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VOLUME 39 NUMBER 2 www.iijpm.com WINTER 2013

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THE JOURNAL OF PORTFOLIO MANAGEMENT WINTER 2013

Bond Market Price Discovery: Clarity Through the Lens of an ExchangeMATTHEW TUCKER AND STEPHEN LAIPPLY

MATTHEW TUCKER

is a managing director in the fixed-income port-folio management group at BlackRock in San Francisco, [email protected]

STEPHEN LAIPPLY

is a director in the fixed-income portfolio manage-ment group at BlackRock in San Francisco, [email protected]

The fixed-income market is an over-the-counter (OTC), bilateral market in which trades occur between pri-vate counterparties at negotiated

prices. The same bond may simultaneously trade in multiple transactions at different prices, but participants are largely unable to observe these price discrepancies in real time. Electronic trading systems for certain fixed-income sec-tors (Tradeweb for U.S. Treasuries, agencies and mortgages; Market Axess for corporate securi-ties, for instance) as well as reporting systems such as TRACE (for corporate bonds) and EMMA (for municipal bonds) have helped improve price transparency, but only on a delayed basis.1

In less-liquid fixed-income sectors, such as the high-yield corporate-bond market, dealers may be reluctant to simultaneously display actionable bid and offer prices. When traders do display two-way markets, spreads are often quite wide—a point or greater in certain high-yield or municipal bonds. As a result, the OTC bond market can be opaque and discon-tinuously liquid, with poor price discovery, especially during periods of elevated market volatility and dislocation.

The equity market’s structure differs sig-nificantly from that of the OTC bond market. The equity market is based on centrally cleared trades that are executed at national best bid- or offer-side prices. Market participants can almost immediately see trade sizes and prices.

Two-way markets are also generally posted for all securities trading on the exchange, so all market participants have nearly the same rapid, transparent access to price information and liquidity. That reduces counterparty risk, increases transparency, facilitates price dis-covery, and generally improves liquidity.

The advent of the fixed-income exchange-traded fund (ETF), a bond portfolio that trades throughout the day on a stock exchange, allows us to examine the implications of a market that simultaneously trades both over the counter and on an exchange. In this article, we consider the price behavior of the traditional OTC bond market and explore the value of the price infor-mation offered by bond ETFs trading on an exchange.

First we compare bond- and equity-market structures, with a particular focus on the impedi-ments to price discovery in the OTC bond market. We then discuss the structural, valuation, and trading attributes of fixed-income index ETFs. We present an empirical analysis based on historical price data, illustrating the cointegrative properties between fixed-income ETFs and the underlying OTC market, as proxied by fund net asset values (NAVs). This analysis suggests that liquid fixed-income ETFs may actually provide price discovery, evidenced by a leading relation-ship versus NAV/index values. Finally, we illus-trate a simple pairs-trading strategy between the ETF market price and the corresponding NAV

JPM-TUCKER.indd 49JPM-TUCKER.indd 49 1/24/13 12:59:15 PM1/24/13 12:59:15 PM

BOND MARKET PRICE DISCOVERY: CLARITY THROUGH THE LENS OF AN EXCHANGE WINTER 2013

based on the prior empirical analysis. The results suggest a potentially high level of information in the ETF market price, particularly in volatile or dislocated markets.

PRICE DISCOVERY IN THE OTC BOND MARKET

Price transparency and trade frequency both create challenges to price discovery in the bond market. In gen-eral, not all bonds trade on a given day (Exhibit 1). For example, within the iBoxx $ Liquid Investment Grade Index, an index of U.S. dollar-denominated investment-grade corporate bonds, fewer than 30% of the index constituents traded at least 20 days in a given month, on average, during the 12 months ending September 2011 (according to TRACE data for trades of $100,000 or greater). Similarly, within the iBoxx $ Liquid High Yield Index, an index of speculative-grade U.S. dollar-denominated corporate bonds, fewer than 10% of index constituents traded at least 20 days in a given month (according to TRACE data for trades of $100,000 or greater), on average, during the same period.2

An individual bond’s trading behavior can be driven by the OTC market’s lack of pricing transparency. In the presence of perceived information asymmetry, market makers may display wider bid/offer spreads. Other struc-

tural factors may also affect liquidity, including an issue’s available f loat (how much of an issue is outstanding and how much of it is owned by hold-to-maturity investors), issue structure (any unusual coupon or call features), and whether an issue fits current patterns of investor demand.

During periods of more extreme market volatility and disruption, secondary trading in the OTC bond market can become significantly impaired. Exhibit 2 illus-trates average daily volume in the corporate bond market during 2008 versus the Barclays Capital liquidity cost score (LCS) for the Barclays U.S. Corporate Investment Grade Index.3 As the chart shows, volume fell sharply in the second half of the year, and spreads widened signifi-cantly as the credit crisis escalated and dealers and clients alike faced severe liquidity and capital constraints.

Discontinuous bond market liquidity leads to degraded price discovery. If bonds are trading thinly in a given sector or index, it may be much more challenging to estimate a price for securities that did not trade and to derive conclusions on the overall value and direction of that sector or index.

