14 April 2011

Understanding Municipal Bond Arbitrage

Introduction

Following the “great recession,” state finances have continued to deteriorate. With many

states now in crisis, municipal bonds have increasingly come under pressure. In the past few

months, investors have fled municipal bond funds1 in increasing numbers. Many now think

that the stress on state finances is so great that the only recourse available to states will be to

default on the outstanding municipal bonds.

Three years ago, a different type of stress hit municipal bonds. In late 2007 and early 2008,

as stress on the financial markets reached a new high, a number of hedge funds and other

investors lost millions of dollars on an investment strategy often labeled as “municipal bond

arbitrage.”2 This strategy, which had generated high returns for many years, garnered losses

during the credit crisis and litigation soon followed. The litigation, much of it still pending,

is of two main types: complaints filed by investors against hedge funds and other sponsors

of these strategies regarding the suitability of such strategies, and complaints filed by hedge

funds against their prime brokers regarding pricing and margin practices.3 In this paper, we

first explain the basic design of the municipal bond arbitrage strategy, then discuss its risk/

return profile, and finally explore in more detail its risk components in order to gain insight

into some of the reasons for losses experienced during the financial crisis.

What is Municipal Bond Arbitrage? Basic Design

Municipal bond arbitrage is a type of investment strategy that is often classified as a “yield

arbitrage strategy.” Such strategies seek to capture the difference in yields on two types of

debt securities. Though there are many variations to the municipal bond strategy, the basic

idea is premised on the following attributes of the municipal yield curve:4

By Dr. Ethan Cohen-Cole and Shuchi Satwah*

www.nera.com 2

1. The municipal yield curve is “positively sloped.” In other words, the yields on long-term

municipal bonds are higher than the yields on short-term municipal bonds. As shown

in Figure 1, over time, the yield curve can shift up or down and become more or less

positively sloped.

2. The municipal yield curve is usually “steeper” than the Treasury yield curve. That is, the yield

difference between municipal bonds and Treasuries after-tax is larger for long-term than for

short-term bonds. As shown in Figure 2, the Treasury curve can also shift up or down over

time and become more or less positively sloped. Generally, Treasury and municipal yield

curves move together and, as shown in Figure 3 below, the yield difference—or spreads

between 20-year municipal and Treasury after-tax yields—is greater than the 10-year

spreads, which in turn is greater than the one-year spreads. Though the yield differences

appear small, significant profits can be earned even after factoring in fees and borrowing

costs by leveraging the transaction three to 20 times.

3. Unlike the Treasury yield curve, the municipal yield curve has never “inverted.” So the yields

on long-term municipal bonds have always been greater than yields on short-term municipal

bonds, as shown in Figure 4.

Thus, to implement a municipal bond arbitrage, an investor can combine municipal and

Treasury bonds in various ways. For example, he may do something as simple as buy short-term

municipal bonds and sell short-term Treasury bonds, or buy long-term municipal bonds and

sell long-term Treasury bonds. The investor may also execute the strategy using only municipal

bonds—buy long-term municipal bonds and sell short-term municipal bonds.6 He may also

add a layer to the last variant by buying short-term Treasuries and selling long-term Treasuries.7

These variations lead to different risk/return profiles as discussed below.

Figure 1. Municipal Yield Curves (as of certain sample dates)

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Source: Based upon daily data obtained from Bloomberg, L.P. Municipal yields are based on Bloomberg Fair Market Value Municipal General Obligation AAA index (tickers 0491Y - 30Y) and are option-free yields.

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Figure 2. Treasury Yield Curves (as of certain sample dates)

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Source: Based upon daily data obtained from Bloomberg, L.P. Treasury yields are based on Federal Reserve US H.15 T Note Treasury Constant Maturity (tickers H15T3M - H15T30Y). Tax rate of 35% is applied to Treasury yields. The Treasury yield curve as of 1/3/2005 does not have a 30-year yield reported because issuance of 30-Year Treasury bonds was discountinued on February 18, 2002 and was re-introduced on February 9, 2006.

