Posted by Peter Orr on Thu, Jun 25, 2009 @ 08:59 AM
"Opportunity is missed by most people because it is dressed in overalls and looks like work."
- Thomas Edison
Over the last decade, many tax-exempt issuers have executed interest rate swaps based upon a percentage of the 1M or 3M London Interbank Bank Offered Rate in order to hedge the interest rate risk inherent in tax-exempt variable rate, or (perhaps unfortunately) auction rate securities. Whether or not these "synthetic fixed-rate" structures are appropriate for all or any tax-exempt issuers is a hot topic these days in light of expected regulatory changes, and one I'm not touching here. What I am going to discuss is something more fundamental to implementation: how does one arrive at the *best* structure to minimize overall debt service volatility, have historical practices led to chronic over-hedging and if so, what are the ramifications.
The usual methodology employed to determine the "right" percentage of LIBOR for the floating leg of the swap is usually calculated based upon some historic average of the ratio of the SIFMA swap index, a weekly tax-exempt floating index, to 1month or 3 month LIBOR. Ignoring tax and accounting issues for the moment, if the goal is to minimize the expected variability of overall net debt service payments this simple averaging method is incorrect in all cases save one: the expected correlation between SIFMA and LIBOR is precisely 1. My personal assessment is that most issuer/advisor/banker participants in this particular market are not accustomed to thinking explicitly about correlation as it relates to their risk management decisions. However, they're making implicit assessments of correlation quite often, sometimes with regrettable consequences.
Let me explain. Any recently test-taking CFA candidate (congratulations by the way) will tell you that the variance minimizing hedge ratio is calculated using the following simple formula:
Volhedged item / Volhedging item * Correlationbetween the 2
This formula has intuitive appeal. If the volatility of my hedging item is far greater than the item hedged, my hedge ratio should fall, which you can see it does. As it relates to correlation and in the canonical edge case, if I have a 0 expected correlation between the item I'm hedging and the item I'm hedging with, we'd expect our hedge ratio to be zero as well; you can't hedge something with something else if you expect no co-movement between the two items.
But is it our best judgment that (changes in) SIFMA and LIBOR will be perfectly correlated going forward? What does history tell us? If we look at the levels themselves, it's clear their correlation isn't perfect. Below are 5 year rolling correlations of one month averaged SIFMA and 1M LIBOR.
What does all this mean? If we expect that SIFMA LIBOR ratios will be 68% going forward (a common and frequently used historically calculated average ratio), then the right hedge ratio would scale this by our expected correlation which likely does not equal 1. A reasonable expected correlation between 85-90% would yield an optimal hedge ratio of between 57.8 and 61.2%. Some banks have gotten to numbers like this by performing regression calculations, which of course are just alternative ways of determining correlation.
So what and who cares? Well, let's compare an issuer with a 70% LIBOR swap paying a 3.5% fixed rate versus one with a 60% LIBOR swap with a 3% fixed rate. The latter has used roughly 14% less swap to do its hedging, which means the 60% LIBOR swap's value is less sensitive to changes in interest rates. This will have important ramifications for mark to markets and collateral posting. For more detail on that and how to capture these effects within a market model, stay tuned for Part2.
Posted by Peter Orr on Mon, Jan 05, 2009 @ 04:24 PM
If you didn't catch it, the NYT magazine this weekend had a cover story on risk which posed the question, was management or specifically risk management more responsible for the current financial mess in which we now sit? Not unexpectedly, Mr. Black Swan himself got a good dose of coverage railing against the utter folly of VaR and seemingly anyone who attempts to quantify anything about risk in finance. The other corner is represented by the leadership at RiskMetrics, Sunguard, etc weighing in with the "calculating risk has benefits" position, given it (VaR) provides relevant and useful information the majority of the time. Taleb's point is the "majority of the time" doesn't matter much after insolvency.
Given the topic, the article provides predictable variations of common platitudes: "Guns (quantifying risk) don't kill people, people (dumb risk management) kill people," and "Those who ignore the lessons of history are bound to repeat it (particularly if you only use 2 years of data as a basis for your VaR calc)."
I couldn't help but notice how much the article echoes the debate about the degree of risk versus uncertainty present in financial management, and what to do about it. In fact, one way to look at the position of people like Taleb/Mandelbrot is that the uncertainty about which Dr. Knight wrote in his 1916 dissertation is really the driving force behind socio-economic variable movement and as such, if you're going to do any modeling, fractals are your best only choice. They argue fractals and power laws are the only things that give you a prayer of appreciating the potential magnitude out in the tails of the uncertainty.
I think the article properly highlighted one VaR shortcoming that has been reasonably well-known but under-addressed, "[VaR] failed to distinguish between leverage that came from long-term, fixed-rate debt…and loans that can be called at any time and…blow you up in 2 minutes." Coincidentally this is highly germane to my disagreement with Dr. Black, and perhaps even the mindset behind a lot of quant training.
I wish there was a bit on behavioral finance. The author hints at that quoting a risk manager, "It has to do with the human condition. People like to have one number they can believe in." It might've been nice if he touched on concepts like availability bias, overconfidence, and herding as additional contributors to the problem. What ramifications this all has for future policy is anyone's guess. In the end, we are still doing this democratic/capitalist experiment and it doesn't appear we're in any danger of getting it *right* anytime soon.
Of course, I'm sure some risk managers out there reveled in one of the author's concluding and resigned ruminations, "Maybe it would have been better if the people in charge had a better understanding of risk." I suppose that would've been nice.