Expected Return Estimation in Mean-Variance Portfolios
Summary
The document considers how to estimate expected returns for mean-variance portfolio optimization, noting that a simple historical average is a basic and potentially inadequate choice. It emphasizes that return estimates are difficult to make reliably because estimation error can undermine the resulting portfolio weights.
The discussion contrasts return estimation with covariance estimation, which is often more tractable. It gives the global minimum variance portfolio as an example of an allocation that can be computed from the covariance matrix without estimating asset means. For investors who do want expected returns, it points to CAPM and Fama-French factor models as empirical frameworks, while noting that these depend on assumptions such as an observable market portfolio. The document offers conceptual guidance rather than a comparison of methods or empirical performance results, and it does not provide a procedure for choosing among return estimators.
Key ideas
- Expected returns are difficult to estimate consistently because estimation error can materially affect portfolio weights.
- The global minimum variance portfolio can be constructed using the covariance matrix without expected return estimates.
- CAPM and Fama-French models are possible frameworks for estimating expected returns.
- Factor-model estimates depend on assumptions, including how the market portfolio is defined.
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# Methods for superior estimates of returns in m.v. portfolio optimization
# Methods for superior estimates of returns in m.v. portfolio optimization
Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-Wolf shrinkage, Oracle shrinkage, MCD (minimum covariance determinant), EWMA covariance etc.) how is it possible to improve the optimization results considering the estimation of the mean return component or rather what methods happened to be more effective and efficient in estimating the returns (both from the empirical and practical point of view)?
Of course the simple linear model (expectation = mean return over the last n years) is quite simplistic.
## Answer by develarist (score 4, accepted)
https://quant.stackexchange.com/a/46070
Expected returns are very difficult to estimate reliably without incurring estimation error as found out by Merton (1980) "On estimating the expected return on the market". This is why estimating volatility/the covariance matrix has become the default approach in the mean-variance model because volatility is easier to predict than returns. Even the global minimum variance portfolio, often considered to outperform other frontier portfolios, can be solved without the asset means:
$$\omega = \frac{\Sigma^{-1}\iota}{\iota^{\top}\Sigma^{-1}\iota} $$
The classical CAPM and Fama-French 3, 4, or 5 factor models, when re-arranged, are available though for those who insist that superior estimates of expected returns can be consistently measured well from empirical (heteroskedastic) data, but even these CAPMs rely on the assumption that the market portfolio is observable (find Roll's critique and the article Beta is dead). Then again, beta itself is computed from the covariance matrix.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.