3 Things that Drive “Advance Refunding Option” Value

Posted by Peter Orr on Tue, May 12, 2015 @ 07:56 AM

     Essentially, all models are wrongbut some are useful.  - George Box

In its refunding policies one large issuer (and my banking friends know…) has indicated that it wants banks trying to get refunding business to provide the “estimated value of the advance refunding option (incremental to the value of the call/current refunding option).”  This leaves a lot of room for interpretation and frankly, leaves many scratching their head. In this article we try to provide some clarity. There are 3 things that must necessarily impact any estimate of the “value of the advance refunding option.” 

  1. Refunding Policy
First and in our opinion foremost, any reasonable estimate of the value of advance refunding bonds needs to be evaluated in the context of exercise criteria more commonly a “refunding policy.” The exercise decision within standard option models crumbles under the weight of its assumptions in muniland. The continuous comparison of hold value to exercise value presumes the hold value is actually attainable to the option holder to begin with; for states and munis it ain't. Welcome to munis!

The issuer in question uses “85% refunding efficiency” as the exercise heuristic that indicates a time to refund. If they used 75% or 95% (and why not?) then these changes would necessary lead to different option values. Though some may try to argue otherwise, this is simple financial reality – the decision trigger upon which an option is exercised MUST impact the value of the option. How could it not? Fortunately, there’s good research on which refunding policies work and which don’t both historically back-tested and on a prospective basis using a real-world market model. For the Cliff notes I just wrote an article on the one that works best in both environments.  And its simple too - fancy models need not apply.   

  1. Yield Curve / Rate View

The hard thing about refunding timing is that it necessarily involves an interest rate call. The muni market is not and, unless tax law changes, never will approach the nice, antiseptic, no-arbitrage market required by standard option models. Issuers have real skin in the game, can’t hedge their positions, and as such fall into the uncomfortable world of rate risk management. So no refunding decision criteria can fully divorce itself from at least an implied rate view. And researches from the SanFran Fed just recently cautioned against using market implied measures (read “forward rates”) for policy purposes.

  1. Muni / taxable view
The third item is specific to munis but is important enough that I think it needs to be broken out from 2.) above. If we’re talking about callable bonds eligible for tax-exempt advance refunding (the issuer policy isn’t 100% clear on this given even callable advance refunding bonds can be advance refunded taxably) then we’re dealing with modeling two distinctly different markets. The tax-exempt market is where the issuer sells bonds; but the taxable (UST or SLGS) market is where she buys the investments for the escrow. Therefore a realistic model of the dynamics of both the tax-exempt borrower and taxable markets must be developed. And this complexity is one reason why we implemented a real-world market model based upon what we consider the best research in fixed-income modeling in the last decade.

But how are these two interrelated but very different markets modeled? What factors drive their variability and what is the correlation between them? Unfortunately there are no observable options that trade where we could see the market implied correlation between munis and US Treasuries. This is another reason why a real-world model is necessary. But any model that credibly handles this multi-market modeling should fully describe how this bridge is traversed; it’s both treacherous and fundamental to the analysis.

Advance Refunding “Option” – Some Real-World Results

Enough gum flapping. Let’s look at some numbers. We created simulated yield curves using our MarketMaker model. Although we created 5 correlated market simulations simultaneously (AAA, AA, A, BBB tax-exempt and SLGS), we assume the issuer is AA and use SLGS markets for the escrow; in the end we only use 2 of the 5. We included 25 years of yield data as input to the variability in the model. Given the eight tenors per market this is a 40 factor model perfectly reproducing the inter- and intra-market correlations/covariance of all 40 tenors.  

Now let's look at two bonds. They both are 5% coupons maturing in 25 years, callable in 5 (5% 25NC5), but one is advance refundable and one is not. Given my comment above about the importance of a market view we examine these two bonds under three different expected yield curve scenarios, ‘Low’,’Medium’, and ‘High.’  


Let’s start by looking at some simple present value savings thresholds. Using first generation simulated refunding savings, we can compare the expected PV (EPV) savings from the advance refundable bond and non-advance refundable bond at various present value savings thresholds for our refunding policy.1 Here we use the Medium rate case. 


Now these bonds have some real juice since there’s 20 years of 5% par callability happening; the issuer doesn’t maximize EPV savings using low pv savings thresholds. But the important thing to look at is the difference between the lines. The higher EPV savings is generally coming from the non-advance refundable bond, implying a negative value to advance refundability – using these refunding policies and under this Medium yield curve view.  What’s happening? Well on average within the model the issuer is generally better off waiting to the call if the refunding timing criterion employed is a simple PV savings threshold. These numbers bear that out. Note we’ve also included a Black-Karasinski bond option value using 15% volatility (as noted in this issuer’s policy guidelines for the refunding efficiency calculation) which is insensitive to PV savings threshold. 

See that at about the 19% PV savings threshold the lines cross, and the advance refundable bond EPV savings begins to go higher than the non-AR bond. This tells us the policy obviously matters, as I posited earlier. 

In the low yield case we'll get the same sort of relationship since waiting when yields stay low, on average, will handicap advance refundability. So let's look at the high yield case. 


With high yields expected on average, as one would expect EPV savings for the non-advance refundable bond (blue line) is having a larger negative impact particular when looking at the higher PV savings thresholds. The advance refundable bond (green line) tends to dominate on any  refunding policy over about 7% PV savings.  Here we also show EPV savings calculations for the Alternative Policy (a two pronged policy, see here for details) to see how it compares. It is known that relatively speaking, the Alternative policy will fare less well in fast rising yield environments. But here we see that there’s consistent performance for both AR (solid black) and non-AR (black dotted) bonds, with the AR bond showing slightly more EPV saving.