There are a number of fixed-income valuation ser-vices that provide daily prices on virtually every out-standing bond in the market. Index providers and asset managers use these prices to generate index and fund

valuations. These services take actual trade information (where it exists) and apply algorithmic or matrix approaches to estimate prices for securities that have not traded recently. Estimates might be based on similar securities’ execution prices, movements in market interest rates (such as U.S. Treasuries and LIBOR), observed credit-spread changes, and changes in the valuation of derivatives (such as credit default swaps). Market participants may not be able to buy or sell at the resulting esti-mated prices, as a security’s true action-able price cannot, by definition, be fully determined without a transaction. As a result, estimation methods may produce prices that exhibit smoothed behavior and may sometimes lag the behavior of more-liquid securities during fast-moving or dislocated markets.4

E X H I B I T 1Constituent Trading Volume for Investment-Grade and High-Yield Indices

iBoxx $ Liquid Investment Grade and High Yield Indices Average Number of Days Bonds Traded (12 months ending September 2011).

Source: TRACE and BlackRock, 9/10-9/11.



We can see this phenomenon in the behavior of index returns over different observation frequencies. Exhibit 3 shows the return volatility of a number of different indices (U.S. equities, U.S. Treasuries, invest-ment-grade corporates, high-yield corporates, and municipal bonds) over different observation intervals (daily, weekly, and monthly) from September 30, 2008 through September 30, 2011.

For investment-grade, high-yield, and municipal securities, return volatilities are smallest when measured by daily observations. This pattern is similar to what we see in smoothed processes.5 Indices based on less-liquid, less-transparent markets, such as those for high-yield and municipal securities, may be slower to ref lect market price information and so may appear to lag more active and liquid securities in volatile markets.

Without actionable trades, individual bond prices may remain unchanged or update more gradually over a number of trading days, until an actual trade clarifies value. As a result, changes in bond valuations and index levels may not show up well on daily measurements, but may become more apparent in weekly or monthly measurements. More liquid, more transparent markets (large-cap U.S. equities and U.S. Treasuries) have mixed patterns that exhibit higher daily volatility and lower weekly and/or monthly volatility. This intuitively makes sense, as price discovery is relatively more efficient in these markets.

As a contrast, Exhibit 4 shows the market price-based return volatility of fixed-income ETFs that correspond with the fixed-income indices listed above.

For all but municipal bonds, volatil-ities are relatively more consistent across observation frequencies, indicating that there is no smoothing process in the return series’ behavior. Volatilities between the index and ETF are most consistent for 20+ Treasuries—not surprising given the relative transparency and liquidity of the market for U.S. Treasury securities.

IMPLICATIONS FOR INVESTORS

Opacity and illiquidity in the OTC bond market can impede price discovery

and create information-transfer frictions. Investors who measure performance relative to a particular benchmark may not really know whether they are under- or out-performing the market, because the benchmark may not ref lect information in a timely manner. Likewise, if only the most liquid securities ref lect market information,

E X H I B I T 2Corporate Bond Liquidity—Average Daily Volume and Liquidity Cost Score

Source: Federal Reserve Bank of New York, Barclays Capital, and BlackRock.

E X H I B I T 3Annualized Index Return Volatility

Source: Markit iBoxx, Barclays Capital, Standard & Poor’s, and Black-Rock, 9/30/08–9/30/11.

E X H I B I T 4Annualized ETF Return Volatility

Source: Bloomberg and BlackRock, 9/30/08–9/30/11.



investors get an incomplete picture of price evolution across a given market, which can lead to incompletely informed investment decisions.

Because equities and fixed-income securities have such different market structures, we might wonder how the OTC bond market would behave if it were valued in a more liquid environment with continuous trading, such as an exchange. Would we see enhanced liquidity and price transparency? Could we observe two-way markets? If so, would bid/offer spreads narrow relative to the OTC market?

We can indirectly address many of these questions by observing the behavior of fixed-income ETFs: port-folios of OTC bonds that trade intraday on an equity exchange. We examine bond price behavior in both the OTC and exchange markets to discover how much OTC price discovery is currently impaired. We also look at fixed-income ETF price behavior to determine whether this may be a guide to future price evolution in the underlying OTC bond market.

FIXED-INCOME EXCHANGE TRADED FUNDS

Fixed-income ETFs are typically 1940 Act open-end fund structures that trade intra-day on an equity exchange. An ETF’s market price depends on the actionable value of the fund’s underlying OTC fixed-income securities, and on the balance between supply of and demand for ETF shares. Authorized market participants can exchange ETF shares for the underlying fund holdings, generally keeping the ETF price in line with the actionable value of the bonds the fund holds.

For example, when an ETF is overvalued relative to its underlying portfolio, new fund shares are typically created. An undervaluation typically leads to fund share redemptions. This arbitrage activity, implemented either through creating and redeeming shares or through rela-tive value trading of the ETF versus correlated securi-ties, generally prevents prolonged dislocations between an ETF’s value and that of its underlying bond port-folio.6 Once fixed-income ETFs reach a critical mass of exchange liquidity, they often become more liquid and offer more trading efficiency than their underlying OTC bond portfolio.

