I gave a talk on Wednesday for a software vendor on the topic risk-adjusted performance measures and began, as I often do, by mentioning Peter Dietz's statements regarding this subject in his 1966 thesis. He pointed out how risk and return should be linked, but offered a fairly naive approach, suggesting that when two portfolios have the same returns, it's easy to see which did better when comparing risk (the one with the lower risk); likewise, if they each have the same risk values, then by comparing the returns we can also draw conclusions as to who did better (in this case, the one with the higher return). However, the likelihood of encountering these situations is quite remote.
Oddly, perhaps, when the late Nobel prize winner Franco Modigliani and his granddaughter, Leah, developed their risk-adjusted performance measure (M-squared), they offered a general approach to determine the risk-adjusted value (which for them is measured in basis points, just like return): we equalize the portfolio's risk with the benchmark's. This trickery is accomplished through their model, which results in a corresponding adjustment to the portfolio's return (downward, when risk is lowered; upward, when risk is increased). The result is an adjusted portfolio return with the same risk as the benchmark, which allows easy (and intuitive) comparison.
Whether or not Franco and Leah were aware of Dietz's earlier statements is unknown, but it's interesting that what appeared to be rather naive is essentially what they've done! And, M-squared happens to be one of my favorite measures, which sadly hasn't been adopted by enough firms, yet.
(Note: I've written an article on this topic ("M-squared: A Double-take on Three Approaches to a Primary Risk Measure." The Journal of Performance Measurement. Summer 2007) in case you'd like to explore this matter further).
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Some statements may appear naive due to their simplicity, but I suspect that the true naivete is found in our confidence in the complex models that contain many factors along with some high power mathematics. While the mechanics of these models may indeed be sophisticated, the true naivete is found in their belief in the absolute certainty of the models themselves. It's as though by expressing some relationship in a complex model (what I call "scientificating it") you make the thing you're trying to explain more knowable than it truly is.
ReplyDeleteFor example, some years ago when interest rates began falling, the refinancing index ("Refi Index") stood at 500. The PhDs and "quants" of Wall Steet were convinced that they had modeled the human behaviors around refinancing home mortgages through their complex mathematical models. It took them by surprise when the index spiked from 500 to 1,500, and so they all went back to the drawing board and returned with "improved"models. In spite of this, Unfortunately, as rates continued falling we saw further spikes that brought the index to 3,000 and then to 7,000.
Having seen this I ask: Who is more naive - the quants who think that a simple model is naive, or the person who makes a simple statement that return is linked to risk (however defined) so that when we see return, we must also be seeing fair compensation for risk? For my money, I'm going with the simpler statement, however "naive" it appears. Too often we find that what we thought was "alpha" turned out to be nothing more than unidentified risk. And sometimes that risk turns around and bites us. Anyone remember 2008?