Knightian uncertainty

In 2004 Alan Greenspan offered the following: "When confronted with uncertainty, especially Knightian uncertainty, human beings invariably attempt to disengage from medium to long-term commitments in favor of safety and liquidity." I stumbled upon this quote in an article by Ricardo J. Caballero and Arvind Krishnamurthy in the October 2008 issue of The Journal of Finance. Their article deals with the common flight to quality events that occurs during severe market jolts and the role that the lenders of last resort (LLR) typically have. My intent at bringing this up isn't to address their subject, although it's quite an interesting one and one that we will be addressing more formally at a later date, but rather to touch on this term "Knightian uncertainty."

If you're like me, it's one that you're not familiar with. It is derived from a book by Frank H. Knight (Risk, Uncertainty, and Profit) that was written in 1921. I was able to find a 1965 edition and haven't yet read it, though I intend to at least skim through to see what gems lie between its covers.

The term "Knightian uncertainty" wasn't coined by Knight (just as "Sharpe ratio" wasn't coined by Sharpe), but probably not by Greenspan, either. A "google search" brought me to the often times reliable Wikipedia site which informs us that Knight distinguished risk and uncertainty. It involves the presence of immeasurable risk. To further quote Wikipedia, "Knightian uncertainty is risk that is immeasurable, not possible to calculate."

The site specifically references the book and provides the following: “Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”

When it comes to measuring risk, many will recognize that most of our common risk measures (e.g., standard deviation, beta, tracking error) are measures of volatility or, if you prefer, variability, which many argue isn't risk. This causes one to ask, "well what IS risk?" The most commonly cited definition deals with the inability to meet an objective, while the potential for loss is also often used. I've seen uncertainty referenced in the past, though on my own wondered how one would measure it. Well, Knight pointed out almost 100 years ago that you can't measure it! I wish someone had told me.

Moving further along I came across http://www.rgemonitor.com/blog/roubini/210688, which offered the following: “Economists distinguish between ‘Risk’ and ‘Uncertainty’: the former can be priced by financial markets while the latter cannot. The distinction between the two was made by the famous economist Frank H. Knight in his seminal book, Risk, Uncertainty, and Profit (1921). In brief, ‘Risk is present when future events occur with measurable probability’ while ‘Uncertainty is present when the likelihood of future events is indefinite or incalculable.’”

Why the need to qualify the term "uncertainty" isn't clear to me, though it's worth understanding a bit more about the term, in general. It is interesting, isn't it, that the basis for much of what we do was addressed years, decades, or perhaps even a century ago, but unfortunately isn't always known to us, for a variety of reasons.

Interpreting the IRR

I recently stumbled upon an article that I found quite interesting: "What Does an IRR (or Two) Mean?," by David Johnstone (Journal of Economic Education, Winter 2008). David is the National Australia Bank Professor of Finance at the University of Sydney School of Business. I found two things in particular quite insightful.

First, you may be aware that with the IRR we run the risk of having multiple solutions. And although there are techniques to help identify the number of potential solutions, the process is still fraught with challenges. David pointed out that multiple solutions will only occur "when the balance in the investment is at one or more times negative. That is, at some stage in its life, more is taken out than exists in the account." (page 79) I found a second article by Eschenbach, Baker & Whittaker ("Characterizing the Real Roots for P, A, and F with Applications to Environmental Remediation and Home Buying Problems," The Engineering Economist, 2007) which supported this claim. Clearly there are cases when the multiple solutions problem will be an issue, but how frequently will we find an investment portfolio go into the red? Dare I say virtually never?

The second insight I gained from David's piece was his "simple but intuitively meaningful interpretation of the notion of IRR." He uses the following example:

• at time = 0 (the starting point), we begin with$1,200
• at time = 1 (end of year 1), the client withdrawals $500
• at time = 2 (end of year 2), the client withdrawals $850
• at time = 3 (end of year 3), we end with $500.

The IRR is found to be 25 percent. So, what does this 25% represent? It's what we earn throughout the period. The following table should help convey this:

	t = 1	t = 2	t = 3
Balance at (t-1)	1,200	1,000	400
Period t interest (25.00%)	300	250	100
	1,500	1,250	500
Cash flow at t	-500	-850
Balance at t	1,000	400	500

We can see that with the IRR, we're able to reconcile our values throughout.

This, of course, is something you can't do with time-weighting. I expect to discuss this at greater length in the August issue of Performance Perspectives.

Jim Johnson, age 68, succumbs to cancer

Jim Johnson, Philadelphia Eagles Defensive Coordinator, died today of cancer (see http://sports.espn.go.com/nfl/news/story?id=4362252). What, you may ask, does this have to do with performance measurement?

On January 28,2005, the Home News Tribune (a NJ paper) ran a story titled "New Challenge for Defense," which discussed the Eagles' victory over the Atlanta Falcons in the NFC Championship game. The article attributed much of the Eagles' success to Johnson's tactical prowess.

