"To confuse the model with the world is to embrace a future disaster driven by the belief that humans obey mathematical rules." - The Financial Modeler's Manifesto, Emanual Derman and Paul Wilmott
Recently I discussed new research by Andrew Ang (Columbia), Richard Green (Carnegie Mellon), and Yuhang Xing (Rice) that maintained that in the presence of transaction costs, advance refundings always destroy value to the issuer. Based on this conclusion the authors proceed to question the tax policy wisdom of allowing municipal borrowers to advance refund at all, a conclusion I believe is not universally popular in the public finance community for a number of sound reasons.
My first reading of the paper was cursory but on more detailed examination I find they make a mistake, big time. It’s a mistake that strikes to the core of their hypothesis, and it’s not really even a mistake in their public finance either. It’s a fundamental error in plain old financial modeling itself, in how they calculate “losses,” and ultimately in their conclusion. It’s a mistake I frankly am very surprised that finance professors would make.
The error shows itself unobtrusively in one seemingly non-controversial but foundational sentence on page 10 which goes both unnoticed and, for the paper's sake, tragically unexamined,
“We can represent the value of any security as the discounted expectation of its payoffs under the risk-neutral measure….”
In a word, WRONG. Dead wrong. Grade F (My dad the navy frogman was tough during homework review...) Where are the grad students and peer reviewers on this stuff? This seemingly innocuous statement naturally avoids detection by public finance practitioners because their jobs simply don’t require an intimate understanding of arbitrage-free (risk-neutral) pricing, for reasons we’ll see more clearly below. And it fails to trip the warning detectors of many financial theorists and academics because that lot is so steeped in the dark arts of asset pricing theory that such a statement is utterly unremarkable and unquestionably obvious. The theory is so established and ubiquitous in academic circles that it fails to even arouse the suspicion of its cultural adherents. And that culture, both academic and practical, chooses at its peril to forget the very tenuous and often unrealistic foundation on which it rests.*
But before unpacking the specific problem with Ang et al’s statement above I would offer that those keepers of the asset pricing mysteries (particularly those teaching our youth!) would do us all a tremendous favor by reading the Modeler’s Manifesto and abiding by its Modeler’s Hippocratic Oath,
- I will remember that I didn't make the world, and it doesn't satisfy my equations.
- Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.
- I will never sacrifice reality for elegance without explaining why I have done so.
- Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.
- I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.
Had the authors committed to and followed the Oath, their paper would be either very different or unwritten.
But back to their statement and it’s fundamental, fatal flaw. To correct their statement one would need to add a very simple but crucial qualifier, which for this paper ultimately renders the statement itself simply incorrect,
One can represent the value of any security as the discounted expectation of its payoffs under the risk-neutral measure IFF the risk-neutral measure EXISTS!
Without going into a lot of unnecessary minutia, the simplest way to assess whether risk-neutral valuation technology might apply to a given problem is to first assess whether or not the security in question is in fact hedgeable.** Hedgeability equals price-ability. Hedgeability is a prerequisite for constructing a risk-free and self-financing hedging strategy and such a strategy is an absolutely necessary prerequisite for any risk-neutral pricing theory to apply.
So how can we determine whether or not a callable municipal bond or bond option is hedgeable? We could ask a dealer. But that work is unnecessary because conveniently we can directly quote none other than the lead author of the paper himself, Andrew Ang, from some excellent research he got published all the way back in 2010. Though the research relates to municipal bonds impacted by the market discount rule, you’ll note that the section below applies to municipal bonds quite generically,
“Municipal issuers are unable to arbitrage the mispricing of…bonds. IRC §148 specifically prohibits arbitrage across municipal bonds and other types of bonds (for example, Treasury and corporate bonds) by tax-exempt institutions…. Unlike Treasury bonds, shorting municipal bonds is very hard because only tax-exempt authorities and institutions can pay tax-exempt interest. An investor lending a municipal bond to a dealer would receive a taxable dividend because that dividend is paid by the dealer, not a tax-exempt institution. Even if an active repo municipal market existed, it may be hard to locate a suitable municipal bond as a hedge because of the sheer number of municipal securities. Shorting related interest rate securities, like Treasuries and corporate bonds, opens up potentially large basis risk. Another reason arbitrage may be limited is because the trading costs are much higher than Treasury markets.”
