The Flaw of Averages, Muni Style: SIFMA/LIBOR and Rates

Here’s a quick quiz. If over the last 10 years 1M LIBOR reset weekly averaged 2.814%, and the average of SIFMA / 1M LIBOR was 82.0%, what was the SIFMA average over the same time period (all rates unadjusted for day counts, holidays etc.)?

A. 2.05%

B. 2.31%  (2.814% * 82.0%)

C. 2.62%, or

D. None of the above but it seems like a trick’s in here somewhere

The correct answer is in fact A, which is a testament to how strongly the Fed has been stepping on the money accelerator over the last decade. Monetary policy aside, if you answered B (simply multiplying the LIBOR average by the SIFMA/LIBOR ratio average) you would’ve made a very common mistake which falls into the category of the Flaw of Averages. Overreliance on simple averages, partly induced by overreliance on simple spreadsheets, can very easily lead to errors of calculation and ultimately judgment. In this case, the seemingly more intuitive answer B is over 25 basis points wrong!      

How does this work? When rates are low, SIFMA/LIBOR has been high and vice versa i.e. the two rates have been negatively correlated. If you don’t capture this fact in your analysis, you’re missing a critical component of how the tax-exempt markets have worked. This ultimately leads to over-hedging, misunderstanding of balance sheet hedges, and other unintended consequences.

Luckily, there are readily accessible public finance analytics that capture these very easily.  

Financial Decision Making: 3 Questions Every CFO Must Ask and Answer

Credit markets are certainly not “normal” (in any sense of the
word) but at least they’re stable enough for issuers to make some decisions. That said, keeping in mind the answers to three deceptively simple yet vitally important questions will always serve CFOs, governing boards, finance committees, and other financial decision makers very well.

Notice that these questions are not framed in terms of some specific risk metric or probability. That’s because they are intended to address decision making in a way that we (as a species) are best suited to understanding. Despite the fact that banking regulation has often focused on extremely remote events like 99.9% annualized confidence intervals i.e. events that happen every 1,000 years, it’s a well researched fact that we human types simply don’t do very well making decisions about such tiny likelihoods. We tend to overemphasize the dramatic remote risks (shark attacks and plane crashes) over the far more dangerous yet mundane occurrences (auto accidents and drowning).   

Can we make it through the worst plausible scenario?

The nature of risk management comes first in defining a plausible event or set of events to be concerned about. Without some sense for what that the downside concern is and how it will impact a corporation’s financial position, risk management doesn’t exist. Notice that this is where the entity’s level of risk aversion comes explicitly to the surface.

“Make it through” will mean different things to different entities since incentives and consequences, including political fallout, are obviously not uniform across institutions. For many, this concept is tied to liquidity access – a topic that’s found a great deal of interest over the last 18 months.

“Plausible” is also an important word here. An issuer I know, when answering this question for themselves, looked at the marks on their swaps if the entire yield curve moved to 0%. This is obviously a definable event and it gives one boundary value for their swaps; some people may consider it so implausible however that it should not be the focus in response to this question.  

How much might we gain in the best plausible scenario?

This is an important question in that if there’s very little gain expected relative to the “do nothing” scenario, absorbing the risk may not be worth it. This question wraps in it whether you want to evaluate the best scenario in terms of the individual transaction in isolation, or evaluate the overall impact against the backdrop of the entire portfolio (debt and/or investment).

The answer to this question in conjunction with the first helps determine the nature of the strategy’s distribution. A remote but large downside with a modest but likely upside is similar to a “sold option” situation. A fairly uniform upside and downside is a simple long position in some risk, etc. 

What is the breakeven?

How far do the factors that affect the performance of the instrument(s) need to move in order for the strategy to break even with the “do nothing scenario”? For instance, do you want exposure to SIFMA based variable rates as a tax-exempt borrower if you believe significant inflation will arrive eventually and you can lock in a rate at 3.75% fixed? How fast to floating rates need to rise for this strategy to break even (download model here)?

Understanding the break even helps us evaluate the likelihood that the transaction will work in your favor in a way that no other calculation really does. It allows us to directly assess a tangible, quantified event and the subjective probability that that event will occur. With that information in hand, evaluation of the best course of action is often much more clear.

For analytics that help answer each of these questions using rigorous, comprehensive decision frameworks see here.

Too Much Raw Data in Your Probabilistic Analysis? It’s Likely

Two people were examining the output of the new computer in their department. After an hour or so of analyzing the data, one of them remarked: "Do you realize it would take 400 men at least 250 years to make a mistake this big?"       Unknown  

I'm a big fan of Riccardo Rebonato. From the book on interest rate models, a required text in my grad school, to the papers he's done on interest rates measures in the "real-world", he's an extremely clear thinker on otherwise murky stuff. I can't recommend more highly his recent book, Plight of the Fortune Tellers. If you or your clients are in the business of making tough financial decisions, it's a must read and enjoyable to boot. Enough gushing (I need payment to go any further ...)

One extremely important concept woven throughout Plight is the difference between the traditional "probability as frequency" concept and the more general Bayesian or "subjective" probability. Probability as a pure frequentist concept is a special case of Bayesian/subjective probabilities that would be appropriate when looking at the likelihood of a head after a coin flip. Outside of a belief the coin is fair, no prior knowledge is necessary to reliably assess the likelihood of such an event. Contrast that with say, the probability that the Jets win the SuperBowl in 2011, or the Republicans retake the House in November, or even that gold goes over $1,500 an ounce by year end. These are all events to which we could also assign a probability, though analyzing purely historical data in a frequentist sort of way will yield few helpful results. We are much more inclined to include and use other relevant information such as the Jets strong defense going into the next season, the anti-incumbent mood of the electorate, and the growth of global money supplies.