This made me wonder about the performance of the Alternative policy for these two bonds in all three yield environments.  


As we’d expect the highest EPV savings corresponds to the lowest expected yield environments and vice versa. But the comparison of the AR and non-AR values is the punch line. In medium and high expected yield environments, the AR bond EPV savings (blue line) inches out the non-AR bond EPV savings (in green).  But in the low expected rate environment the fact that the non-AR bond forces the issuer to wait to do a current refunding doesn’t hurt EPV savings. In fact it helps, implying again that the ARO value is negative in that case. 

But that leads us to the semantic and perhaps existential question, "Can an option have negative value?" In a traditional financial economic sense the answer is clearly no. But once again, we’re not in Kansas any more. This is muniland’s veritable Oz. Here the answer is, “It depends.”  

1 For details about the computatoin of expected pv savings see Aalyzing Municipal Refundings Using a Real-World Market Model.




Tags: advance refunding, refunding efficiency, bond option, refundings

Press (and Fed): Market-based expectations wrong for issuers and investors

Posted by Peter Orr on Sat, Apr 25, 2015 @ 07:00 AM

We’ve written a number of articles talking about financial forecasting being a necessary evil, implied forward yields being miserable predictors of realized yields, and recently the inappropriate use of option pricing models (requiring market-based inputs) when doing refunding analysis. We even wrote a paper on it as we see a lot of misunderstanding by pubfin practitioners on this point.


But what I didn’t expect was for the press to actually make news out of it. Last  week a financial advisor friend and (u)ncalculated risk contributor pointed out a short but important BondBuyer article written by Gary Siegel, who picked up on an economic letter published by the San Francisco Fed that re-iterates this theme. Now I’ve been known to critique the press from time to time, but have to give props to Mr. Siegel on this one. 

In customarily gentle tones the Fed researches, Michael D. Bauer and Glenn D. Rudebusch of the SanFan Fed, say “policymakers should be cautious in relying on the expectations information in market prices…market-based expectations do not correspond exactly to real-world expectations because asset prices also reflect the compensation that investors require for making risky and somewhat illiquid investments.” For munis, “somewhat illiquid” definitely constitutes a glass-is-half-full descriptor. Plus munis are even more complicated because of their uncertain tax treatment, a significant risk to the investor.

Mr. Siegel in his Bondbuyer article goes on,

“The authors suggest distinguishing between ‘real-world’ and ‘market-based’ expectations. Real world expectations are defined as those "based on the standard 'true' probabilities of everyday interpretation," while market-based are strictly figured through prices in financial markets. Statistical models are used to calculate real-world expectations.”  
This is precisely why we at Intuitive Analytics have implemented the best real-world, yield-curve and market model we can find, so investors and issuers can test policy for just about anything that has market sensitivity within a consistent, coherent framework. And this model happens to perfectly capture the real-world behavior of all relevant markets using whatever history the modeler determines is relevant. And on that note, I love the way Messrs Bauer and Rudebusch describe the policymaking process,

“…choosing an optimal policy under uncertainty involves two steps: (1) assigning probabilities to uncertain future outcomes depending on the choice of the current setting of policy, and (2) ranking the relative desirability of different policy choices by evaluating their expected benefits and losses. …a policymaker would use real-world probabilities to calculate the expected net benefits of a variety of possible policy actions, and then choose the policy action that maximizes that net benefit.”

So easy! And eminently sensible. And it happens to be exactly what we did in analyzing refunding policies in our paper identifying the best refunding policy yet known. And as we recently described, evaluating muni callables by both issuers and investors involves assigning real-world probabilities to refunding outcomes driven by the complicated and simultaneous dynamics of multiple yield curves, no small task. 

Congrats to Mr. Siegel and the BondBuyer for picking up on an important piece of the forecasting and policy-making puzzle. Note we are not paid by the Bondbuyer in any way. Quite the contrary; think our 2015 renewal statement’s on my desk (we’d certainly take a subscription discount though…hint hint).  But I don’t want anyone to get the mistaken impression that all we do is press bash here. 

If you’re reading this the chance that you’re a central banker is relatively slim. However, you may well be in a position where you have to forecast financial variables (bond yields, perhaps?) in order to evaluate fixed vs floating, a 4% vs 5% coupon, expected muni hedge performance, a 7 year call feature, a refunding candidate, or even a broader financial policy. In any event, it’s the real-world expectations that matter.

Tags: financial forecasting, press

New Headline: Muni Issuers Make Outstanding Speculators

Posted by Peter Orr on Sat, Apr 18, 2015 @ 07:00 AM

The path is smooth that leadeth on to danger.  – William Shakespeare
Take calculated risks. This is quite different from being rash.  – George S. Patton
Never tell me the odds.  – Han Solo
Muni bond issuers are at their core, speculators; even ones with the oh-so-safe sounding “no speculation” provisions in their official debt policies. I know this may come as a shock to some but it is simply a definitional truism.  Any entity that isn’t fully hedged i.e. has financial short positions matched by long ones and vice versa, is a speculator. They have to take an interest rate view. And last time I checked states, municipalities, 501c3s and other municipal issuers (most corporates too) are generally not in the luxurious and enviable financial position of having assets in size and scope to match off, even approximately, against their liabilities.

At the point the muni treasurer or 501c3 CFO gets a “Thou shalt borrow” commandment from above - city calculated_risk_piccouncil, school board, legislature, or board of directors – she or he must make a financially speculative decision. Fixed or  variable? Variable with a swap? Put bonds? Perhaps a short call feature? Public offering or private placement? etc etc. These are all decisions that expose the entity to some sort of financial risk, if only the risk that one of the alternatives might in hindsight, have turned out better. Some may consider this “opportunity risk” pretty low grade, but risk is risk.