- Ang, Bhansali, and Xing, Taxes on Tax-exempt Bonds Journal of Finance (2010)
Couldn’t have said it better myself. This paragraph provides exactly the reasons why municipal bonds are effectively unhedgeable. But the undeniable and incontrovertible consequence is that risk-neutral pricing theory therefore CANNOT apply. Ang 2010, where were you when Ang et al, 2013 did this research!?!?! The ultimate ramification for the paper is that the “loss” calculations the authors create, which they base entirely on (25+ year old) risk-neutral models using risk-neutral inputs, are figments of the authors’ highly educated imaginations. Unicorns are pretty too but they don’t exist, and existence is (I believe still) a really important feature if you’re using loss estimates to try to influence national fiscal policy.
I know that to some, the above may largely be high concept gobbledygook. The bottom line is this: "losses" must be relative to some value that is actually attainable, or else it’s very tough to realistically call them “losses.” So where’s the strategy whereby a municipality actually captures the value the authors characterize as loss? The research only mentions the use of devices such as interest rate swaps to hedge the rate risk an advance refunding otherwise eliminates. This is a reasonable answer for those tax-exempt entities who maintain the risk appetite, liquidity reserves, management expertise, legal authority, and political will to execute swaps. And could those borrowers who satisfy all of these criteria please raise your hand? Now how much of the over $1.5 trillion in outstanding, unrefunded, callable, fixed-rate muni bonds is on the books of those swap-happy borrowers with hands up? 10%? 5%? Now there’s a research question worth answering. And that question can be rolled into an investigation of the number of misleading press articles written and careers cauterized or destroyed due to the use of municipal derivatives. Here’s a case study contribution to kick off that new paper – my exchange with the editors of the NYT on their coverage of muni swaps.
Though currently the danger of thoughtful new reform of any sort being considered in Washington is remote (maybe get the SLGS window open first?), I maintain that should it ever occur, this paper demonstrates more an example of professors inebriated by the exuberance of their own quantitative verbosity than it does some new discovery that would inform the prudent revision of the Tax Code.
*See 'The Formulat that Killed Wall Street' for a unique and fascinating bit of research on the culture of financial modeling and its contribution to the financial crisis via the CDO market.
**From a variety of sources, "The lack of arbitrage is crucial for existence of a risk-neutral measure."
***For a truly excellent article describing the types of rate models that different players should use in their respective situations (including munis explicitly), see What Interest Rate Model to Use - Buy Side versus Sell Side.
One of the (few) benefits of leaving a perfectly functional Street job is that I'm now free to have a free dialogue with the free press using my now free(er) speech. To that end, I decided to engage the NYT a few weeks back regarding Gretchen Morgenson'sThe Swaps That Swallowed Your Town article. This is the first of 3 posts recounting the transcript as surprisingly, they did engage.
Most of the press on municipal swaps, as already critiqued here, is now as much concerned with drawing an emotional response from the reader usually with the mild sacrifice of fact or perspective. On this particular article, Peter Shapiro has already done the yeoman's duty of correcting the numerous inaccuracies on the LinkedIn Municipal Bond Forum; the exchange there is worth a read. I had a more narrow objective with the NYT; get a correction published of this sentence, "The contracts, however, assumed that economic and financial circumstances would be relatively stable and that interest rates used in the deals would stay in a narrow range." My first salvo of my triple attempt at a correction, and the senior editor's response is below.
The article "The Swaps That Swallowed Your Town," through a healthy dose of misinformation coupled with basic misunderstanding, does a great disservice to the very talented municipal and state finance officials that manage complex capital programs. No different than the homeowner who must decide to use either a fixed or adjustable rate mortgage, these officials must make tough decisions about interest rates. Most of the time they employ traditional fixed rate bonds. However, history has indicated that over substantial periods variable rates often offer lower cost than fixed rate. As a result, states and municipalities frequently allocate a certain percentage of their borrowing to variable rate bonds in order to save the taxpayer on expected interest costs. One way to manage some of the risks inherent in these variable rate bonds is through the use of interest rate swaps.
