Portfolio Optimization, Forecast Bias, and Independent Risk Assumptions
Summary
The document raises a concern that portfolio optimization can be circular when a portfolio manager supplies expected returns and covariances based on views that already shaped the current portfolio, and a risk manager then uses those same inputs to judge its allocation. The response argues that this reasoning assumes both managers share identical forecasts. In practice, a risk manager can challenge return assumptions, use more conservative expected returns, form an independent view of risk, and run scenario analysis. Different assumptions can therefore produce a different assessment of what allocation is appropriate. The response also distinguishes this concern from broader critiques of optimization, such as the sensitivity of results to uncertain inputs, which require their own remedies. Finally, it notes that optimization can still clarify how expected returns and variances relate to weights in a simplified maximum-Sharpe setting. The discussion is conceptual rather than empirical; it offers no worked portfolio example or evidence that a particular set of assumptions will improve realized performance.
Key ideas
- Optimization depends on expected returns and covariances, which are uncertain inputs rather than objective facts.
- A risk manager can assess a portfolio using independent or more conservative assumptions.
- Scenario analysis can expose risks that are not apparent under the portfolio manager's forecasts.
- Input uncertainty is a separate challenge from the specific concern about circular judgment.
- Simplified optimization can clarify how expected return and variance influence portfolio weights.
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Full text
# Portfolio allocation question: is it not circular reasoning? # Portfolio allocation question: is it not circular reasoning? Is portfolio allocation not circular reasoning? Say we have a portfolio manager, Michael, and a risk manager, Vito. Michael has a portfolio and would like to determine the optimal allocation of his portfolio. So Michael goes to Vito and says "hey Vito, what is the optimal allocation?". Vito then sets up and solves a portfolio allocation problem. However, in order to do so, Vito needs some input from Michael: the mean returns $\mu$ and covariance matrix $\Sigma$ of the market! Obviously Vito does not know any of this. He's just a risk manager, he can do the math but he cannot predict the future. And sure, he can calculate historical returns and covariances, but they are not reflective of the future. The only person in this context who can provide $\mu$ and $\Sigma$ is thus Michael... however, Michael's current portfolio allocation (before any optimization has been done) has, at least to a certain extent, been made with Michael's views on $\mu$ and $\Sigma$ in mind. Therefore, if we use these as input in our portfolio allocation model, we will find that Michael's current allocation may appear (close to) optimal, not because it actually is, but because Michael's input was used to judge Michael's allocation, which obviously leads to a bias. So I really don't see what the point of portfolio optimization is? It just seems like circular reasoning, or like being your own judge. ???? ## Answer by Antoine (score 2) https://quant.stackexchange.com/a/61442 You are making some kind of circular reasoning and then dismissing portfolio optimization. I believe you are beeing confused by portfolio optimization on its own and how it's used in practice. In my opinion, there seems to be 3 problems in your argument: - Your reasoning is circular because you assume the risk manager will use the the same expected return and covariance matrix than Michael's and that "a portfolio is optimal" is some kind of absolute statement. A risk manager will not do that. His job is to challenge assumptions made by the portfolio manager, hence his view on expected returns will be more conservative: at best 0. While his view on risks should be his own. Risk managers run scenario analysis to assess portfolio's risks. Given different assumptions, they will have different opinions of what's a optimal portfolio. - It's not because you have found a scenario under which portfolio optimization is useless that it really is. There is actually a great wealth of academic litterature of why portfolio optimization is dangerous and how to remedy it, but this has nothing to do with your argument. See for instance here. - Portfolio optimization has merits on his own, independently of who is using it. In it's simplest form it says: if you know your expected return and covariance matrix (say diagonal), then the optimal allocation in the maximal sharpe ratio sense gives optimal position weights: expected return divided by variance. It's already a good insight.
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