Index-based fixed-income ETFs are passive funds, designed to track a specific fixed-income index, such as the Barclays U.S. Aggregate Bond Index. Throughout the rest of this paper, the term “fixed-income ETFs” will

refer specifically to unlevered, index-based, fixed-income ETFs. Because fixed-income ETFs are essentially bond portfolios that trade intraday in a continuous-trading environment, their behavior can provide information on the valuation of the fund’s bond portfolio. As the entire portfolio trades on the exchange, so do the indi-vidual bonds that comprise that portfolio, even though the individual bonds may not trade actively in the under-lying OTC bond market. The OTC valuation estimate may differ, sometimes significantly, from the bond price implied by the ETF portfolio’s exchange value. Can we determine the correct price?

One view holds that the “correct” price is the price at which a trade actually occurs, not the estimated price. Fixed-income ETFs trade throughout the day, so they offer a fairly continuous implied exchange price for all portfolio holdings. ETFs must be large and liquid enough to offer any significant information; asymmetric trading f lows can distort information from smaller, illiquid ETFs. In liquid, well-functioning fixed-income ETFs, the arbitrage function generally prevents ETF prices from persistently diverging from the underlying bond portfolio’s value.

In the following section, we examine fixed-in-come ETFs’ trading behavior and analyze the informa-tion content they may provide about the underlying bond market.

VALUATION AND TRADING BEHAVIOR OF FIXED-INCOME ETFS

In order to understand the price discovery features of fixed-income ETFs, we should ideally compare their behavior to the appropriate fixed-income indices that they are designed to track, as a proxy for the underlying cash bond market. But this analysis would introduce a number of factors (including fund income distributions, management fees, and differences in bond composition between an ETF and a market index) that could obscure the relationships we are trying to measure. In order to adjust for these differences, we will instead use the ETF net asset value as a proxy for the market index.7

Fixed-income index valuations and fund NAVs, including both mutual funds and ETFs, are typi-cally calculated using bid-side pricing for the under-lying bonds. These prices are generally sourced from a pricing provider and include observed execution levels,



as well as estimates derived from algorithmic or matrix methods.

The index level (or NAV) is simply the arithmetic, market-weighted average of individual bid-side bond prices. In the U.S. fixed-income markets, these prices are usually captured as of 3:00 p.m. Eastern time, which is widely viewed as the bond market close, even though fixed-income securities can continue to trade after 3:00.

Fixed-income ETFs are exchange-traded instru-ments, so their official closing prices are calculated as of 4:00 p.m., the equity market close. This can lead to some peculiar observations in more-liquid bond mar-kets. U.S. Treasuries and other liquid bonds can be quite active after 3:00 p.m. A U.S. Treasury ETF that stops trading at 4:00 p.m. will capture this additional price action. This timing difference can mean a difference between a closing ETF market price and its index value. To adjust for this effect, we use 3:00 p.m. market prices in analyzing ETF behavior.

Fixed-income ETFs trade on an exchange at market clearing prices that can, and often do, differ from NAVs (Petajisto [2011]). Fixed-income ETFs that experience buying pressure and inf lows should trade at a premium (i.e., closer to the offer side of the underlying bond market), as a sufficient level of ETF demand means the potential creation of new fund shares.

In creating new fund shares, authorized participants source bonds, likely closer to the offer side of the under-lying market. The ETF price ref lects the bid/offer trans-action spread incurred in the underlying bond market as a premium to the NAV, as the NAV calculation is based on bid-side prices. Conversely, fixed-income ETFs that experience selling pressure and/or outf lows should trade closer to NAV (i.e., the bid side of the underlying market).

Under most market conditions, f ixed-income ETFs trade at a premium to their NAV. The premium is a function of the balance between buy and sell activity on the exchange and the bid/offer spread of the under-lying bond market.

In dislocated, volatile markets, the underlying bond portfolio’s arithmetic-weighted-average bid-side price, represented by NAV, may not correspond to the action-able price for the entire portfolio (i.e., the risk-adjusted price for a large number of bonds, based on liquidity and volatility conditions). The difference between the cal-culated NAV and the actionable portfolio price explains why a fixed-income ETF may trade at a discount to the

NAV or at a premium beyond the underlying bond port-folio’s offer-side price.8 Such trading behavior in ETFs was pronounced during the 2008 financial crisis across all f ixed-income sectors and, more recently, during dislocations in the municipal market (November 2010 through January 2011) and the credit market (August and September 2011).

Because of these premiums and discounts to NAV, many market participants erroneously conclude that fixed-income ETFs are not functioning properly. Most critiques of fixed-income ETFs rely on one central premise: that bond prices generated by pricing providers are the bond market’s most accurate representation of actionable liquidity. In the sections that follow, we dem-onstrate that the market price of an established fixed-income ETF and its benchmark (as proxied by the NAV) are cointegrated, and that the ETF’s market price can often lead price movements in the underlying bond market, as represented by the NAV or benchmark.9

PRICE DISCOVERY PROPERTIES OF FIXED-INCOME ETFS

As discussed in the previous section, the market price of a fixed-income ETF can often diverge from its fund’s index value or NAV. Exhibit 5 illustrates the total returns of AGG, a $13 billion index ETF benchmarked to the Barclays U.S. Aggregate Bond Index.

