M-squared's view of negative Sharpe ratios

In The Spaulding Group's January newsletter, I expanded upon a recent blog post where I introduced a couple graphics in an attempt to "make sense out of" negative Sharpe ratios. Two pillars of the investment performance community, Carl Bacon and Steve Campisi, chimed in with comments, which will appear in the February newsletter. In the mean time, I will take this topic a bit further, with inspiration from both gentlemen.

Would it not be useful to see how the Modigliani-Modigliani risk-adjusted measure responds to negative Sharpes? I believe so. And in truthfulness and full disclosure, I will admit to being kept awake last night thinking about this (graphing it in my head), until I got up to put the materials together.

On the positive side. Let's begin by recalling how the M-squared looks when we're dealing with positive returns.

Recall that we first plot the benchmark (in the risk/return graph), and draw a line from the risk free rate and through it; this is the "market line." We can next plot the portfolio, and draw a similar line. Here I show a case where the portfolio and benchmark have identical returns, but the portfolio has taken on added risk. Note that its line falls below the benchmarks, meaning it will end up with a lower M-squared value.

The fundamental step in this method is to equalize the risks, and this is done graphically here, where we shift the portfolio's point to the left, so that it aligns with the benchmark's risk; and, as predicted, we have a lower return.

What happens on the negative side?

I again chose a case where the portfolio has the same return as the benchmark, and where it also has taken on greater risk. But notice that it plots above the line. We again adjust the portfolio's risk, so that it aligns with the benchmark's, and we see that it has a higher return.

This is what people find confusing: more risk, same negative return, why not a lower Sharpe ratio (risk-adjusted return)? Do the graphics help? Perhaps in some cases, but surely not all.

That's why I hold to the notion that we would expect that by taking on more risk, the portfolio should have a much lower return; however, it doesn't, and thus it gets rewarded. Perhaps if we inverse the thinking a bit: the benchmark took on less risk but did equally bad (i.e., it managed to do as badly as a portfolio that took on more risk, so it somehow captured even greater negativeness than one would have anticipated.

Please let me know your thoughts. I plan to tackle this subject from a beta perspective, too!

Marrying Performance and Risk

I have been invited to join the CFA Institute's Jonathan Boersma and Neuberger Berman's Leah Modigliani to speak on the subject of risk, at an evening event at the NYSSA (New York Society of Security Analysts). The program takes place at 6 o'clock on January 26.

I am particularly looking forward to this, simply to hear Leah once again discuss the risk-adjusted measure she and her Nobel Prize winning grandfather, the late Franco Modigliani, developed; to me, this alone, is "worth the price of admission." As I understand it, Jonathan will discuss GIPS' (Global Investment Performance Standards) new risk reporting requirement; I will briefly provide an overview of a variety of measures, and then Leah will discuss M-squared (I guess we could say that she's "one of the M's" in this model!).

Hope you can join us; I guarantee you'll benefit!

A risk measure to consider...

Bruce Feibel, author of Investment Performance Measurement, spoke at the Performance Measurement Forum's North America chapter's Fall meeting on the topic of risk. I was quite pleased when he expressed his support for the risk-adjusted measure, M-squared, also known as Modigliani-Modigliani, named for its designers, Franco and Leah. This grandfather/granddaughter duo developed what Bruce and I feel is a superior metric to evaluate risk.

Unlike the other risk-adjusted measures, its results are highly intuitive. To me there's a parallel to the way we show gross and net performance, as well as pre- and after-tax results. For example, from a gross/net perspective we might see:

• Gross return = 17.45%
• Net return = 16.68%.

The net result reflects the impact of the advisor's fee. From a tax perspective:

• Pre-tax return = 19.35%
• After-tax return = 16.45%.

Well, with M-squared we could see:

• Before adjusting for risk = 18.27%
• After adjusting for risk = 16.45%.

Granted, we might not label our  results this way, but I'm simply trying to convey how the results align with what we often see today. Our return has been adjusted for risk, unlike the other measures. And unlike the other measures, its reported in percentage terms, which are much clearer to comprehend.

If you're not including M-squared in your reporting, you should be!

And, if you'd like more information on this measure, send me a note.

Peter Dietz and the Modiglianis

While I doubt that they were aware of it, when Franco and Leah Modigliani developed their risk-adjusted return measure, M-squared, they were extending an idea first promulgated by Peter Dietz in his 1966 thesis, from which we obtained the notion of time-weighting and the Dietz return formulas.

Peter recognized that return without risk didn't show the full picture. But, if we are comparing two managers or a manager with his benchmark, even when risk is shown it's difficult to draw any conclusions when the two return and risk measures are different. For example, if Manager A has a return of 3.00% and the benchmark has a return of 2.95%, and the manager's standard deviation is 1.02% vs. 0.98% for the benchmark, what can we conclude? We must somehow bring these numbers together.

Dietz felt that if the portfolio and benchmark had the same return, then we can compare their risks, or vice versa, but as long as they were different we had a problem. Well, since then we've seen the development of numerous risk-adjusted measures that are able to handle this situation.

Franco and Leah, however, implemented Dietz's idea, so to speak, by equalizing the risk measures so that we end up with a simple comparison of returns. Theirs is the most intuitive of all the risk-adjusted measures and the one I champion the most.

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To learn more about risk-adjusted returns, join us on August 19 for our next webinar. And, to learn more about M-squared, I suggest you read my article: "M-squared: A Double-take on Three Approaches to a Primary Risk Measure," The Journal of Performance Measurement, Summer 2007.