Adding Subjective Risk Penalties to Portfolio Optimization
Summary
The document considers a real estate portfolio whose historical return series may understate risk because it reflects market averages and contains gaps. It asks how an optimizer can incorporate concerns about particular property types or locations when estimated volatility alone does not capture those concerns.
The answer presents two ways to express these preferences in a quadratic portfolio optimization. One is to impose linear exposure limits for individual locations, asset classes, or investments. Another is to assign each candidate an undesirability score and add the score, scaled by its portfolio weight, to the objective being minimized; the total score can also be constrained. The score’s scale matters: it should influence the solution without overwhelming the covariance term. These approaches allow judgment-based risk preferences to supplement statistical risk estimates. The response gives no calibration procedure or empirical evidence for choosing scores or limits, so their values require careful interpretation and validation by the portfolio decision-maker.
Key ideas
- Linear constraints can cap exposure to locations, property types, or individual investments.
- An undesirability score can represent risks that historical volatility estimates miss.
- Weight each candidate’s score by its portfolio allocation when adding it to the objective.
- Scale penalties so they affect the optimization without overwhelming the covariance term.
- A portfolio-wide limit can constrain the combined undesirability score.
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Full text
# Optimise Portfolio with exogenous risk estimates # Optimise Portfolio with exogenous risk estimates I am working on optimising a real estate portfolio. I have a total returns series for various property types and locations. I am comfortable with my expected returns estimates, but I have significant concerns with the estimates on risk. The series is more of a market average, which provides a false sense of security as to how volatile the asset is. Also, the historical data is often patchy and looking at volatility alone does not provide sensible results. I have been reading around but haven't had much luck here. Are there methods to help me to choose my own risk measures? I would like to add penalties for certain asset classes and locations which clearly aren't being penalised enough in my current models. I have been working on this in R. ## Answer by Dimitri Vulis (score 3) https://quant.stackexchange.com/a/58297 This is language and asset class-agnostic, and applies to any quadratic optimization. There are two approaches. - impose linear constraints for every location and every class. (I guess with real estate, you could say something like, no more than 10% in Las Vegas, and no more than 15% in shopping malls. And, of course, no more than n% in any single investment.) - Assign some undesirability score to each candidate (e.g. 0 - you're not concerned, 1 - you're concerned a little, 2 - you're concerned a lot) and include it (multiplied by the weight) in the objective function being niminized. (Be sure to scale it so it affects the optimal portfolio, but does not overwhelm the minimum-covariance part of the objective function.) And/or, impose a linear constraint on the total undesirability score of the portfolio.
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