What does this have to do with the use of raw historical data in financial decisions support analytics? A lot. Certain financial questions are better answered using frequentist concepts. Others are far more judgment-based relying on more subjective criteria and professional experience. But how do you know which situations are which? Though no hard and fast rules exist, there are basically four criteria:

Data frequency - The more relevant data you have, the more inclined towards a frequentist approach.

Time horizon - the longer the horizon of analysis, the more likely a subjective analysis will be more relevant.

Rarity of event - the more rare the event, the more the analysis calls for a Bayesian/subjective approach. 

Time homogeneity of data - Were there no regime changes or other tectonic shifts in the underlying phenomena from which data was gathered? If so, analysis will tend more towards frequentist methods.

So for long time horizons, a scarcity of data, significant changes through time in the realm in which the data lives, and highly improbable events, we land squarely in the realm of subjective probabilities. Though historical/frequentist data isn't ever completely irrelevant, in these circumstances professional judgment of the situation at hand trumps pure number crunching. Unfortunately, from rating agencies to regulators to a large swath of finance professionals, this is not well understood. Things are just much more clean and simple if we allow ourselves to believe that 100 data points and a fancy model will yield 99.97% confidence precision. This is a particularly dangerous type of belief in finance, as acutely borne out over the last 18 months.  

The good news is that whether frequentist or subjective, widely available probability-based models should always be used to capture risk metrics, evaluate best and worst outcomes, assess breakevens, and ultimately to avoid the ever pervasive flaw of averages.

Behavioral Finance, Spreadsheets, and Bad decisions

"The whole secret of mysticism is this: that man can understand everything by the help of what he does not understand. The morbid logician seeks to make everything lucid, and succeeds in making everything mysterious."

- G.K. Chesterton

Behavioral finance has been heralded as at once a new sunrise and false dawn in the annals of financial economics. However, behavioral finance has no unifying theory at this point though it has exposed a number of "cognitive illusions" which we human types tend to display when making financial decisions. And as often as those would claim that insights from behavioral finance sound the death knell for the efficient market hypothesis, others say it's impossible to determine whether the market is truly inefficient or that the market model being tested is wrong. Since behavioral finance offers no model of its own, it's impossible to test market efficiency under its finding. I wouldn't presume to add any real insight into this debate; I say let the debate rage on and a thousand more PhDs be granted. That said, I do question how or if the financial technology we surround ourselves with has been a contributor to our current situation…

Some behavioral finance findings relate to heuristic decision-making, the "rules of thumb" or educated guesses that we make in the face of complicated problems and uncertainty. For example, availability bias is the tendency towards overweighting information that is easily attained. Anchoring is the tendency towards extrapolating recent trends, possibly leading to an under-reaction to changing conditions. Overconfidence leads people towards over-estimating their predictive skills. Each of these three phenomena has been studied and documented as common in the human condition; even evolutionary psychologists have reasonable theories for some of these behaviors. But so what?

Consider these findings as they interrelate with our technology. The one nearly ubiquitous tool available to the masses in finance is the spreadsheet. I love spreadsheets. Spreadsheets can't be beat for certain purposes. However, I find that for measuring potential variability in a multi-factor risk setting, unenhanced spreadsheets display some pretty major shortcomings which I won't belabor here. Suffice it to say that in the absence of any other tool to more powerfully process information, if a spreadsheet is all that's available, an analyst will use a spreadsheet. People are forced to make a decision with what they've got, so often the only information that goes in is the stuff that can be reasonably quickly generated in a spreadsheet. Further, our natural inclination towards anchoring with recent data, as well as natural overconfidence in forecasts makes the spreadsheet the ideal medium for us to completely delude ourselves.

A MAD Example

Let me give you just one (of many) examples that frankly doesn't make any sense to me, particularly in this modern financial era. One liability related metric understandably deemed important by many analysts and certainly the rating agencies is MADS, or Maximum Annual Debt Service. It is supposed to represent the maximum of principal and interest payments that might be made by an issuer of debt over an annual fiscal cycle. It is one of those metrics that can be easily calculated in a spreadsheet by a user with only modest skills. However, this same user and likely worse, the audience for her/his analysis may be suffering badly from the cognitive issues described above.

The number of misunderstood, under-appreciated, and heroic assumptions that go into calculating MADS can be staggering. What assumption was used for calculating possible debt service on variable rate bonds or commercial paper? How about the performance of hedges such as interest rate swaps? Any basis variability? How about the likelihood of debt acceleration? Or perhaps a liquidity crunch which leads to either expensive or unavailable letters or lines of credit? What happens to debt service and MADS then? What does the "maximum" in MADS mean when all of the market assumptions that go into it are based upon some 10 or 20 year average, whose sole redeeming feature is that it's easily entered in a spreadsheet?

And MADS is an important number because it often is the denominator for statistics like debt service coverage ratios which are relied upon by investors, rating agencies, and even bond trustees. These are legally required calculations, and yet the amount of time and energy that goes into understanding their potential variability is often next to nothing.

IMHO, this is low hanging fruit which must be changed if we're going to improve disclosure, increase the value of our information and the density of its content, and ultimately enable people to make better decisions. What am I missing? What do you think?