Very few people would dispute that if you’re a muni asset manager, you have to take and manage risk. What sort of duration will you have in the portfolio? How will you analyze call risk and redemptions? What’s the credit exposure? What’s the benchmark and how can I beat it? But when we look at a muni debt manager, they are just as much a risk taker and manager. Aren’t debt managers just asset managers with a minus sign in front of their “holdings”?

But for the dedicated and chronically under-resourced municipal and not-for-profit professionals who manage these often multi-billion dollar debt portfolios on shoestrings, the right interest rate choice has almost zero upside. For example, many issuers have determined that having a certain amount of variable rate debt in their debt portfolio is a good and prudent thing and will probably lower cost over the long-term. There have been hundreds of billions of unhedged tax-exempt variable rate bonds outstanding for years. And over the last few decades that decision has saved taxpayers hundreds of millions of dollars. Is this a widely reported fact? Of course not. What’s the headline? “Variable rate bonds perform great for [insert issuer name]”?  Or “Treasurer [name] Brilliantly Pushed for Variable Rate structure in Series 2003A Bonds]”?  Nope. Haven’t seen anything like that.

Some issuers decided to issue variable, but also implemented a strategy to hedge some part of the variable rate risk with an interest rate swap. The hope being that this would actually be less risky than natural, unhedged variable rate bonds. That decision, unfortunately for some issuers, involved taking on more of their own credit risk than they expected. That is, the market value on these swaps, which moves more negative as rates go lower, becomes a real potential liquidity problem if the borrower’s own credit deteriorates sufficiently to trigger collateral provisions under the swap documents. Once the credit rating falls enough, the borrower actually has to post collateral to the bank counterparty, exacerbating the liquidity position of an already stressed credit.1 And the amount of these swap values hasn’t been helped with the 10 year UST hovering sub 2%.   

But what has happened to those thousands, if not tens of thousands, of tax-exempt entities that really rolled the dice, made an interest rate call, issued variable rate bonds and look like geniuses in hindsight? Where’s the press on this? Who will highlight some of the countless stories of these unsung heroes of muni interest rate risk-taking? Who will wax long about the prudent, but still risky, decision making that’s led to millions in interest cost savings? No one. And on this, the press is nowhere.  That is….until interest rates start going up.

1See Jefferson County, Detroit and other distressed names that at this point, likely regret using interest rate swaps

Tags: Financial Decisions, decision support, swaps, municipal swaps, variable rate bonds

Why this is the Best Refunding Policy Ever

Posted by Peter Orr on Fri, Apr 10, 2015 @ 06:50 AM

"I don't think necessity is the mother of invention. Invention, in my opinion, arises directly from idleness, possibly also from laziness - to save oneself trouble."  - Agatha Christie

Recently we created some new research on the efficacy of issuer refunding policies. After implementing a new and powerful market model that allowed us to capture refundings with greater fidelity than ever before, we decided to test real-world refunding criteria and see which ones actually maximized expected present value (EPV) savings. Of course, any prospective refunding analysis in part depends on an interest rate view. If your rate model is static and goes to 50% tomorrow and stays there for the next 30 years, any criteria that has you refund every bond with a $1 of pv savings today will be the best policy around. You can download the full research here (Fig 12 on pg 17 for the summary table punch line).

Once we looked at refunding guidelines currently in use, we decided to test different combinations of criteria issuers have not used in order to find a best single refunding policy, as measured by greatest EPV savings. Eventually we used an optimization algorithm (see graph below) to determine the best solution parameter; one of the benefits of using a comprehensive model.

Under the bright light of empirical performance we found that the combination of a simple PV savings threshold plus a basic sensitivity calculation trounced every other refunding policy in use today – including all the (unnecessarily complicated) varieties of refunding “efficiency” people throw around. We dubbed this uber-savings generator the Alternative Policy.


The Alternative performed so well we first didn’t believe it. Was there some mistake? Did we miss a minus sign? Did we have an over-specified solution that wouldn’t work in practice? We decided to do a second piece of research backtesting the Alternative Policy and all the others using actual historical muni yields dating back to 1964 (thanks Delphis Hanover and Austin Tobin).  Summary results are on Tables 6 and 7 but the bottom line: the Alternative Policy is real. It crushed the other tested policies in every period for both premium and par bonds except in a couple of 2 year periods in the 70s with the most rapid yield increases. In fact, the Alternative's measured outperformance was more dramatic historically than it was in the initial simulation-based research. 

We recently ran some refunding probability numbers for a whole portfolio of issuer bonds comparing a variety of different PV savings thresholds with the Alternative Policy. Results are shown in the graph below. Substantively all of the PV savings thresholds look very similar. Naturally the lowest PV thresholds lead to the highest overall probabalities of refunding. Note you can see the call dates for clusters of bonds as vertical blips in refunding activity; when the drag of negative arbitrage drops away, higher PV savings occurs triggering refunding activity and a bump up in refunding probability. For all of the PV savings criteria, bonds are refunded with increasing probability until a flat line is reached where the bar is just too high and no more bonds are taken out. And this pattern is something we saw in our research for all refunding policies  including all manner of elaborate decision criteria including every variety of refunding efficiency we could think of. That is, for all refunding policies except the Alternative.


As you can see, the Alternative policy starts out at a PV savings equivalent threshold that looks to be between 7 or 8% but over time the effective PV equivalent falls (i.e. the black line rises) as the remaining life of the callable bonds declines. Note that the Alternative is the only policy that ultimately gets to 100% refunding across all callable bonds in this portfolio. I'm reluctant to use this word to describe a very simple hueristic but for this purpose, the Alternative simply exhibits more intelligence than all of the other refunding policies. And as a result it does a better job maximizing expected present value savings relative to every other refunding policy we've seen. Though we issue this challenge: if you think you've got a better performing refunding policy that we have not tested, send it to us and we'll take a look. 

