Optimise Portfolio with exogenous risk estimates

Question

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 1

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.