Figure 3. Municipal and Treasury Yield Spreads Compared for Different Maturities March 1, 1991 - December 31, 2010

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Source: Based upon daily data obtained from Bloomberg, L.P. Yield spreads are calculated as municipal yields minus Treasury yields for the relevant maturity. Municipal yields are based on Bloomberg Fair Market Value Municipal General Obligation AAA index (tickers 0491Y, 04910Y, 04930Y). Treasury yields are based on Federal Reserve US H.15 T Note Treasury Constant Maturity (tickers H15T1Y, H15T10Y, H15T20Y). Tax rate of 35% is applied to Treasury yields.

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What is the Risk/Return Profile of a Municipal Bond Strategy?

The simplest way to look at return is under a “hold-to-maturity” measure. For example, a plain

vanilla version of the municipal bond strategy involves the following two steps:

1. Issue debt, either through shorting existing securities such as Treasuries, or through direct

issuance, and

2. Invest in municipal bonds.

Anytime the debt issuance is cheaper than the investment return, these two steps constitute

a profitable strategy. For example, the table below shows the basic math associated with this

strategy under a simplified set of assumptions. It assumes that the maturity of the municipal

bonds and the maturity of the Treasury bills are matched, the two positions are held to maturity,

and there is no default. Though oversimplified, this table illustrates how attractive returns can

be earned through leveraging yield differences, especially in a low-interest rate environment.

Figure 4. Municipal Term-Yield Spread Compared to Treasury Term-Yield Spread March 1, 1991 - December 31, 2010

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Source: Daily data obtained from Bloomberg, L.P. Term-Yield Spreads are calculated as 20-year yields less two-year yields. Municipal yields are based on Bloomberg Fair Market Value Municipal General Obligation AAA index (tickers 0492Y and 04920Y). Treasury yields are based on Federal Reserve US H.15 T Note Treasury Constant Maturity (tickers H15T1Y, H15T10Y, H15T20Y). Tax rate of 35% is applied to Treasury yields.

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Basic Strategy

Table 1: Basic Strategy – 10x leverage

Investment Quantity Annual Return Annual Profit

Buy Municipal Bonds $1000 4.05% $40.50

Sell Treasury bills $900 3.89% -$34.98

Fees -$1.00

Net Asset Value $100 4.52% $4.52

However, the strategy, like any other strategy, faces a changing risk profile over its life. Some of

the risks in this strategy are:

• Market risk: Both municipal bonds and Treasuries have volatile prices. If price swings and

yield curve shifts in the municipal yield curve are uncorrelated with the Treasury yield curve,

this strategy can suffer big mark-to-market losses. A leveraged portfolio is also subject to

early unwind risk, that is, the risk of mark-to-market losses being realized through liquidation

of the portfolio. Liquidation may occur if the lender withdraws financing altogether or

increases the costs of financing through larger margin calls.

• Refinancing risk: Issuing/selling short-term securities to fund long-term municipal bond

investments is a classic carry trade and is subject to refinancing risk. To the extent this

strategy relies on maturity mismatch, it brings forth the risk that when the short-term

securities mature, lenders may be unwilling to provide new funding. Such risk is magnified

during periods of market uncertainty.

• Liquidity risk: In part because of the refinancing risk associated with short-term financing,

the long-term municipal bond portfolio may have to be liquidated on a short notice. In

a liquid market, this type of de-leveraging can be simple and have a smaller impact on

profitability than in periods of crisis.

• Credit risk: While municipal bonds have repayment histories that are considerably stronger

than equivalently rated corporate issuers,8 defaults do exist. Moreover, since most municipals

are insured, the AAA-rated municipal obligations are highly dependent on the credit quality

of the insurer rather than that of the municipality.

In order to illustrate the impact of risks, particularly market and refinancing risks associated with

this strategy, we constructed a sample portfolio and generated a distribution of returns through

historical simulation.

