When to Forecast Portfolio Returns Directly or by Asset
Summary
The document compares forecasting each security’s return and combining the predictions with forecasting a portfolio return directly. Its central point is that, for linear return models, portfolio characteristics or factor exposures are weighted averages of the corresponding security values. Under a coherent linear model, applying the model to the portfolio exposure gives the same expected return as weighting the individual forecasts. CAPM and Fama–French models are cited as examples.
That equivalence depends on the model’s structure; unrelated or inconsistent estimation procedures need not produce matching aggregate predictions. The answers also distinguish separate regressions from joint multivariate estimation, noting that joint modeling can represent relationships among securities. The discussion cautions that expected-return estimates are difficult and error-prone, and suggests that volatility and covariance may be more tractable forecasting targets. GARCH, EWMA, and Ledoit–Wolf covariance estimation are named, but no comparative results, implementation details, or forecast horizon are supplied.
Key ideas
- In a linear return model, portfolio exposures can be computed as weighted averages of security exposures.
- A coherent linear model produces equivalent portfolio forecasts from aggregated exposures or weighted security forecasts.
- Separate and joint estimation can differ when securities or model inputs are interdependent.
- Expected returns are difficult to estimate, while volatility and covariance may offer more reliable forecasting targets.
- The document names several volatility and covariance methods without comparing their empirical performance.
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Full text
# Predicting portfolio returns # Predicting portfolio returns I suppose there are roughly two approaches to predict portfolio returns. Either predict the returns of all underlying stocks and aggregate all individual stock predictions, or predict the portfolio returns directly. What would be better? Or e.g. what would the advantages/disadvantages be of both approaches? ## Answer by Jason p (score 1) https://quant.stackexchange.com/a/45122 A portfolio is often a collection of securities. A portfolio represents the weighted sum of each security's return. I believe when you say "aggregate all the prediction" is a synonym of "predict the portfolio return." To my knowledge, calculating portfolio returns are always driven by the underlying security exposure to risk. ## Answer by Dave Harris (score 1) https://quant.stackexchange.com/a/45127 It rather depends on how you mean separate estimation versus joint estimation. For example, if by separate you mean that you would run a separate regression for each security, one at a time, versus a vector regression, then you will always be less accurate with separate estimations unless the variables are intrinsically independent. However, nothing prevents you from creating a vector regression. It would give you both the predictions for the portfolio and the parts. If you are using a coherent method then the sum of the parts will equal the value of the whole. If you are not, then that is not automatically true. ## Answer by Alex C (score 1) https://quant.stackexchange.com/a/45129 Most models of return are based on "characteristics" or "exposures" of the stocks. These are different things but they share the property that they are linear across a portfolio. You find the characteristic (or exposure) of the portfolio by forming the weighted average of the characteristics (exposures) of the stocks in the portfolio. As a result, the 2 approaches you suggest give the same result: For example in CAPM there is only one exposure, known as Beta. You can either compute the expected return of each stock and then form their weighted average, or you can first form the beta of the portfolio and apply the CAPM to the portfolio beta. The results are identical. The same is true for FF3, FF5 and other linear models of return. ## Answer by develarist (score 1) https://quant.stackexchange.com/a/46059 Even when predicting asset returns with classical CAPM or Fama-French 3, 4, or 5 factor models, estimates will tend to have significant estimation error, and as explained by the others, univariate vs multivariate are equivalent. The difficulty of predicting asset means has been well known since Merton (1980) and that's why most people, at least in asset management, decide to forecast the second moment of asset returns instead, volatility. Asset volatility can be more reliably predicted than asset means can, and there are a variety of univariate volatility estimators out there, as well as multivariate volatility models for the covariance matrix in the case of portfolios, that will give you better results. GARCH, EWMA, and Ledoit-Wolf covariance models that reduce the volatility of risk estimates through the introduction of bias are some examples. How far ahead your forecast horizon is is the next thing to consider.
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