Over shorter timeframes, the NAV-based total return and market price-based total return differ, as market price movements may not coincide perfectly with NAV movements. Over longer time frames, the market

E X H I B I T 5AGG Total Returns

Source: BlackRock, as of September 30, 2011. Inception date for AGG is September 22, 2003.



price and NAV-based total returns converge. This is ini-tial evidence of a cointegrated relationship, one in which two time series may diverge in the short term and con-verge over longer time periods. Exhibit 6, which depicts AGG’s price and NAV relationship, illustrates this effect. Short-term choppiness can occur in the relationship, but the longer-term directional relationship is evident.

An ETF’s long-term price/NAV relationship is governed by arbitrage relationships between the ETF and the underlying basket. In order to properly evaluate the fixed-income ETF price/NAV relationship’s longer-term behavior, we must test a sample set of sufficiently

liquid ETFs. Smaller, less-liquid ETFs can incur greater price/NAV volatility, as arbitrage trades are potentially more challenging to execute when anomalous behavior occurs. Exhibit 7 depicts eight established, fixed-income ETFs that have higher assets under management and experience relatively high average daily dollar trading volumes within their respective sectors.

We can use established statistical procedures to test whether a particular fixed-income ETF has a cointe-grated relationship between its market price and NAV. Exhibit 8 illustrates the results of one such procedure,10 performed using log levels-based regressions over a three-year period (September 2008 to September 2011) on the daily market price/NAV relationships of the fixed-income ETFs highlighted above. The regression has the form of:

LN PXPPt tPXPP( )NAVtVV ( (LNLLLNLL )) +β ε (1)

where, LN(NAV

t) is the natural log of the NAV level at

time t α is the intercept term (a function of the fund premium/discount) LN(PX

t) is the natural log of the market price level

at time tβ is the cointegration coefficientε is the error term

For reference, we include the regressions’ cointe-gration coefficients and standard errors.11

The results strongly suggest the presence of a cointegrated relationship between the market prices and NAVs of the selected fixed-income ETFs, despite any

short-term (e.g., daily) dislocations. We can expect short-term dislocations between price and NAV to correct through time.

Is the cointegrated relationship between f ixed-income ETF price and NAV levels the result of the ETF leading the NAV or the reverse? To make this determination, we examine regressions of coincident NAV returns versus various lags in market price returns, and vice versa.

As an example, consider HYG. Exhibit 9 details the results of coincident NAV returns versus three days of lagged price returns and coincident price returns

E X H I B I T 6AGG Market Price vs. NAV

Source: Bloomberg, September 30, 2008 to September 30, 2011.

E X H I B I T 7Select Fixed-Income ETFs

Source: Bloomberg and BlackRock, as of Q3 2011.



versus three days of lagged NAV returns. Exhibits A1 and A2 in the Appendix detail the coefficients and t-sta-tistics for coincident and multiple lagged returns for each candidate fund.

The NAV return versus lagged price return regres-sion gives us a relatively high adjusted R-square and significant test statistics for the lagged price-return vari-ables. The converse price regression returns versus lagged NAV returns gives us a low adjusted R-square measure and statistical significance on only the first lagged NAV return variable. This suggests that lagged price returns have a statistically significant impact on coincident NAV returns, rather than the converse. Note, however, that tests for Granger causality proved inconclusive.12

We then investigate the degree to which the ETF market price may provide information about future NAV and index returns. To answer this question, we expand the methodology already described and regress coincident NAV returns against coincident and five days of lagged market price returns. The regression has the form of:

NAVrNN etrr PXretrrt i t ii

n

= +=∑∑βα + ∑ ε

0

(2)

where,NAVret

t is the coincident NAV return

α is the intercept (approximately zero)βι is the market price return coefficient for lag i PXret

t-i is the market price return associated with

lag iε is the error term

As an example, using market price and NAV data for HYG from September 30, 2008 through September 30, 2011, we observe the following relationships in Exhibit 10:

The f itted relationship illustrates that 16.9% of the coincident price return is ref lected in the coincident NAV return, 15.2% of the prior day’s ETF price return is ref lected in the coincident NAV return, and so on. The individual test statistics for the lagged price variables are highly significant and generally decrease in magnitude rela-tive to the lag. This observed relationship is intuitive, as the most recent ETF price returns have the largest impact on NAV,

while the further lagged returns have the least impact. A relationship in which the ETF market price leads index values and NAVs implies that a f ixed-income ETF’s market price contains information about the underlying bond market’s level and path.