We begin as above with a fund with $100 in equity. It sells $900 of one-year Treasury bills

and buys $1000 of one-year maturity municipal bonds. Both positions are established at par

one-year yields as of January 1st, 2000. To generate a distribution of monthly returns that

can be earned by this portfolio over a one-year investment horizon, we conducted a historical

simulation using a block-sampling method.9 The dataset used for sampling returns consists

of historical monthly data on Treasury and municipal yields observed from January 1991 to

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December 1999. We defined a block to consist of 12 consecutive monthly returns. Thus, if the

first return randomly sampled from the historical dataset was January 2005, the monthly returns

for the following 11 months in both the municipal and Treasury market would be picked up as a

block in order to preserve return correlations across time and between markets.

Thus, our simulation allowed us to generate 10,000 possible interest rate paths for the sample

portfolio consisting of both the Treasury and municipal holdings. For each of the 10,000 paths,

we marked-to-market the portfolio at the end of each month. This, in turn, allowed us to

construct a set of possible profit/loss outcomes faced by this fund over a one-year investment

horizon. Figure 5 reports the mean, the fifth, the twenty-fifth, the seventy-fifth, and the ninety-

fifth percentile outcomes of these 10,000 draws.

Figure 5. Distribution of Returns on Basic Strategy Sampling Period: January 1, 1991 - December 31, 1999

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Note: The basic strategy consists of buying $1,000 of the one-year municipal bond and selling $900 of a one-year Treasury bill. The returns are calculated on $100 equity.

This exercise produced a few interesting results. First, we can see that a portfolio constructed

with only one-year maturity instruments shows zero variance of returns at the end of one year.

At this point, the instruments have matured and, barring a default, the holders show the full

hold-to-maturity profit from the strategy.10 Second, the zero variation in potential returns on

equity at maturity is in stark contrast to high variation in the short run. In the first few months,

there is a significant probability that the basic strategy shows negative returns. Recall that such

negative returns can lead to margin calls, declining profits, and perhaps even liquidation of the

portfolio. As a result, some funds may be unable to carry the investment strategy to maturity.

The general conclusion from this analysis is that there is an explicit trade-off between risk and

return in this strategy. Similar to most other investment strategies, the high positive returns

emerge as a result of investor taking and managing a variety of risks (see above for list).

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Complex strategy

To this basic strategy, an investor can add a few additional types of risk. Each of them can make

the investment more profitable and potentially more risky if not carefully managed. For instance,

an investor’s returns can further increase if maturity mismatch is introduced in the portfolio. This

results from the fact that long-term interest rates for most securities are normally higher than

short-term ones. See Figures 1 and 2 above. The investor, however, now needs to refinance

many times over the course of the investment. The new payoff structure now is:

Table 2: Complex Strategy

Investment Quantity Annual Return Annual Profit

Buy Long Term Municipal Bonds $1000 5.09% $50.90

Sell Short Term Municipal Bonds -$900 4.05% -$36.45

Sell Long Term Treasury Bonds -$900 4.19% -$37.73

Buy Short Term Treasury Notes $900 3.89% $34.98

Fees -$2.00

Net Asset Value $100 9.70% $9.70

Again, as this is just a static view, we repeat the historical simulation using the full set of

investments listed in Table 2. The return distribution on the complex strategy over a one-year

holding period is shown in Figure 6. Unlike Figure 5, Figure 6 does not converge to a hold-to-

maturity profit because we have only simulated a one-year time frame on a portfolio that has

longer-term securities in it. As seen in this figure, the range of returns during the first year of

the strategy can be very wide when maturity mismatch is introduced in the strategy.11

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Did the risk/return profile change in the 2000s?

The above simulations are illustrative of the range of returns that a fund may expect on this

strategy based on a historical simulation using data from the 1990s. In order to understand the

impact on this range of actual interest rate relationships observed during the following decade,

we replaced the sampling dataset. Instead of using historical monthly returns during January

1991-December 1999, we used historical monthly returns during the period January 2000-

December 2008 to run another simulation on the complex strategy.

The simulation results are shown in Figure 7. This figure shows that the payoff to the complex

strategy changed in two ways. First, this decade saw lower average returns. Second, the range

of profit/loss outcomes shrank, with the profitable outcomes decreasing significantly while the

loss outcomes appear to remain steady.

