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!

Standard Deviation ... a risk measure or not?

Standard deviation is a much misunderstood measure, in spite of its common use.

First, is it a risk measure? It depends on who you ask. It's evident that Nobel Laureate Bill Sharpe considers it to be one, since it serves this purpose in his eponymous risk-adjusted measure. Our firm's research has shown that it is the most commonly used risk measure.

And yet, there are many who claim that it does anything but measure risk. What's your definition of risk? If it's the inability to meet a client's objectives, how can standard deviation do this? But, for decades individuals have looked at risk simply as volatility.

As to volatility, is it a measure of volatility or variability? In an e-mail response to this writer, Bill Sharpe said that the two terms can be used in an equivalent manner.

The GIPS(R) (Global Investment Performance Standards) 2010 exposure draft includes a proposed requirement for compliant firms to report the three year annualized standard deviation, which appears to have survived the public's criticism and will be part of the rules, effective 1 January 2011. But, will it be called a "risk measure"? This remains unclear.

Interpreting standard deviation is a challenge, since the result's value will vary based on the return around which it's being measured. Example: your standard deviation is 1 percent; is this good or bad? If your average return is 20%, then to know that roughly two-thirds of the distribution falls within plus-or-minus 1% doesn't seem bad at all, but if your average return is 0.50%, then doesn't 1% sound a lot bigger? In reality, it's better to use it to compare managers or a manager with a benchmark. Better yet, as part of the Sharpe Ratio, as this brings risk and return together.

I could go on and on, but will bring this to a close. Bottom line: it's easy to calculate (if we can agree on how (didn't address this today)), in common use, and has a Nobel Prize winner's endorsement. Will it go away? Not a chance. If you're not reporting it, you probably should be.

Risk-adjusted returns & money weighting

Most academic articles that deal with "returns" are actually dealing with risk-adjusted returns. In the course of writing an article on this subject I came across countless such articles. In The Journal of Performance Measurement we've tackled both this subject as well as pure returns (i.e., returns without the adjustment for risk), as both topics have value.

One topic which I don't recall seeing anything on is risk-adjusted performance relative to money-weighted returns. Given my general preference for the IRR, it's high time I took on this topic. Later today I will conduct a webinar on risk-adjusted performance but sadly won't be including anything on money-weighting as the subject hasn't yet gotten enough of my attention.

When evaluating the risk of money managers, clearly the standard approach of measuring risk-adjustment relative to time-weighted returns makes sense. But what about cases where the returns should be money-weighted: should the risk-adjusted measure likewise be? I would think so. But how to accomplish this might require some further thought; something I intend to invest in the coming weeks. So stay tuned!

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.