Forecasting Relative Stock Performance: Model Returns or Excess Returns
Summary
The document compares two ways to forecast a stock’s performance relative to a benchmark: model each asset’s returns separately and subtract the forecasts, or model the relative return directly. It frames the problem as a weekly time-series forecasting task with possible exogenous variables such as calendar effects and corporate actions, and asks about implications including stationarity.
The response favors forecasting the two return series when broader evaluation is useful, because separate forecasts preserve information about each asset and allow the researcher to derive and assess alternative relative-performance measures. Directly modeling the spread can be adequate when that metric alone is the objective. It recommends comparing both approaches against realized relative returns, but supplies no empirical test, specification guidance, or definitive statistical result. The choice therefore depends on the forecasting objective, and the suggested comparison should be treated as an evaluation approach rather than evidence that one design always performs better.
Key ideas
- Relative performance can be forecast by subtracting separate asset forecasts or by modeling the relative return directly.
- Separate forecasts retain information about each asset and support broader evaluation choices.
- A direct relative-return model may suffice when relative performance is the only target.
- Compare both approaches against realized relative returns; the document reports no empirical comparison.
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# Prediciting outperformance - choice of statistical design? # Prediciting outperformance - choice of statistical design? I want to predict relative outperformance between a stock and an associated benchmark index using statistical time-series models (e.g. ARIMA) and some exogenous variables (day of the week, corporate actions etc.) on a weekly basis. Two different statisitcal designs come to my mind: - Estimate and predict the returns for stock and benchmark index separately and calculate outperformance based on the two predicted returns - Calculate outperformance beforehand and use this to estimate the model and predict outperformance directly What could be statistical implications or pros and cons using the one or other approach (e.g. still having a stationarity process in approach 2 etc.)? Any feedback appreciated! ## Answer by Pleb (score 2) https://quant.stackexchange.com/a/65724 #### If I have understood your question correctly, the first approach would be better: This is just my thoughts, which stems from intuition: For two forecasted returns of the financial assets, you will always be able to calculate a predicted outperformance value and compare it to the realized version when available. However, forecasting the outperformance metric only (assuming it is some sort of transformation/distance measure between the forecasted returns) you will not be able to back out the values of both forecasted returns (accurately). Therefore, the first method offers you the freedom to use alternative metrics and statistical evaluations on the forecasted returns, giving you a more nuanced picture of your predictions as-well as your statistical models. In the end, you can do both. Try and observe how much the forecasted outperformance metric (found from a statistical model, ie. your second method) deviates from the realized counterpart as-well as the forecasted outperformance metric calculated from the forecasted returns (your first method). See which method is closer to the realized values. If the difference is marginal, I would opt for the first method. Nevertheless, if your only goal is to forecast the outperformance metric, then the second method should be fine. If you want to do an extensive analysis on the financial assets, including alternative metrics and statistical evaluations, then the first method should be your choice. I hope this provides some feedback.
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