Figure 6. Distribution of Returns on Complex Strategy Sampling Period: January 1, 1991 - December 31, 1999

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Note: The complex strategy consists of buying $1,000 of the 10-year municipal bond and selling $900 of the one-year municipal bond. It also involves simultaneous selling of $900 of the 10-year Treasury bond and buying $900 of the one-year municipal bond. The returns are calculated based on $100 equity.

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It is important to note the differences between return distributions generated based on a

historical period that covers the period 1991-2000 versus 2000-2008. The comparison illustrates

that yield relationships did change in a significant manner. Perhaps the most notable change in

the complex strategy simulations is the persistent presence of short-term losses combined with

a lower level of profitability over a one-year horizon. We see that the fifth percentile line hovers

between a loss of 10-20% in both simulations. The average returns decline from a little over

20% to almost 10%, while the ninety-fifth percentile line drops from about 50% to about 30%.

While the comparison clearly illustrates reduced profitability, what were the conditions that

caused some of these strategies to experience large losses during the credit crisis?

Why did the Strategy Experience Losses During the Credit Crisis?

The strategy at its core is a leveraged play on a combination of risks. Each of the risks

mentioned are potentially small—and as a result the returns to the strategy without leverage

were relatively small. Similar to other leveraged strategies, when fundamentals move against

the investor, short-term losses can accumulate quickly and in large quantities. Some of the

fundamentals that led to changes in risks are described below.

Figure 7. Distribution of Returns on Complex Strategy Sampling Period: January 1, 2000 - December 31, 2008

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Note: The complex strategy consists of buying $1,000 of the 10-year municipal bond and selling $900 of the one-year municipal bond. It also involves simultaneous selling of $900 of the 10-year Treasury bond and buying $900 of the one-year municipal bond. The returns are calculated based on $100 equity.

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Increases in volatility and changes in correlations increased market risk

Both municipal bonds and Treasuries have volatile prices. For this strategy to remain profitable,

prices of the two would need to move in perfect unison. To the extent that price swings

and yield curve shifts are uncorrelated, the strategy can quickly experience stress. Figure 8

shows the 60-day yield variance for Treasuries and AAA municipal securities to illustrate that

the volatility is rarely the same. The shaded area shows the difference between Treasury and

municipal volatility on the right hand axis; where this shaded area is greater than zero, it

indicates that volatility of Treasuries is greater than that of municipal bonds.

Figure 8. Annualized Volatility of Treasury and Municipal Yields April 1991 - December 2010

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Source: Based upon daily data from Bloomberg, L.P. Volatility is calculated on a rolling basis using preceding 60 days of daily data. Volatility Difference is calculated as the volatility of one-year Treasury minus the volatility of one-year municipal bond. Municipal yields are based on Bloomberg Fair Market Value Municipal General Obligation AAA index (ticker 0491Y). Treasury yields are based on Federal Reserve US H.15 T Note Treasury Constant Maturity (ticker H15T1Y).

Notice that annualized volatility increased to approximately 40% in 2003 and 2004 before

returning to historically low levels between 2005 and 2007. The first wave of financial crisis

(late 2007-early 2008) saw volatility increase as high as 80% in both markets. The volatility of

Treasury yields increased dramatically again in the fall of 2008. Both markets have remained in

60-100% volatility range since mid-2009.

Frequent changes in price can also have the effect of triggering margin calls. When municipal

bond prices fall too far, lenders require greater capital on hand. The associated margin calls can

increase investor costs as more capital is deployed. It might also lead to forced de-leveraging

and reduction of positions. As a result, a hedge fund holding a portfolio that may have been

profitable in the long run, or if held to maturity, may not be able to realize these potential

profits if short-term volatility swings lead to mark-to-market losses and liquidation.

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Moreover, as shown in Figure 9 below, Treasuries exhibited the highest volatility during the

financial crisis, even though they are considered “safe” investments. This safety criterion

of Treasuries is based on their credit risk characteristics, not mark-to-market risk. In fact,

Treasuries are well known to see increased demand during crisis time, a phenomenon known

as flight-to-quality.