If there is a cointegrated relationship between a f ixed-income ETF’s market price and index value/NAV, and the ETF market price tends to lead move-ments in index values and NAV, how long might it take for index values/NAVs and ETF market prices to con-verge? By examining the serial correlations of residuals from levels-based regressions performed on the market price and NAV of each candidate ETF (Exhibit 8), we determine the half-life of price/NAV convergence for each fund: the time it takes to close half the distance between any abnormal divergence between market price and NAV. (Recall that there can and should exist some difference between market price and NAV due

E X H I B I T 8Test for Cointegration of Market Price and NAV

Source: NYSE ARCA TAQ, Bloomberg and BlackRock, September 30, 2008 through September 30, 2011.

E X H I B I T 9HYG Price vs. NAV Regressions




to bid/offer spreads in the underlying bond market, short-term ETF supply/demand imbalances, execution risk, and so on).

The time that it takes for an ETF market price and NAV to revert to a long-term relationship is a func-tion not only of underlying market liquidity but also of the creation/redemption mechanism. As discussed, some ETFs employ an in-kind exchange for physical mechanism,13 exchanging ETF shares for a basket of underlying bonds. For ETFs that employ an exchange for physical creation/redemption mechanism, half-life values can be a ref lection of transparency in the under-lying market. In less-liquid markets, it may take longer for an abnormal divergence in the market prices of an

ETF and NAV to reconcile. Because less-liquid markets often lack daily trading, individual bond prices are slow to update, and it may take longer to close any apparent arbitrage opportunity that does arise.

Alternatively, an ETF may employ a traditional mutual fund creation and/or redemption mechanism, exchanging cash directly for shares rather than for the underlying securities. In theory, a cash creation/redemp-tion mechanism would allow for a more rapid adjustment of price/NAV divergence, as a market participant would be able to quickly create or redeem shares and act on a market dislocation without the burden of the underlying OTC bond execution. The inherent tradeoff is that the burden of the trade execution falls on the ETF fund man-ager (as opposed to authorized participants in the in-kind exchange for physical process). Fund performance may suffer due to cash drag and the internalization of trading costs. Liquidity and trading conditions in the underlying market are no longer ref lected in the ETF’s market price, as they would be in a pure exchange for physical transac-tion. Instead, the fund internalizes them and eventually ref lects them in the NAV performance, albeit in a slower, more diffuse fashion.

Exhibit 11 shows the results of half-life calcula-tions across the sample ETFs. We examined three years of data to compare behaviors during the financial crisis and the years following.

Broadly speaking, ETFs that track more-liquid markets (U.S. Treasuries and investment-grade credit) tend to have shorter half-lives than those that track less-

liquid markets (municipals and high yield). However, periods of elevated volatility and market dislocation, such as the 2008–2009 financial crisis and the 2010 municipal market selloff, can cause aberrations.

As an example, LQD, an invest-ment-grade credit ETF, appears to exhibit some unexpected behavior in 2008–2009. Its half-life is longer than that of any other sample ETF. We would expect an ETF that tracks the investment-grade credit market to be more efficient than an ETF that tracks the municipal or high-yield markets, given the relative transparency of the investment-grade market. The sig-

E X H I B I T 1 0HYG NAV Returns vs. Lagged Market Price Returns

E X H I B I T 1 1Half-Life (Days) Convergence Between Market Price and NAV


Source: BlackRock.



nificant elevation in LQD’s half-life during the 2008–2009 financial crisis is likely a function of the impaired liquidity that existed in the underlying bond market during that time, and of the fund’s exposure to financials, which were particularly dislocated during the crisis14. Indeed, by the third sample period (September 30, 2008 through Sep-tember 30, 2011), LQD had reverted to a shorter half-life than any of the remaining ETFs, with the exception of TLT (the long-duration Treasury ETF).

Municipal ETFs’ behavior also illustrates the effects of market dislocations. The half-lives of MUB and SHM fell noticeably in 2010, following the financial crisis. However, the municipal dislocation of late 2010 through early 2011 caused the half-lives to widen again, as liquidity in the municipal market became severely impaired.

Interestingly, ETF trading volume may increase significantly during market dislocations. As an example, LQD average daily volume increased from roughly $20 million (August 2008) to a single-day peak of $270 mil-lion during September 2008; MUB average daily volume increased from roughly $12 million (October 2010) to a single-day peak of $128 million during November 2010. ETFs allowed for market-clearing prices while the underlying market liquidity remained impaired during these periods—hence the time extension for the market price and NAV to converge.

The half-life of TLT, a 20+ year U.S. Treasury ETF, was quite small (less than one day), ref lecting the high level of information symmetry between the ETF and the underlying market.

MARKET SIGNAL AND TRADING IMPLICATIONS

The presence of a cointegrated relationship between NAV and market prices in fixed-income ETFs suggests that ETF price behavior contains information about future index and NAV behavior. Potential relative-value trading opportunities between an ETF and its under-lying basket (or other correlated securities) may exist, especially given the leading relationship between ETF market price and NAV and index values. The behavior of an established, fixed-income ETF could serve as a signal for price evolution in the underlying OTC cash market.

To identify temporary dislocations between the ETF market price and net asset values, we can determine a fair value for NAV returns and then measure actual NAV changes against that fair value. A simple error-correction model for NAV-based total returns may be developed from a time series of ETF market price and NAV levels.