What exactly is the Alternative Policy? After millions of dollars and thousands of lives, we will share that the Alternative policy indicates a bond is a viable candidate if these 2 criteria are met:

  1. Minimum 0.25% PV Savings
  2. Maximum 20% increase in PV Savings when issuer’s yield curve is reduced in parallel by 25 bps (what to do with escrow curve? Email peterorr AT intuitive-analytics.com)

Yes, it is a bit anticlimactic. It's a simple hueristic but actually every refunding policy is a simple hueristic. Some just work emperically a lot better than others. And that's why the concept of "efficiency" as it relates to refundings is so cognitively dissonant to me. "Efficiency" implies there's some perfect, market-timing ideal against which every decision is benchmarked and towards which we all should strive. When it comes to refunding timing, this is nonsense. If only it were that simple. But more on that in a future article.

Who will be the first issuer to put this in practice? Some are moving in that direction. As this excellent TED talk points out, to start a movement – it takes two.

ps And sorry MAs. I think we may have just triggered your fiduciary obligation so better go back and read that research thoroughly! 

Tags: refunding, advance refunding, refunding efficiency, bond option, callable bonds

Why Corporates don’t get Munis – It’s Refundings, Stupid

Posted by Peter Orr on Sat, Mar 14, 2015 @ 08:18 AM

Yesterday I spoke at a luncheon (many thanks to MAGNY for a great event) where, during Q&A, a number of people commented on how difficult it is for those who grew up doing corporate bonds to try to cross over into muni-land’s veritable Oz. With all the talking trees and flying monkeys, munis can be pretty disorienting. And I’ve seen it happen many times myself; graveyards are indeed littered with the corpses of corporate types who come to munis and just never get it, both on the buy-side and the banker/sell-side. They show up bright-eyed and bushy-tailed talking about “benchmark this” and “OAS that” but ultimately wind up crouched in a corner mumbling something about 5 and 10 year bullets.

I once asked a public finance investment banker and former bond attorney friend of mine why one of our former colleagues was going over to corporates. He replied bluntly, “I’ll tell you why. Corporates are easier.” Now I know I may be inviting some controversy here, and I certainly don’t want to minimize the challenges inherent in doing corporate bond work. Hitting the download button on those oh-so-promptly-filed 10k disclosures from Edgar can understandably strain the fingers, if not the wrist. But I think it’s time we call a spade a spade and try to address this problem head on in order to avoid any further needless human suffering.

Now my experience is that the corporate species is able to handle the non-call bonds ok. Yes, the serialization of the first 10 to 12 years of the curve in a bond issue causes some angst. But they ultimately grasp that income to the investor is exempt from Federal, and potentially state income taxes. No, I think the bulk of the loss of life is caused by the $1.35 trillion in fixed-rate, unrefunded, callable munis outstanding today - and specifically the refunding analyses thereon. So let’s pull the curtain back on what really goes on with refundings and fully dispense with all the lovely little (over)simplifications that, although so elegant and applicable in corporate-land, just don’t cut it in Oz. 

The standard optional redemption feature that exists in tax-exempt bonds is owned by the issuer. So our real-world economic analysis must begin there. And modeling the issuer’s decision well (sitting down, my corporate friends?) involves 2, and possibly 3 entirely different markets. The initial cut for a tax-exempt issuer is to look at refundings on a matched maturity basis, replacing the existing bond with one of matched maturity, but presumably lower carrying cost. But if the existing bond isn’t first callable until some future time, the issuer also cares about the yield to the call date. But this isn’t the yield to call on the borrower’s yield curve. It’s the yield to call for the reinvestment of proceeds in a refunding escrow, usually SLGS or UST, an entirely separate and taxable market! It is this basis, tax-exempt to UST, which is a critical and non-trivial driving factor in a refunding analysis.

 yield curves in refunding small

And this gets even more complicated from the investor’s perspective. The issuer no longer really cares much about the refunded bond post refunding; that’s the responsibility of the escrow agent. But the investor now holds a security that still has the tax characteristics of the original bond, but is now riskless; it’s essentially a tax-exempt UST otherwise known as a “pre-re,” this brings in yet another yield curve. And last, if we’re dealing with a bond that is callable but ineligible for advance refunding (private activity or advance refunding bonds), we may be interested in the borrower’s taxable yield curve. So for a single bond from the investor’s perspective, a comprehensive analysis would begin by capturing the dynamics of not just 3 or 4 separate points on a yield curve, complicated enough, but 3 or 4 separate correlated but distinctly different markets. And these are markets that muni investors know, all too well, hardly move in lockstep.

Does technology exist to model 4 separate but correlated yield curves at the same time, ideally perfectly capturing their historical dynamics? Yes! Doubt me?  Test it free for yourself with CurveQuiz on either iOS or Android. Only with a model like this can anyone faithfully replicate the complicated decision dynamics issuers face. And we think is an essential tool for anyone, buy side or sell side, working in the tax-exempt markets. With that we can see things like average time to refunding, expected percent of bond payments that are risk-free (see below for a 20NC5 bond at different ratings), even the portion of value of the bond derived from the “credit pop” when a bond is refunded i.e. goes pre-re.    

Expected risk free payments resized 600

So the next time someone ruefully asks why all that corporate stuff - standard, single-factor option pricing models and traditional OA analytics - hasn’t caught fire in the municipal bond market, you’ll know it has absolutely zero to do with tax-exempt issuers, bankers, financial advisors, or investors being unsophisticated, backward, slow or somehow "behind corporates." Muni people just understand their business and a little thing corporate types don’t need to concern themselves with; it’s called Section 148 of the Internal Revenue Code. But if you want to keep it simple, just say “It’s the refundings, stupid.”