Figure 9. Comparison of Annualized Volatility of Returns in Different Markets: Treasury, Municipal, Swap, and S&P Index April 1991 - December 2010

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Source: Based on daily data from Bloomberg, L.P. Volatility is calculated on a rolling basis using preceding 60 days of daily data. Municipal returns are based on Bloomberg Fair Market Value Municipal General Obligation AAA index (ticker 0491Y). Treasury returns are based on Federal Reserve US H.15 T Note Treasury Constant Maturity (ticker H15T1Y). Swap returns are based on Bloomberg mid-market par swap rates (ticker USSW1). S&P returns are based on S&P 500 Index (ticker SPX).

Perhaps more importantly, note that correlation also changed. For the complex strategy to

work, one needs Treasuries and municipal bonds yields to be highly correlated. When the yields

are not correlated, risk remains. The volatility differences that emerged during the crisis indicate

that correlations declined and that the residual risk was large.

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Stresses in markets for short-term financing increased refinancing risk

The municipal bond strategy involved selling short-term securities and buying long-term

municipal bonds. Like any strategy that relies on maturity mismatch, it bears the risk that

when the short-term securities mature, lenders may be unwilling to provide new funding. This

phenomenon was well covered during the financial crisis as structured investment vehicles

(SIVs) used by banks to fund mortgage-backed securities failed because investors grew wary

of providing short-term funding. Municipal bonds structures very similar to SIVs (called Tender

Option Bonds) faced similar funding problems. Various short-term financing markets, such as

the repurchase (“repo”) markets, auction-rate securities markets, and asset-backed commercial

paper (ABCP) markets exhibited signs of severe stress during the credit crisis. Even if these

markets are not directly related to municipal arbitrage strategies, they can certainly have

spill-over effects and accentuate liquidity, as well as credit risk. A municipal arbitrage strategy

could fail as a result of an inability to obtain short-term financing; that is, short-term liquidity

problems can generate the need to liquidate a portfolio that would have been profitable if

held to maturity.

Increased trading may have depressed prices, leading to increases in liquidity risk

In part because of increased margin calls or failed refinancing, many investors had to off-load

municipal bonds on short notice. In a liquid market, this type of deleveraging can be simple.

However, municipal bonds as an investment class are relatively illiquid. All municipal bonds

trade on an over-the-counter basis and many municipal bonds do not trade regularly. This can

potentially make the large-scale sale of municipal bonds difficult on short notice.12

In aggregate, however, municipal bond volumes have been relatively constant, even through the

crisis. Indeed, on a relative basis, municipal bond trading looks similar to Treasuries even during

the highest stress period (see Figure 10 below). Increased trading volumes, though, are likely to

depress prices, leading to losses on sales. As shown in Figure 11, the daily count of trades did

increase in the municipal market.

It is plausible that prime brokers began placing margin calls and/or changing the nature of

lending relationships with hedge funds that participated in municipal bond arbitrage strategies.

As a result, collateral requirements increased for hedge funds, forcing them either to liquidate

positions or raise new capital, which in turn depressed prices for municipal bonds.

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Figure 10. Daily Par Amount of Municipal and Treasury Trades January 1999 - December2010

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Figure 11. Daily Count of Muni Trades Reported to MSRB January 1999 - December 2010

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The declining credit quality of monoline insurers and of municipalities increased credit risk

Because many municipalities are too small to rate or have shaky finances, many municipal bonds

are issued with a guarantee (insurance) from a bond insurer. When monoline insurers faced

insolvency fears of their own, many municipal bonds as well as Tender Option Bond structures

were downgraded. The bond yields increased as markets priced in the increased chance of

default of the insurer.

While municipal bonds have repayment histories that are considerably stronger than equivalently

rated corporate issuers,13 defaults do exists. Municipal bonds also have greater credit risk than

US Treasuries. Notably, the default probabilities of many securities have moved over time. The

current state and municipal budget crises have pointed toward increased defaults on municipal

bonds. This concern has been widely reported.14

Conclusions

We have provided a short explanation of municipal bond arbitrage, its risk factors, and a risk/

return profile of the strategy over time. Broadly, we have concluded that this strategy was one

that profited from taking on a range of risks. During the 10–15 years leading up to the crisis,

the profile of this strategy changed but nonetheless stayed profitable on the margin.

