RV, RAV, BPV, etc) exist. If the goal is to find the best estimator for stock volatility, and volatility is latent, how do I know which estimator performs the best when the mathematical definition for these estimators are all different? ``` Realized variance = sum[(return at t)^2] in a day Realized absolute value = sum|return at t| in a day Bipower variation = sum |return at t-1|*|return at t| in a day ``` If I use a linear model and substitute each of these estimators as the regressor, doesn't this mean I can't compare the results directly, but I can only compare how well the linear model is able to predict itself based on MSE, R^2, and so on? ## Answer by Matt Wolf (score 1, accepted) https://quant.stackexchange.com/a/7154 I would not call them "estimators" but rather measures because this is volatility on historical returns. The reason why there are different such measures is because each one represents volatility in different ways in order to measure the volatility of different dynamics, be it price, return, upside price moves only, down side price moves only, intraday dynamics. For example: - There are measures of intra-day price volatility, such as Parkinson or Garman-Klass - Measure that only concerns itself with deviation without regard to signage, such as variance on absolute values or squared deviations - Measure that represents variability of an asset relative to a benchmark, Beta There are a lot more but I guess you get the point. In Summary, different measures of volatility in order to capture variation of different dynamics.
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