What does Bill Sharpe have to say?

Bill Sharpe read my recent blog post on addressing negative Sharpe ratios, and  offered the following:

Your blog post seems fine.

About the only alternative I can offer is this:

The (original) Sharpe ratio in effect compares two alternative combinations of treasury bills and portfolios (funds). The one with the higher (ex post) ratio provided a better (or less bad) average return per unit of risk. Thus if portfolio A had a higher ratio than B, a combination of bills and A with the same risk as a combination of bills and B had better (or less bad) performance.

Unfortunately such comparisons are likely to common these days, so keep up your campaign.

I think sometimes think that they don't make sense, but deep down they do. I confess to falling into the belief that negative Sharpe ratios were a problem,  but I've come to believe that they are correct. The same issue often happens with time-weighted returns that sometimes don't make sense at first glance, but in reality are perfectly correct.

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!

Let's take risk reporting to the next level

The Global Investment Performance Standards (GIPS(R)) now require compliant firms to include the 3-year, annualized standard deviation for the composite and its benchmark. And while this was a somewhat controversial move, it's here, so we live with it. But, why stop there?

For example, while conducting a recent GIPS verification for Reams Asset Management, a division of Scout Investments, I found the following shown for their Unconstrained Fixed Income Composite:

What can we tell from this? Not much.

Okay, the composite had a significant out performance relative to the index (more than 200 bps); but, look at that standard deviation; looks like a lot of risk was taken! If one truly believes in the value of standard deviation, might it be a good idea to move to the next  step?  That is, to require a risk-adjusted measure, such as (what seems to be the logical choice in this case, given that the risk measure is standard deviation) the Sharpe ratio?

But also observe that we are showing a one-year return and a three-year standard deviation, meaning the match up isn't perfect (and is arguably misleading), and so, let's report what isn't required (but perhaps should also be?): that is, the three-year annualized returns!

A lot more insightful,  right?

In this particular case, the benchmark is an absolute index, so the differences are a bit more pronounced than they might otherwise be. But the point is, I believe, still valid: to compare one-year returns with three-year risk statistics is, as we like to say, mixing apples and oranges. And, showing returns and a risk measure doesn't quite do the job.

And so, I encourage the GIPS Executive Committee to:

1. Require, in addition to the 3-year annualized standard  deviations, the corresponding 3-year annualized returns
2. Require the Sharpe Ratio.

What do you think?

Making sense of negative Sharpe ratios

I'm teaching an in-house Fundamentals of Performance class this week in Canada, and, as usual, we touch upon the Sharpe ratio, and how negative Sharpe ratios can produce results which appear inconsistent with our expectations.

To help try to communicate what's going on, I constructed the following graphic:

What you're seeing are two different cases: one where we're dealing with a positive Sharpe ratio, and the other where we have a negative. In both cases, the portfolio's risk exceeds that of the benchmark, and in both cases the portfolio's return equals that of the benchmark. On the positive side, given the higher risk, we would expect a higher return for the portfolio; but because it failed to do that, we end up with a lower Sharpe ratio. On the negative side, we would expect to see a lower return, given the higher risk; but failing to see this occur, we are rewarded with a higher Sharpe ratio.

This may not be clear enough to comprehend, and I will take the subject up later this month, in our monthly newsletter. So, consider this a "warm up"!

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.

Annualized standard deviation ...yes!

Okay, so the decision has been made: effective January 2011, GIPS compliant firms must report a 36-month annualized standard deviation, on an annual basis (that is, for all years starting with 2011). Further clarity is in order.

First, is standard deviation risk? There is hesitation to call it that, because a lot of folks don't consider it risk. But if it's not risk, why show it? Granted, not everyone thinks of volatility as being a risk measure, but most firms report that they use standard deviation as a risk measure. If volatility isn't risk, then is volatility such a valuable measure that we need to see it reported?

I think it's a mistake NOT to call standard deviation risk: the fact that not everyone agrees shouldn't be a reason not to. There is disagreement about much of the standards, but that doesn't stop these items from being included. It's even more confusing not to call standard deviation risk. Is someone going to be offended if we call it "risk"? I think not.

Is the Sharpe ratio a risk measure? Technically it's a risk-adjusted return. And, what risk measure is used to adjust the return? Yes, you're right: standard deviation. But if standard deviation isn't risk, then I guess the Sharpe ratio can't be a risk-adjusted measure. Who's going to tell Bill?

Okay, and so HOW do we calculate standard deviation? First, use 36 months ... not days, not quarters, not years: months! You will also be required to include the annualized return for each 36 month period. What if you don't have 36 months' of composite returns? Then don't show this until you do (well, actually, you arguably can show a standard deviation for the period you have, but you're not required to until you reach 36 months).

Do we divide by "n" or "n-1" (where "n" is the number of months (i.e., 36))? No decision has been made yet, though it appears from comments at this week's conference that "n" might win out. We use "n" for the population and "n-1" for a sample; some might argue that it would be wrong to use "n," while others would argue that it's wrong to uses "n-1." This is debatable and controversial, no doubt. And, no doubt more details will follow.

Negative Sharpe ratios

In our newsletter I've commented on the perceived problem with negative Sharpe ratios: that the results appear to be counter intuitive. When excess returns are positive, if the portfolio did a better job of managing risk, it will show a higher Sharpe ratio; however, when returns are negative, the inverse occurs. While some find no problem at all with this, others are challenged by these results.

Craig Israelsen has written a couple of articles on this topic and, at our request and urging, provided one for The Journal of Performance Measurement, and will appear in our upcoming (and unfortunately delayed) Summer issue.

Until the last year or so, although this problem was known by many, it didn't seem to be much of an issue because the bull market often meant that the long-term excess returns were positive. However, because of the devastation that was wrought upon the investment community last year, many are seeing negative excess returns and the accompanying oddity with the Sharpe ratio (and, by the way, the Information Ratio, too!).

Space doesn't permit me to go into detail on this topic in one sitting, so I'll return to it again. I encourage you to become familiar with Israelsen's piece, as well as the writings of others who have chimed in on this subject.