As the crisis hit, a number of key components of the strategy changed. Price volatility in

the municipal bond market and the Treasury market increased. As volatility spiked and the

correlation between the two changed, this had the potential to hurt an arbitrageur. Similarly,

as refinancing options thinned with the collapse of Tender Option Bond structures, arbitrageurs

faced difficulty in rolling over maturity-mismatched portfolios. Anecdotal evidence further

supports that these liquidity shortages were particularly severe during key periods. We find that

aggregate trading volumes of municipal bonds were relatively stable, but individual off days

could lead to severe consequences depending on portfolio holdings at that point in time.

Over all, we conclude that municipal bond arbitrage strategies were not fundamentally

flawed and guaranteed to lose as some have suggested. Instead, the strategies indeed carried

risk, which when hit by “a perfect storm,” or a sequence of events in the credit crisis, indeed

lost money.

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* Dr. Cohen-Cole is an Assistant Professor in the Finance Department of the University of Maryland Robert H. Smith School of Business, and a Special Consultant in NERA’s Securities and Finance Practice. Shuchi Satwah is a former NERA Vice President.

1 See http://www.businessweek.com/news/2010-12-30/bond-funds-see-third-week-of-withdrawals-as-stocks-pull-in-money.html

2 See “Muni bond funds hit by perfect storm,” Market Watch, 25 August 2007, and “Muni Hedge Funds hit by margin calls, says PIMCO,” Market Watch, 29 February 2008.

3 The former usually involve arbitrations under the Financial Industry Regulatory Authority (FINRA)’s dispute resolution process. For example the actions filed against Citigroup Global Markets, Inc. by investors in the ASTA Series of funds allege breach of fiduciary duty, common law fraud, negligent representation, negligent management, negligent supervision, and breach of contract.

4 Many reasons have been provided for these attributes, including the callable feature of municipal bonds. The municipal yield curves used in this paper, however, are option-free.

5 In this paper, all references to Treasury yield curves are to tax-adjusted Treasury yield curves. Par swap curves exhibit a similar relationship to municipal yield curves and hence are often used instead of the Treasury curves. For ease of explanation, we limit the discussion in this paper to only Treasuries.

6 Tender Option Bond (TOB) structures utilize this strategy by investing in long-term municipal bonds the proceeds from issuing short-term debt. The return earned on long-term municipal bonds is used to cover the cost of issuing the short-term debt and to generate a profit for the sponsors of the structure. Closed-end municipal bond funds may also utilize a variant of this strategy by investing in long-term municipal bonds and issuing preferred shares in the auction-rate securities market.

7 Adding Treasuries to the “municipals-only” strategy hedges interest rate risk.

8 See US Municipal Bond Defaults and Recoveries, 1970-2009 Moody’s Investor Service.

9 In a historical simulation, the dataset used for sampling returns consists of the actual returns observed during a certain historical period. The simulation involves sampling the dataset numerous times in order to create numerous paths that can then be used to generate return distributions. The block sampling method simply involves picking up a certain number of consecutive historical returns in order to preserve correlations.

10 The profit of 5.52% shown in Figure 5 is calculated without taking into consideration the fees and therefore is greater than the 4.52% net profit after fees shown in Table 1.

11 The Treasury positions are usually adjusted dynamically to hedge the interest rate risk. To keep our analysis simple, we have not adjusted the Treasury positions.

12 See Municipal Market Advisors – Market Insight, 28 February 2008 for a discussion of liquidity shocks in early 2008.

13 See U.S. Municipal Bond Defaults and Recoveries, 1970-2009 Moody’s Investor Service.

14 http://online.wsj.com/article/SB10001424052702304180804575187973704815244.html. http://online.wsj.com/article/SB10001424052748704067504575304782084631368.html. http://www.cnbc.com/id/38001354/City_Symbolizes_Budget_Crisis_Facing_Many_Across_US.

End Notes

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