Return Direction and Magnitude: Forecastability and Volatility Clustering
Summary
The document separates returns into direction, represented by their sign, and movement size, represented by absolute return. One response notes that direction is a binary outcome while magnitude is continuous, and cautions that neither can be predicted perfectly. It argues that the binary nature of direction may make it somewhat easier to predict, but provides no supporting analysis for that comparison.
A second response, specifically about equities, takes the opposite view: magnitude is more predictable than direction because volatility is more predictable than equity risk premia. It links this to volatility clustering and mean reversion, describing alternating calm periods and periods with larger moves in either direction. These are competing claims rather than a settled conclusion. The text gives a conceptual rationale but no data, forecasting test, horizon, or accuracy measure, so the relative predictability should not be treated as universal.
Key ideas
- Returns can be considered in terms of sign and absolute magnitude.\nThe responses disagree about whether direction or magnitude is easier to forecast.\nOne equity-focused explanation links magnitude forecasts to volatility clustering and mean reversion.\nNeither component is presented as perfectly predictable, and no empirical results are supplied.
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Full text
# Predict Market Direction, What is forecastable/unforecastable?
# Predict Market Direction, What is forecastable/unforecastable?
Let's decompose the return process $R_t$ as follows :
$$R_{t} = sign(R_{t}) * |R_{t}| $$
What's part of the equation is forecastable?
## Answer by SRKX (score 4)
https://quant.stackexchange.com/a/7494
The two components you refer to in your questions are:
- Market direction (the sign of the return)
- Change magnitude (the absolute value of the return)
First, I'm sure you realize that neither of these are predictable at a 100%, otherwise there would be no way to make profit (you make profit by seeing things other didn't).
To answer the question, I would say that predicting the direction is a bit easier in a sense than the magnitude simply because of the possible outcomes:
- the sign is a discrete variable with 2 possible outcomes;
- whereas the magnitude is a continuous variable).
Other than that, there exists techniques for both, but neither will give you 100% accuracy, (or even close to that).
## Answer by vonjd (score 4)
https://quant.stackexchange.com/a/7498
I think this one has a clear answer (I am solely talking about equities here): The change magnitude is much more predictable than the direction.
The reason being that equity volatility is much more predictable than equity risk premiums. Volatility is nothing else but change magnitude and due to the stylized facts of volatility clustering together with mean reversion more predictable than the whole package, therefore also including direction. Basically the pattern is that there are phases when most movements are big in either direction and phases where everything is calm.
For a nice exposition see also this paper by Andrew Ang: Equity market levelShown 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.