To determine the error correction term, we rear-range the levels model used to test for the presence of a cointegrated relationship:

ε βLN α β− PXPPt tα βα β PXPP( )NAVt ( (LNLLLNLL )) (3)

We incorporate the one period lagged error term from Equation (3) into Equation (4).

NAVrNN etrr PXt t t= +PX t +γ+PXretrr ε μt +−2t γtPXretr +PXretrr tPXretr 1 (4)

where,NAVret

(t) is the coincident ETF NAV return

γ1 is the coincident price-return coefficient

PXret(t) is the coincident ETF price return

γ2 is the lagged error term coefficient

ε(t-1)

is the residual or error term from the prior day’s levels-based regression fit, as determined by Equation (3)μ is the residual value for Equation (4)

The error correction model incorporates both long-term information via the price level versus NAV level, as captured by Equation (3), as well as shorter-term information via the daily return and error correction, as captured by Equation (4). As an example, using data from September 2008 through September 2011, we fit the two models to HYG’s trading behavior:

Equation (3):

LN − + PXPPt t+ PXPP( )NAVtVV (− (LNLLLNLL ))31 1

Equation (4):

Δ Δt t t tLΔ NLLNL, ,t t ( )PXPP ) . (− −LΔ NL )PXP )1 1t tΔt t1 N t( )N V ( −t t( ) ( 177 ε 11) + μ

For reference, the parameters for Equation (3) and (4) of each sample fund are provided in Exhibit 12.



CASE STUDY: HYG

We test this methodology using recent market data. Specifically, we examine HYG’s market price and NAV behavior beginning August 5, 2011, the Friday before S&P downgraded U.S. sovereign debt. Risk markets had been selling off since the end of July; this sell-off accelerated sharply with the downgrade. Exhibit 13 illustrates predicted and actual NAV returns, based on Equations (3) and (4).

As of the 3:00 p.m. market close on August 5, 2011, HYG traded at a 1.41% discount to NAV, based on a market price of $86.69 and a NAV of $87.93. Liquidity in the underlying cash bond market was impaired, sug-gesting that HYG’s exchange-market price may have ref lected information that was not yet incorporated in the underlying bond market (as proxied by the NAV). Using Equation (3), we may calculate a residual, ε, of:

ε = − + =LN LN( . ) (− .+. ( . )) .93 0 317 1 069 69 0 023

The fact that ε differs significantly from zero (based on the standard error 0.0175 in Equation (3)) suggests that

the differential between the market price and NAV is too high relative to the model prediction, indicating that a correction is likely. We use the value of ε as an input for Equation (4) to predict the NAV return on the following trading day, based on that day’s market price return. On the following Monday, August 8, 2011, HYG’s market price closed at 82.84. The day’s predicted NAV return would therefore be:

t t LN LNLL, ( )NAV . ( ( . ) (LNLL . ))− LNL

−1 0 8484 86

0 1.17711 023 23( .0 ) .1 %μ

The NAV declined from $87.93 to $86.34, giving an actual NAV return of -1.82% and a relatively small forecast error of -0.59%.

Forecast errors over the remaining series were fairly noisy and some were quite large. There are a number of potential reasons for this. Daily returns are fairly vola-tile in general and are subject to a high degree of noise. Other factors also drive the price-to-NAV relationship (the underlying market’s bid/offer spread, the ETF’s f low

balance, and the level of risk adjustment ref lected in the market price), which may obscure the relationship changes that are due purely to information convergence.

MEASURING AND VALUING INFORMATION CONTENT

To quantify the value of the informa-tion that may exist in a fixed-income ETF’s market price behavior, we develop and test

E X H I B I T 1 2Regression Parameters for Error-Correction Model

Source: NYSE ARCA TAQ, Bloomberg, and BlackRock, 9/30/08–9/30/11.

E X H I B I T 1 3Error-Correction Model Predicted vs. Actual NAV Returns for HYG

Source: NYSE, ARCA TAQ, Bloomberg, BlackRock.



a hypothetical trading strategy. We will hold long posi-tions in the ETF and short positions in the underlying market, as proxied by the corresponding index or NAV, any time the ETF price looks significantly cheap to NAV. We will execute the reverse trade when the ETF’s price appears expensive relative to the NAV.

As a threshold for identifying a trading opportu-nity, we compare the absolute value of the residual value given by Equation (3) with a threshold equal to two times the level of the standard error of the Equation (3) regression fits described in Exhibit 12. We use a high threshold to best isolate truly anomalous behavior. We reverse implemented trades once the dislocation falls back below the threshold.