I have used this headline in our attribution classes since that time as an example of attribution. I just learned of Johnson's death when visiting the ESPN website, and felt it appropriate to acknowledge this in light of my regular use of the article and the citing of Johnson's exceptional skills.

We ALL know folks who have died from cancer, be it parents, spouses, other relatives, or friends. It's a dreaded disease that touches us all. As an Eagles fan, I know the team will miss him, as will his family and friends.

VaR...not as hard as one might think

This past week I spent a day dealing with the single topic of Value at Risk (VaR). This was in a class I'm taking in my doctoral program. Our professor, Aron Gottesman, did a fantastic job showing how VaR isn't nearly has challenging as one might think. As a result, we will be holding a webinar dedicated to the topic and will also have this as a topic at our upcoming PMAR VIII.

Just about everyone in the industry has heard of VaR, but not everyone understands much about it. Concepts first: it reports the most money that can be lost, for a specific time period, at a specified confidence level. For example, the most your portfolio can lose over the next ten days is $100,000, at a 98% confidence level.

At PMAR VI I debated Robert Mackay on this topic, arguing that VaR is "voodoo," while he took the position that it has value. While I lost the debate, I still question the accuracy of the results given the way VaR works. Robert returned this year to PMAR VII and acknowledged that the results, as predicted last fall, were somewhat optimistic, given the significant downturn we saw. That's the challenge with VaR: it bases its predictions on past performance, which can often be met with a shock. And while these "one in a thousand year" events don't happen all the time, they clearly occur a lot more often than once every thousand years.

When using VaR, one must be careful as to how much credibility they place in the results. I'd argue that one thing we know is true: that the results are in error because of the faulty assumptions. However, they do provide valuable information. The recipient should understand what the assumptions were in providing the information and recognize that it's an estimate that may under or overstate reality.

If VaR is important or of interest to you, please join us when we hold our VaR webinar. And, consider joining us for PMAR VIII, when we'll go into a bit more detail on the topic. The webinar date will be announced soon.

Discretion...does this help?

GIPS(R) compliant firms are required to include all actual (i.e., a REAL account, not a model), fee-paying (i.e., that the account pays fees, though this may change with GIPS 2010 to mandate the inclusion of non-fee paying accounts, too), discretionary accounts into at least one composite. Let us turn our attention to the word, "discretionary." What is meant by this?

First, the term is admittedly confusing. We are already aware of the legal definition: that is, a firm is legally discretionary if they have granted the portfolio manager the right to trade on their behalf. Great! Is that what we mean here? NO! Then what DO we mean?

We mean GIPS discretionary. In order to know if an account is discretionary from a GIPS perspective, it already has to be legally discretionary. And here we're speaking of the cases where accounts have placed certain restrictions on the manager (e.g., no "sin" stocks). The manager gets to decide if the restriction has impeded their ability to execute their strategy.

While teaching a class recently I came across this metaphor (or analogy, if you prefer), which I think may help. Let us turn our attention to the world of cooking.

For roughly 35 years I have had the responsibility to make the stuffing whenever we have turkey. And each year I turn to my wife's trusty Betty Crocker Cookbook for the recipe. And each time I prepare the stuffing, I do it the same way.

Now let's suppose that I've been asked to prepare the stuffing for someone else and they ask me to substitute wheat bread for the white bread, or perhaps to add a cup of chicken broth to the mix. Can I do this? Yes, of course. But, can I predict what the result will be? Am I comfortable taking the praise (or criticism) for the result? Maybe not. You've altered my normal recipe...my normal strategy for executing my process to prepare the stuffing. And so, I may say "yes, I can do this, but you get the credit for this idea." Thus, I might say that it's nondiscretionary.

Returning to investing, I wouldn't say that the client gets the credit. Clearly, I've agreed to do something for the client and the result is influenced by whatever that was. But, I may not feel that the result matches what would have occurred had I not had the adjustment made and thus declare it nondiscretionary for GIPS purposes.

Hope this helps! Please let me know your thoughts.

Standard deviation: dispersion vs. risk

Standard deviation is a commonly used statistic, well known by many long before they enter the world of performance measurement, which serves multiple purposes and thus engenders confusion.

The GIPS 2010 draft proposed a requirement that a 36-month annualized standard deviation be shown by GIPS(R) compliant firms. While it remains unclear whether this will stick (because of the opposition expressed by those who commented), it remains a commonly used risk measure. It reports the volatility in returns over some time period.

GIPS requires compliant firms to report a measure of dispersion when there are six or more accounts present for the full time period (e.g., if reporting for 2008, you're required to show a measure of dispersion if there were six or more accounts in the composite for the full year). Standard deviation is often used for this purpose. It shows the dispersion of the returns across all of the accounts for that period. For example, if for 2008 the firm reported a return of 13.04%, we would look at all of the individual account's annual returns and compare them.

Hopefully, the accompanying graphic helps contrast the uses of standard deviation.

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.