You hired a value manager. Three years later you own a growth fund with the same name on the door. Style analysis is how you find out, and it comes in two forms with a clean division of labour.
How does returns-based style analysis work?
Returns-based style analysis is Sharpe's method, published in the Journal of Portfolio Management in 1992: regress the fund's return series on a set of style-index return series, with the coefficients constrained to be non-negative and to sum to one, so they read as an implied portfolio. It needs nothing but returns, which means it works on any fund whose holdings you cannot see, and it works on a whole universe at once. Its output is a statement about what the fund behaved like, and the fitted R^2 says how much of the fund's variation the style mix explains. The residual is what the style indices could not account for, and the intercept is a selection return.
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With two style indices the constrained problem has a closed form you can compute by hand, which is why Worked Example 5 uses two. Setting the weights to w on value and 1 - w on growth, minimising the tracking error against the style mix is a univariate regression of (r_F - r_G) on (r_V - r_G), and the slope, clipped to the interval from zero to one, is the value weight. With three or more indices the constraint set requires a quadratic program, but the interpretation does not change.
Holdings-based style analysis computes the same exposures from the actual portfolio, by scoring each holding on the style characteristics and weighting up. It is more precise, it reacts immediately to a change in positioning rather than after a window of returns has accumulated, and it needs the holdings, which the returns-based version does not. The two disagree in a specific and diagnostic way: a fund whose holdings-based value exposure is high while its returns-based exposure is low is usually holding value-labelled stocks that have started behaving like something else.
How do you detect style drift?
Drift is detected by running the analysis over rolling or adjacent windows and watching the weights move. The question is always whether the movement is larger than the estimation error, and that is answerable: each weight has a standard error, and the difference between two windows has a standard error of sqrt(se_1^2 + se_2^2). On Worked Example 5's fund the value weight falls from 0.7758 to 0.3452, a drift of 43.06 percentage points against a standard error of the difference of 0.0653, so the t-statistic is 6.60. That is not noise, and the fund is not the fund that was hired.
Two cautions keep the technique honest. Style analysis is a regression, so every diagnostic that applies to regression applies here: the style indices are correlated with one another, which makes individual weights unstable even when the fitted values are fine, and a short window over a calm period will estimate almost anything. And a drift finding is a question, not a verdict. Managers drift for defensible reasons, including a genuine change in where value is available. What is not defensible is drifting without telling the client, because the client's own asset allocation was built assuming the exposure they were sold.