Tags: yield curve modeling, refunding, municipal finance software, call option, bond option, refunding adjusted yield, callable bonds, municipal investor, refundings

New Tech for Investors: Refunding Adjusted Yield (RAY)

Posted by Peter Orr on Fri, Mar 06, 2015 @ 07:00 AM

“I have two ways of learning from history: from the past, by reading the elders; and from the future, thanks to my Monte Carlo toy.”   Nassim Taleb, Fooled by Randomness

One of the most important and oft-cited metrics we look at in the world of bonds is the yield. And yet, when we look at $1.5 trillion+ unrefunded, fixed-rate, callable municipal bonds, we often are dealing with simply the yield to worst. The “kick” in premium callable bonds is just an artifact of MSRB Rule G-33. But we know that just because an investor survives the first call date, does not mean she atomatically achieves the yield-to-maturity, despite what regulations currently dictate on a holdings statement. This standard simply does not serve the municipal investor community very well.

What do other markets do? For ones that are roughly no-arbitrage (think taxable corporate), we can use standard, 20+ year old option models that do a respectable job. OAS works fine there. For markets with more complex calling behavior than standard option models capture, a prepayment model is used. Assumptions are made about the behavior of the issuer, who obviously owns the right to do what s/he will with the call feature, cash flows are calculated based on this modeled behavior, and then a yield is determined based upon those adjusted cash flows. Can’t we do something like this for the $1.5 trillion+ in callable, unrefunded muni bonds outstanding? At the risk of repeating myself from an article for muni issuers a few weeks back, cars are driving themselves, a machine beat the pants off humans in Jeopardy and is moving on to replacing oncologists, and generally software is eating the world at an accelerating rate. There must be something we can improve on here in the muni market!

Modelling muni callables is hard. First, the municipal bond market simply is not a no-arbitrage environment so standard bond options are at best a round peg in a square hole.As Matt Fabian said at a recent MAGNY lunch, the only way to short munis is to not own munis which eliminates the underpinnings of no-arbitrage. And a good model of muni refunding behavior must start with capturing dynamics of two yield curves simultaneously – the issuer’s yields on the refunding bonds but also the treasury market for the reinvestment of proceeds (the escrow). These two markets do not move in lockstep and as such, modeling both of them in a real-world manner is a hard problem. But new research on yield curves allows us to do just that, and perfectly capture the behavior of whatever markets we’re looking at, simultaneously. Don’t believe me? Check for yourself and see if you can identify real vs simulated yield curves; here for Android and here for iOS (iphone/ipad), both free. 

But that’s actually the hard part, and it's done! With that significant threshold crossed and armed with complete simulated yield curves for the issuer and the escrow, we can replicate the calculations issuers use in determining when to refund, in full fidelity. In most cases, this is just a simple present value of cash flow (PV) savings the issuer would receive from refinancing the bond. This allows us to get complete probabilities of refunding, like this for a 5% maturing in 20, callable in 5.

Refunding probabilitiesNote that each line corresponds to a different issuer behavior. The blue line at the top uses 1% PV Savings as the criterion for when the bond is assumed to be refunded. The line at the bottom is 12% PV savings.  Intuition serves us as the lower the savings threshold the higher the probability of refunding and vice versa. 

What happens after a refunding, from an investor’s perspective, is also a bit more complex (and I think more interesting) than other markets. Obviously, cash flow is now shortened to the call date. This has implications for the expected cash flows of the bond, its average life, and risk metrics like duration.3 But with new expected cash flows we can calculate a new yield using the bond’s current price– a Refunding Adjusted Yield (RAY) for the investor.  This RAY, along with other metrics above, is appropriately sensitive to the refunding behavior of the borrower, as shown in the table below for a 20 year bond, callable in 5 and priced at 110.

RAY table

Here we have the issuer's refunding behavior changing from 2% PV savings to 12% PV savings in the first column, which changes the Refunding Adjusted (RA) average life in the second. But we also get a statistic that we believe is new and valuable for investors, the average time to refunding. In the 4th column we see the RAY, and again, as we go down the column from most to least aggressive behavior, we get an increasing yield given the cash flows are outstanding for a longer period of time. If we subtract the yield to call of 2.84% from the RAY we get a refunding adjusted kick, a far more accurate metric to use than the standard 1.40% one would get comparing YTC and YTM. And last, this framework allows us to calculate the percentage of the bond’s cash flows expected to be supported by the escrow i.e. are risk-free. And again, as expected this percentage decreases with more conservative refunding behavior. But it’s interesting to note that for the more aggressive refunding, this bond is modeled as essentially half a US Treasury, a fact we think could be very relevant to credit analysts looking at a single bond, or whole portfolio.

One benefit of this framework is it opens a huge door to those muni participants who are in the business of really knowing and comparing muni credits. All of these statistics are impacted by the expected refunding behavior of the issuer, which I think intuition tells us should be the case. RAY shines light on how issuer behavior might impact all of these metrics and ultimately the value of owning municipal bonds.

I’ll be talking about these muni market innovations and others at the Municipal Analyst Group of NY lunch on next Fri the 13. Hope to see you there! 

1 For more detail The Right and Wrong Models for Evaluating Callable Municipal Bonds

Additional research forthcoming on refunding behavior. 



Tags: monte carlo, advance refunding, call option, bond option, refunding adjusted yield, callable bonds, municipal investor

Trinity Uses RAY to assess 4s vs 5s - 2nd Gen Refunding Matters!

