Single factor model of financial price data
Consider a data matrix which contains the log-returns of assets over time periods (say, days).
A single-factor model for this data is one based on the assumption that the matrix is a dyad:
where , and . In practice, no component of and is zero (if that is not the case, then a whole row or column of is zero, and can be ignored in the analysis).
According to the single factor model, the entire market behaves as follows. At any time ( ), the log-return of asset ( ) is of the form
The vectors and has the following interpretation.
While single-factor models may seem crude, they often offer a reasonable amount of information. It turns out that with many financial market data, a good single factor model involves a time profile equal to the log-returns of the average of all the assets, or some weighted average (such as the SP 500 index). With this model, all assets follow the profile of the entire market.
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