Autocorrelation in Global Equity Factor Models
Summary
The document explains how asynchronous market closes can distort factor model estimation for global equities. In a cross-sectional model, factor returns and asset-specific residuals are estimated from asset returns and exposures; return series then inform estimates of factor covariance and residual risk. When assets trade in different time zones, close-to-close returns may overlap imperfectly, creating measured cross-autocorrelation even when the underlying return relationship differs.
It presents three possible responses: calculate returns at a common absolute time, add a market-close-time exposure, or aggregate returns over longer windows. Under the stated assumptions of jointly normal log returns with independent increments, correlation in overlapping measured returns is attenuated according to the fraction of overlap; aggregating increases that fraction and moves measured correlation toward the true correlation. The document does not settle which method is best. Common-time pricing may be difficult, a close-time factor raises interpretation questions, and aggregation discards observations, reducing the effective sample size.
Key ideas
- Asynchronous market closes can induce cross-autocorrelation in global equity returns.
- Factor and residual risk estimates can be affected by correlation measured from close-to-close returns.
- Using prices from a common absolute time is one possible way to reduce timing mismatch.
- A market-close-time exposure may capture timing effects, but its factor return and risk interpretation are unclear.
- Longer return aggregation can bring measured correlation closer to the underlying correlation while reducing sample size.
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# How to account for autocorrelation in factor models?
# How to account for autocorrelation in factor models?
In BARRA style factor models, asset returns are modelled as a linear function of factor exposures $$ R_t = X_tf_t + \varepsilon_t, $$ where $R_t$ is the return vector, $f_t$ the factor returns, and $\varepsilon_t$ the residual (asset-specific) return. $X_t$ the factor exposure matrix, which contain information about each asset, such as its country, industry, or growth rate.
The coefficients $f_t$ and $\varepsilon_t$ are estimated using cross-sectional regression. Given a time series of factor and residual returns, we can then model their distribution, and compute sample statistics (i.e. factor covariance matrix and residual variance).
The estimation universe typically contains a large number of global equities, traded across different time zones. If $R_t$ contains returns computed at market close, this can lead to problems for model estimation. For example, if (actual) asset returns are correlated, this leads to (cross) autocorrelation in $R_t$. My question, is how to properly account for this autocorrelation when estimating a factor model?
The obvious solution is to compute returns using the same (absolute) point in time. However, closing prices are often readily available, and using them avoids after-market prices, which can come with their own problems.
Another solution could be to add an additional factor to the exposure matrix $X_t$, such as market closing time, in the hopes of catching this effect. But how then do we interpret the return attributed to this factor, as well as the "risk" it implies?
Edit: A third option is to aggregate returns over time. Suppose we have two stocks, whose (log) returns are jointly normal with correlation $\rho$, and independent increments. If measured returns $\tilde{R}_t$ are computed at overlapping increments, their correlation will be $a\rho$, where $a$ is the fraction of overlap.
Aggregating across $N$ increments, effectively changes the fraction of overlap to $a_N = 1-\frac{1-a}{N}$, and thus measured correlation will tend to the true correlation, as the aggregation window increases.
However, aggregation throws out a lot of information, essentially decreasing the sample size by a factor of $N$.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.