Posted by Peter Orr on Wed, Feb 25, 2015 @ 07:00 AM

"Prediction is very difficult, especially if it's about the future."  - Niels Bohr

The other day one of our clients, Melio & Co, helped Trinity Health determine final deal structure on their $1 billion+ issue using Refunding Adjusted Yield (RAY). There were a variety of different coupon and optional redemption structures in play and Trinity needed to know where the market was offering attractive value. Melio & Co used RAY's real-world modeling to deliver exactly that insight to Trinity. And RAY does this by faithfully modeling the sometimes messy economics of refunding.   

To test what the market offered, Trinity decided to use a 7% net present value savings criterion in the RAY calculation. As Mark Melio said, “One of the attractive features of RAY is its ability to incorporate an issuer’s actual refunding criteria.”

Refunding probability

A powerful feature of the market model embedded in the RAY calculation is its ability to create both non-call and callable yield curves. This is in contrast to no-arbitrage yield curve and bond option models that not only fail to capture realistic changes in yield curve shape, but almost invariably force the use of non-call curves - notoriously difficult to estimate in the municipal market.

With callable borrower yield curves in hand, RAY quantified not only first generation refunding savings but also the refunding of the refunding bonds i.e. the 2nd generation refunding. Of course, expected tax law is respected; advance refunding of callable advance refunding bonds can only be done taxably, or precluded altogether as selected by the modeler.  

The table below shows some key results of the RAY analysis for 2 callable bonds. They allow us to draw some interesting conclusions.1  The yield to maturity on the 5s is higher than the 4s as our intuition would tell us. But when looking at RAY1 (the “1” indicating only 1st generation refundings), the 4s looked about 5bps more attractive to Trinity than the 5s, 3.752% vs 3.802%.


Yield to Maturity



4% Coupon Bond, 10Y call




5% Coupon Bond, 10Y call





However we also know that relative to the 4s, the 5s are likely to be refunded earlier and more often. Given our modeled refunding bonds were themselves callable after 10 years, this means the 5s are likely to be refunded with callable bonds more frequently, which in turn will lead to greater 2nd generation savings. And the full RAY calculation, capturing both 1st and 2nd generation refundings, quantifies this greater benefit directly. 

Adding the 2nd generation refundings reduces RAY on the 4s by about 3bps while the 5s fall by about 13bps. This changes the answer entirely and actually leaves the 5s looking about 4bps cheaper and ultimately more attractive to Trinity than the 4s.

How would RAY change with a 5.50 coupon? Or an 8 year call? What about different refunding criteria? Excellent questions all. Stay tuned or better, we'd love to hear from you.

info@intuitive-analytics.com, 646.202.9446x101

1Results have been modified slightly to preserve confidentiality.

Tags: yield curve modeling, public finance analytics, municipal finance software, debt structuring, refunding adjusted yield

Why Option Pricing Models are Wrong for Tax-exempt Issuers (Part 2)

Posted by Peter Orr on Fri, Feb 06, 2015 @ 03:30 PM

In Part 1 (a suggested read if you’re getting to this article first) we proposed 3 questions that determine whether bond option pricing models, in contrast to real-world option models, are appropriate for tax-exempt issuers analyzing their callable bonds:

1) Is the market for all components of the option complete (defined in context below)?

2) Are markets for the items in 1) free of arbitrage profit due to trading activity sufficient to drive such profits to zero?

3) Is the purpose for using the model one of pricing and/or hedging?

Reviewing the bidding for our beloved tax-exempt/muni  market, we have a “Maybe” on 1) and a solid “Absolutely Not” on 2).1 This brings us to question 3), one of the least discussed but critically important questions for understanding suitability. Is the purpose for using the model by issuers one of option pricing and hedging? Or is it more aptly described as risk and/or performance management? Are munis simply figuring out the right hedging strategy to implement so they can make an arbitrage-free option price? That doesn’t sound like a muni or tax-exempt borrower to me; that sounds like an options dealer.2

Aren’t munis taking real risk in managing these call features? Of course they are. TheySee the light aren’t running some sort of matched options book (which in munis, doesn’t exist anywhere anyway). Issuers own a bunch of options through the sale of callable bonds, and in trader parlance, they are naked long. Refund too early and the opportunity for greater budgetary benefit may be precluded; refund too late and an attractive interest rate market may never return. It is decidedly not a simple engineering exercise of coming up with an option price based on highly liquid underlying instruments, predicated on conditions that, in muniland, just do not exist. So the answer to 3) is also an unmistakable, “Not remotely.”3 

But here let me circle back to the original LinkedIn question and provide a nice piece of research germane to the topic of fixed-income option model suitability. It is by two of the world’s foremost authorities on yield curve models, Riccardo Rebonato and Sanjay Nawalkha. The article is both free and meaningfully titled, “The Right Interest Rate Models to Use: Buy Side vs Sell Side” published in the Journal of Investment Management, 2011.   

The points made in the paper apply more broadly than to just tax-exempt entities. But as I explained in the first article on this topic, this is where we need to go to learn about lawnmower engines and how they might work in a go-kart. Though the paper focuses on one particular type of option pricing model, the popular LMM-SABR model, the points made about option pricing models being “useless at best and dangerous at worst for the buy-side institutions” are completely general and unnequivocally apply to tax-exempt borrowers.

The Cliff’s Notes: tax-exempt borrowers clearly fit into the paper’s “Buy-side.” Unlike dealers, buy-siders “are not in the business of making money by ’trading’ interest rate derivatives while maintaining zero interest rate exposures. This is the major difference between sell-side dealer banks and the buy-side borrowers and investors.” The authors further go on to describe “less sophisticated buyers such as, cities, counties, foundations, charities,…etc.” So tax-exempt issuers are clearly in the “buy-side.” Easy enough.

