Sample Question #150 (finance – portfolios)

What are some of the criticisms of the mean-variance portfolio optimization model?

(Comment: as I’ve emphasized many times, when you study a model — be it financial or mathematical or statistical — try to think like a scientist and understand both its strengths and its weaknesses. Most decent textbooks will tell you what may be wrong with the model. It pays to pay attention to these details — after all, the quant job always demands a detail-oriented individual.)

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I personally really like questions like this — and I ask them as an interviewer — because I think it’s more important for a quant to understand when to and when not to use a model, rather than memorizing the model’s details, which can be looked up easily. If you use the wrong model, no matter how "elegant" or "sophisticated" it is on paper, it’s still wrong. Remember the adage: garbage in, garbage out. (This aphorism applies to both the modeling framework and the data.)

There are many issues with the mean-variance approach, including:

— it assumes a specific form of the investor’s utility function

— it requires estimation of too many unknown input variables

— its results are very sensitive to the inputs

— its real-world result is no better than randomly chosen portfolios

Tip: when you are given a question like this, first write out the model, and then look at each assumption behind the model as well as each mathematical term in the model and try to imagine what can go wrong with these elements. For instance, the mean-variance model requires a risk-aversion parameter; you can then say, "this is unrealistic" or "this does not allow us to capture the different risk appetites across individuals and across time," etc.