As of the bond market close on September 30, 2008, the NAV of HYG was $84.13; the market price was $81.65. Inserting these values into Equation (3) gives a residual value of 0.044, which is more than two times the standard error of Equation (3) (0.0175). As HYG’s market price appears signif icantly discounted to the NAV (and therefore the under-lying bond portfolio), we initiate a long position in HYG at the market price of $81.65 and a short position in the NAV at $84.13. The following day, HYG’s market price and NAV were $84.07 and $82.44, respectively, as of 3 p.m. Equa-tion (3) gives a residual value of -0.0075, which is well within the standard error. Accordingly, we terminate the position for a net return of 4.97%, excluding any transaction costs.15

To assess the amount of informa-tion in different markets, we examine HYG, JNK, MUB, SHM, LQD, and TLT (high yield, municipals, investment-grade credit, and U.S. Treasuries).

Exhibit 14 shows the results of $100 invested in the trading strategy (assuming daily rebalancing) using the price of the ETF and the NAV of its underlying bond portfolio from September 30, 2008 to September 30, 2011.16 Exhibit 15 shows the strategy’s key summary statistics.

As Exhibits 14 and 15 illustrate, such a strategy (were it to be actionable)

could have generated significant returns over the three-year period, particularly during the peak of the financial crisis (the fourth quarter of 2008) and the immediate aftermath (the first half of 2009). Other periods of dis-location also resulted in strong strategy performance, including the Flash Crash (May 2010), the municipal market sell-off (November 2010 through January 2011), and the intensification of fiscal pressure in the U.S. and eurozone (August and September 2011). The return pattern is also intuitive, in that the most information seems to reside in high yield, followed by municipals, investment-grade credit, and U.S. Treasuries. During the latter half of 2009 and the majority of 2010, we saw

E X H I B I T 1 4Trading Strategy Cumulative Profit and Loss of $100 Investment

Source: NYSE, ARCA TAQ, Bloomberg, BlackRock, 9/30/08–9/30/11.

E X H I B I T 1 5Trading Strategy Statistics Summary

Source: NYSE, ARCA TAQ, Bloomberg, BlackRock, September 30, 2008 through September 30, 2011.



lower market volatility that resulted in a relatively stable price to NAV relationship and few opportunities for the trading strategy.

The back-test assumes that all transactions occur at 3 p.m. closing prices and ignores a number of important sources of friction, such as trading costs, which can be quite large in the municipal and high-yield markets. It’s not pos-sible to transact efficiently at fund NAV or index levels, as many individual bond prices are value estimates and may not be actionable, as we discussed previously. It would also be difficult to quickly and efficiently trade the underlying OTC bond portfolio which, in the MUB example, is com-prised of more than 1,500 municipal bonds. (The ability to trade such a portfolio as a basket is one of the benefits of the ETF itself.) Nonetheless, the exercise illustrates that the ETF market price contains information relative to esti-mates of the underlying market (based on NAV), and that it may be possible to use this information as the basis for a more realistic trading strategy.

CONCLUSIONS

The growth of the fixed-income ETF market has provided investors with a valuable new tool for under-standing and measuring movements in the OTC bond market. Price discovery creates challenges for investors of all sizes. By bringing the OTC market onto an exchange through the ETF structure, we can more readily observe the impact of new information on fixed-income markets. The presence of the creation/redemption mechanism, in which physical securities are exchanged for shares,

pairs with exchange liquidity to offer price informa-tion that’s ref lected more readily in ETF prices than in estimated prices of individual bonds that trade less fre-quently. Not only does the ETF price move in line with the bond market over time, it appears to absorb price information more rapidly. As a result, price movements in fixed-income ETFs can often lead price movements in individual bonds and market indices.

These developments may have powerful implica-tions for investors. First, an ETF may more quickly cap-ture and value changes in investor sentiment and so serve as a guide to price evolution in the underlying OTC market. For more opaque fixed-income sectors, true market price discovery and volatility may be observable for the first time, in the form of an exchange traded, cash bond–based instrument.

Second, these findings shed light on the misper-ception of ETF premiums and discounts. An apparent dislocation between ETF price and NAV may be the result not of ETF mispricing but of actual price dis-covery on the ETF’s part. This opens up a variety of applications, from hedging to asset allocation, including potential opportunities to capture differences in the speed of price discovery between ETFs and the OTC bond market and related instruments.

A P P E N D I X

See full disclaimers at: www.ishares.com/bondetfdisclosures.

E X H I B I T A 1NAV vs. Coincident and Lagged Price Returns

Source: BlackRock, September 30, 2008 through September 30, 2011.



ENDNOTES

1Madhavan and Hendershott [2011].2The iBoxx $ Liquid High Yield Index contains 144A

designated issues. The trading activity of such issues may not be fully captured in the TRACE data, thereby potentially understating the percentage of issues traded daily.

3The liquidity cost score is an estimation calculated by Barclays Capital that serves as a proxy measure for bid/offer spreads. See Dastidar and Phelps [2009].

4A similar phenomenon has been observed in hedge fund and private equity portfolios, as well as in real-estate appraisal values. See Getmansky, Lo, and Makarov [2004], Conner [2003], Case and Quigley [1991], and Geltner [1991].

5A cursory analysis of the behavior of the iBoxx $ Liquid HY Index, the iBoxx $ Liquid Investment Grade Index, and the S&P AMT-Free National Municipal Bond Index suggests the presence of potential autoregressive processes of varying orders. In general, conditions of serial correlation, heteroske-dasticity, and other violations of normality typical of financial time series may result in inconsistent measurements of vari-ance over different observation frequencies.