Cutting to the chase, the authors then say “…buyside practitioners and sellside banks need different types of interest rate models.” The buy-side institution “is interested in knowing whether the derivative is priced too cheaply or too expensively by a realistic model that can simulate the risk and return trade off under the physical measure.” Translation: issuers need a real-world (synonymous with “physical measure”) model  to provide an estimate of value to compare to what the market might provide. As an aside, we think the best practice version of this uses the issuer’s actual refunding criteria, something that is accomplished naturally with a suitable real-world model.   

To be clear, these models that buyers (tax-exempt issuers) should use are not arbitrage-free pricing models such as Black-Derman-Toy, Black-Karacinski, or Hull-White. Buyers need a real-world (physical measure) interest rate options model like Bernadell, Coche, Nyholm (2005), Rebonato (2002, ppt file), or the more powerful one we use to calculate Refunding Adjusted Yield (RAY), Deguillaume-Rebonato-Pogudin, 2013. 

But most municipal market practitioners know this, even if they don’t have the technical background to explain exactly why. If decades-old option pricing models really applied so neatly to tax-exempts than bankers, financial advisors, salespeople, traders and issuers would’ve been using them successfully for years. But the vast majority of them have not, and rightly so. Now with truly appropriate and far more powerful alternatives available, why should they?


1In the words of MMA's Matt Fabian at today's Municipal Analyst Group of NY lunch, "There's only one way to short munis; and that's don't own munis."

2But of course there can be no real option dealers in the muni market because the answers to questions 1) and 2) are a joint “No” to begin with. 

3The fact is, even if the answer to 1) and 2) had been a resounding “Yes”, if the answer to 3) is a “No”, then option pricing models would still not be appropriate. The answer to all 3 must be “Yes” for option pricing models to be appropriate.

Tags: interest rate model, yield curve modeling, refunding, advance refunding, public finance analytics, call option, bond option

Why Option Pricing Models are Wrong for Tax-exempt Issuers (Part 1)

Posted by Peter Orr on Tue, Feb 03, 2015 @ 07:00 AM

"It's not how we make mistakes, but how we correct them, that defines us."  - Anonymous

The other day I was asked in the Tax-Exempt Debt Structuring (TEDS) group on LinkedIn to provide some "scholarly" references (outside of our own) that support my comment that “option pricing models are inappropriate for issuer’s use in looking at option value or refundings.” To put a finer point on it, there are two main types of option models: pricing models or more accurately, relative pricing models (some regrettably call these “standard” models as if anything else is non-standard) and real-world models. The question at hand is which type of model is the right one for tax-exempt issuers, or any bond issuer for that matter, to use when analyzing their optional redemption features.   We’ve been dancing around this topic for a while now and think it’s time the matter was set definitively straight.1

The original LinkedIn question to me was odd as it stipulated the reference(s) should be from the narrowWhoops realm of municipal finance alone, a notoriously sparsely researched area (no offense, MFJ). Let me analogize briefly to explain why this is silly. Let’s say we live in a world with only engineless go-karts. Then someone comes along and says, “Hey we have these great things called ‘lawnmower engines’ and they’ll really make these go-karts go!” The LinkedIn question is akin to saying, “Show me some literature from the engine-less go-kart community that says these lawnmower engines are inappropriate for us.”  Doesn’t make much sense, right? Why would anyone from the engineless go-kart community publish such a thing in the first place? In order to properly answer the question we’d need to comb the annals of the Journal of Lawnmower Engines to study up on details of the engines, the conditions under which they work properly, their weight, the torque they deliver, etc. Only with that information in hand, coupled with our knowledge of engineless go-karts, could we ascertain whether small engines and unpowered go-karts would indeed be a winning combination.

All that’s to say we better learn something about bond option pricing models generally if we’re going to determine whether they make any sense for municipal and tax-exempt issuers. And so we have. The fact that option pricing models are the wrong ones for issuers is obvious if you look at three simple questions. The applicability and suitability of option pricing models to any situation rests on a "Yes" answer to all of these basic questions:

1) Is the market for all components of the option complete (defined below)?

2) Are markets for the items in 1) free of arbitrage profit due to trading activity sufficient to drive such profits to zero?

3) Is the purpose for using the model one of pricing and/or hedging?

In the remainder of this article we’ll address 1) and 2) as these speak to the foundational assumptions for any option pricing model to be valid. Question 3) we’ll save for tomorrow’s second and final installment.

  1) Is the market for all components of the option complete?

For standard option pricing models to apply the market must be complete. This means in essence that there are non-call bonds of the issuer in question trading across all relevant parts of the non-call yield curve and without “friction.” What are the relevant parts? The parts that cover the term of the option being modeled. Now some could argue that we can write a non-call yield scale for an issuer, which is true. But writing some best-guess, non-call tax-exempt scale is a far cry from having the full complement of non-call bonds across the curve to trade, both to buy and sell short. Andrew Ang et al discuss the difficulty of selling munis short in their paper, Taxes on Tax-exempt Bonds (more below). And we won’t even mention the “frictions” involved in trading munis. So the answer to 1) is probably a “Not really” but let’s just be charitable and call it a “Maybe...sort of”.  

  2) Are markets for the items in 1) all free of arbitrage profit due to trading activity sufficient to drive such profits to zero?

So with the answer to 1) wobbly at best, let’s look at Question 2). Are muni markets free of arbitrage profits? Pose this question to any muni salesperson, trader, investment banker or professional investor and wait for the belly laugh. This is a non-starter. You can’t short munis due to the tax-treatment. And the one flavor of research you could call plentiful in the muni market is the type that concludes with some variety of, “It’s inefficient”, “It’s fragmented”, “It’s unhedgeable”, “It’s expensive” or “It’s broken” You could imagine someone trying to mistakenly argue that it’s arbitrage free, by virtue of the simple fact that you can’t implement an arbitrage trading strategy that captures a bond’s mispricing to begin with. But that’s not arbitrage free, that’s just prohibitively expensive and insufficiently tradable. To quote Ang et al, in Taxes on Tax-exempt Bonds,

"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."