The article is not inconsistent with the above (though I believe frankly sensationalizes at the expense of clarity). The writer runs amok, and unfortunately this is the thrust of most of the article, when she states, "The contracts, however, assumed that economic and financial circumstances would be relatively stable and that interest rates used in the deals would stay in a narrow range." This is factually INACCURATE...Interest rate swaps hedging variable rate bonds are designed to work and have worked in any and all interest rate environments. To report otherwise is simply false. If the Times cares about correctly reporting information it will retract this statement immediately and visibly.
Further, what happened during the meltdown that really affected municipalities had two primary components:
1) an overreliance on risk-laden bond insurers to raise money in a very thin auction rate securities market and
2) banks retreating from providing support for variable rate bond programs.
But both of these problems had nothing to do with interest rate swaps. The Lehman collapse, if anything, showed municipalities that the swaps market functions incredibly well even with the implosion of a major player. Billions of notional were assigned in an orderly fashion to other dealers in a way that actually wound up making most affected states/municipalities better off.
Thank you for your time and I hope to see the correction quickly and visibly noted. As someone who has worked in the industry for 15+ years, this type of misinformation is both unnecessary and damaging. I hope the Times can admit when it has exaggerated a story to the point of inaccuracy. I understand it's the exaggeration that may sell more papers, but I expect the Times to hold itself to higher standards.
Peter C. Orr
The reply surprisingly went into basis differential between swap and bond rates and even LIBOR index issues. Of course, this was not directly mentioned anywhere in the article.
Dear Mr. Orr,
We considered your request for a correction and have decided that the article does not contain any correctable errors. The writer, Gretchen Morgenson, noted:
That is the 'narrow range' we referred to in the column. It is not narrow anymore and that is what is causing problems for issuers."
"The only way the swaps would work as they were supposed to was if the interest rate the municipality paid out to its bondholders was close to the interest rate it received from the bank that entered into the swap (which was a percentage of 30-day LIBOR). This has not been the case and that is why these swaps are causing trouble for municipalities--they are paying out more than they are receiving.
But what instrument made this basis blow out??? Read it in pt 2
"It is better to understand a little, than to misunderstand a lot."
The prior two posts came to one simple conclusion: most tax-exempt issuers who have used LIBOR based swaps to hedge variable bonds are over-hedged (see prior posts for details why). This conclusion has two primary ramifications:
- If you hedged with, for example, 15% more swap than necessary than the issuer paid 15% more to the swap dealer than necessary. Across an estimated $1.5 billion+ in compensation to swap dealers over the last several years on these, its real dough
- In high rate environments, the overall cost of funding will be lower than expected and in low rate environments higher
Let's look at a simple example. AnyCity, USA uses a 3.50% $100 million 68% 1M LIBOR to hedge $100 million in tax-exempt variable rate demand bonds (VRDBs). This 68% number was determined using an historic average and an implicit assumption of zero correlation between 1M LIBOR and SIFMA/1M LIBOR ratios. If one had assumed correlation of -.35, which is more consistent with what we've seen and might reasonably expect, then the right hedging index would be 58% LIBOR plus 0.52%. Both of these swaps carry a fixed rate of 3.5%.
When rates are low, the floating leg of the swap at 68% of 1M LIBOR is less than the 58% of LIBOR plus 52bps. On our $100 million swap for AnyCity, the graph of LIBOR rate level versus annual benefit to having the 58%+52 basis point leg looks like this:
Now obviously as rates go higher the benefit becomes a loss, but that's the point: this is no longer a hedged position as there's an inherent interest rate view within the structure. The overall synthetic fixed-rate structure (variable rate bonds swapped to fixed) performs worse than expected in low rate environments but better than expected in high rate environments. This is due to the fact that we expect SIFMA/LIBOR ratios to be somewhat higher on average in low rate environments and vice versa (the negative correlation between rates and ratios). What does this all mean? Well, few issuers are entering into new synthetic fixed rate deals so it matters more for those that are doing restructuring. What is the optimal portfolio-wide level of LIBOR based swaps for hedging tax-exempt variable rates? Probably less than one might think. What's an issuer to do? Well, if you have more swaps than you need than you could unwind some swaps now though in this rate environment they're likely under water. You could wait for rates to rise and unwind when the swaps are closer to a zero mark or even an asset. Have to be careful though...that'd be speculating.