6Although market makers generally take advantage of differences between an ETF’s NAV and trading price through arbitrage opportunities, there is no guarantee that they will do so.

7The net asset value of the specified ETF ref lects all fund distributions and expenses, allowing for a more direct comparison to the ETF market price.

8For more detail on factors that drive fixed-income ETF premiums and discounts, see Tucker and Laipply [2010].

9Similar behavior has been observed between more-liquid instruments and their underlying holdings. For example, Hasbrouck [2003] observes such behavior between S&P 500 futures and the S&P 500 index.

10Using MATLAB, we performed the Engle-Granger test for cointegration on a daily series of NAV and market price values for each ETF to assess the null hypothesis of no cointegration among the time series.

11The expected cointegration coefficient value was 1.0. Actual differences from 1.0 may be attributable to limited sample size as well as to ETF premium/discount volatility.

12The Granger causality tests consist of comparing restricted and unrestricted regressions on coincident market price and NAV returns versus three trading days of lagged market price and NAV returns over the sample period Sep-tember 30, 2008 through September 30, 2011. The F-sta-tistic for the null hypothesis that price returns do not Granger cause NAV returns was 22.3, while the F-statistic for the null hypothesis that NAV returns do not Granger cause price returns was 25.8.

13As of the time of this writing, AGG, HYG, MUB, LQD, and TLT primarily employed an exchange for physical-based creation/redemption methodology. The specific cre-ation/redemption methodology primarily employed by the other ETFs in the sample was not known with certainty.

14According to www.iShares.com, LQD’s exposure to f inancials was approximately 42% as of September 30, 2008. As of September 30, 2011, LQD’s exposure to finan-cials was 35%. Note that in September 2008, the iBoxx $ Liquid Investment Grade Index was comprised of 100 equally weighted bonds. The index transitioned in mid-2009 to a broader market cap weighted index (see www.markit.com for details).

15The return on the ETF long was $84.07/$81.65 − 1 = 2.96%, while the return of the NAV bond portfolio short was –(82.44/84.13 − 1) = 2.01%. The net return was 2.96% + 2.01% = 4.97%. Based on the current market price return and the prior period error term, Equation (4) would suggest a NAV return of −0.27% versus the realized NAV return of −2.01%.

E X H I B I T A 2Price vs. Coincident and Lagged NAV Returns

Source: BlackRock, September 30, 2008 through September 30, 2011.



16Where possible, we adjust ETF market prices to coincide with early closes in the U.S. fixed-income markets (typically 2 p.m. on select dates). Because intraday NAVs are not directly observable, it was not possible to adjust for early closes in the U.S. equity markets (typically 1 p.m. on select dates). We believe that the small number of early equity closes (typically two per year) does not materially impact these results. (For more information on holiday schedules, see www.sifma.org for the bond market and www.nyse.com for the equity market.)

The limited sample size precludes robust out-of-sample testing. However, a cursory analysis that bifurcated the three-year time series into two years of sample data and one year of test data yielded similar results.

REFERENCES

The authors are grateful to Eric M. Neis for his input and invaluable technical advice. We also thank Ananth Mad-havan, Daniel S. Morillo, Christopher T. Downing, Michael Gates, Antti Petajisto, and Marcia Roitberg for their many contributions. Any errors or omissions are our own.

Case, B., and J.M. Quigley. “The Dynamics of Real Estate Prices.” The Review of Economics and Statistics, Vol. 73, No. 1 (1991), pp. 50-58.

Conner, A. “Asset Allocation Effects of Adjusting Alternative Assets for Stale Pricing.” The Journal of Alternative Investments, Vol. 6, No. 3 (2003), pp. 42-52.

Dastidar, S., and B. Phelps. “Introducing LCS: Liquidity Cost Scores for U.S. Credit Bonds.” Barclays Capital (October 6, 2009).

Geltner, D. “Smoothing in Appraisal-Based Returns.” Journal of Real Estate Finance and Economics, Vol. 4, No. 3 (1991), pp. 327-345.

Getmansky, M., A.W. Lo, and I. Makarov. “An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns.” Journal of Financial Economics, Vol. 74, No. 3 (2004), pp. 529-610.

Hasbrouck, J. “Intraday Price Formation in U.S. Equity Index Markets.” Journal of Finance, Vol. 58, No. 6 (2003), pp. 2375-2399.

Madhavan, A., and T. Hendershott. “Click or Call? Auction Versus Search in the Over-the-Counter Market.” Working paper, BlackRock, 2011.

Petajisto, A. “Inefficiencies in the Pricing of Exchange-Traded Funds.” Working paper, New York University, 2011.

Tucker, M., and S. Laipply. “Understanding Bond ETF Pre-miums and Discounts: A Conceptual Framework.” Journal of Indexes, September-October (2010), pp 40-48.

To order reprints of this article, please contact Dewey Palmieri at [email protected] or 212-224-3675.


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