Well, there it is. Let’s review the bidding. The answer to 1) is an iffy “Maybe”, the answer to 2) is an unqualified “No.” The foundational assumptions on which bond option pricing models rest simply do not get there in the municipal market. And it's not just a foundational crack, this foundation's built on sand. Can we just sweep these facts under the rug, hold our nose, and blithely hit the Calc button? To what end? So we can generate some winged-horse numbers using sexy models that work nicely in other markets? Where's the benefit?

We could stop here because all 3 questions need a Yes for standard option pricing models to apply. But wait, there’s more! Question 3) is probably the most important of all.  And we’ll cover it fully in our next article. Spoiler alert – muni issuers aren’t options dealers. 

1We tried to set the matter straight with The Right and Wrong Models for Callable Municipal Bonds published back in 2013. But we understand. It took the Royal Navy fifty years after James Lind definitively showed citrus fights scurvy in 1753 to keep fresh oranges on British ships. These things take time.  

Tags: interest rate model, financial model, yield curve modeling, Financial Engineers, call option, bond option

The Right Analysis for Refundings – MSRB, Take Note

Posted by Peter Orr on Thu, Jan 29, 2015 @ 07:15 AM

We see a lot of confusion in public finance as to how to analyze refundings. Unfortunately I think much of it stems from people outside of public finance coming in without a complete understanding of the environment in which a tax-exempt issuer operates i.e. the muni market. These interlopers get excited when they see option specifications in an official statement, then cry out, “We’ve seen these before. We have fantastic models used everywhere else, they must apply here too!” Unfortunately the foundational assumptions underpinning these models do not exist in the muni market leading this statement to be bunk (technical term my father used to use…). In fact those elegant bond options models do not apply in the muni flea market.

Let’s start with a simple assumption. While we're here it is very important to understand the assumptions of any financial model, particularly so with options. The complexity andbiz peep at whiteboard elegance of the math involved in options can temporarily blind the most clear-thinking practitioner to the fact that important assumptions are just not satisfied in the muni market.   

The assumption I make is simply stated but has far-reaching and critical implications for the right financial economic analysis for refundings:

An Issuer can ONLY achieve value from an optional redemption by performing an (advance or current) refunding

That is, the only way to lock in economics is to actually exercise the option. Some may argue that this is an extreme assumption. Ang et al in their irretrievably flawed paper on advance refundings take issue with this very topic, lamenting that issuers should more efficiently manage the undeniable interest rate risk in their optional redemptions by using derivatives. In the ivory tower they enjoy the luxury of ignoring patently unbalanced exposés like this one on Chicago Public Schools use of synthetic fixed-rate debt. Very real political considerations aside, suffice it to say that the number of states, munis, or tax-exempt entities comfortable with swap contracting and its attendant liquidity and credit risks is unfortunately very small. For the vast majority, swap is currently a four letter word. 

So let’s assume the above statement for the moment; what are the ramifications? In short, it means the beautifully elegant models increasingly brought to bear on municipal optional redemption features do not apply. Option Adjusted Yield, lognormal short-rate models, no-arbitrate conditions – they don't work for munis. In an article on stock options discussing option owners who cannot sell, Paul Wilmott (himself a veritable LeBron James of financial engineering) puts it this way:

“In many situations, the only way of locking in the profit may be to exercise the option early. The ‘theory’ says don’t exercise, but if the stock does fall then you lose the profit. At this stage it is important to remember that the theory is not relevant to you [emphasis added].

On Exercising American Options: The Risk of Making Too Much Money  Ahn Hyungsok and Paul Wilmott, 2003

Issuers are in exactly the same spot. They can’t just sell their options. Nattering about the right volatility or mean reversion input to use in your standard bond option model (BK or BDT or the like) is a lot of misspent energy. As research has detailed recently, for many reasons above and beyond the simple one stated here, these are simply the wrong models for issuers to use to solve the refunding timing problem, which is a risk management problem if ever there was one.

So if we can’t use all that admittedly Nobel-worthy theory in analyzing refundings, what are we to do? In short, get real. Use a real-world market model of both issuer and SLGS yield curves, capturing the complicated way those two markets move. And with that real-world model in hand search for good, robust signals that help issuers decide when to refund. And do this by testing actual issuer refunding criteria: PV savings, escrow efficiency, the NYS/MTA table, the opportunity index used by the state of Wisconsin and any and all combinations thereof.

Two pieces of research do just that, by testing roughly 40 different refunding policies (read “signals”) both on a 50 year historical basis and prospectively on a simulated basis. One result that may surprise is that refunding efficiency (using one of those standard bond option models) doesn’t fare so well under the bright light of both historical and simulated performance. In fact, 100% refunding efficiency was ranked dead last among all policies. And lower percentage refunding efficiencies behave in practice a lot like the far simpler signal of 5-6% present value savings. More interesting, an Alternative Policy was identified, currently not in use to my knowledge, that trumps all others – and not by a little. More on this in future articles.

As the MSRB drafts its curriculum for educating municipal financial advisors, I hope the realities of the municipal market are kept front of mind when they cover options. They have the choice between propagating the mistakes currently happening far too often in the municipal market, or helping advisors and ultimately issuers understand the right types of analysis and models that apply and why. I’m crossing my fingers for the latter. 

Tags: Financial Engineers, Financial Decisions, refunding, advance refunding, refunding efficiency, call option, bond option