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Arbitrage crashes:Slow-moving capital or market segmentation?∗
Jens Dick-NielsenCopenhagen Business School
Marco RossiUniversity of Notre Dame
Keywords: Convertible bonds; arbitrage crashes; market segmentation; slow moving capital.
JEL: G01; G12; G13.
∗Thanks to Lasse Heje Pedersen, Brian Henderson, Neil Pearson, Paul Schultz, and participants of theFDIC Conference (2011), Indiana State Finance Conference (2011), and the Copenhagen Business SchoolFRIC and Notre Dame seminars for their helpful comments. Special thanks to Sophie Shive for her precioushelp with an earlier version of this paper. Jens Dick-Nielsen gratefully acknowledges support from the Centerfor Financial Frictions (FRIC), grant no. DNRF102.
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Arbitrage crashes:Slow-moving capital or market segmentation?
Abstract
The predominant explanation for arbitrage crashes is a lack of investor capital to exploitmispricing. This paper shows that slow moving capital is only partially responsiblefor the 2005 and 2008 arbitrage crashes in the convertible bond market. Even whenconvertible bonds where underpriced, investors were still buying strictly dominatedstraight bonds from the same issuers. This finding suggests that market segmentationexaggerated the convertible arbitrage crashes. Furthermore, it is possible to exploit themarket segmentation with a long/short trading strategy providing positive abnormalreturns. The strategy is profitable even after accounting for transaction cost.
Keywords: Convertible bonds; arbitrage crashes; market segmentation; slow moving capital.
JEL: G01; G12; G13.
1 Introduction
The global convertible bond market represented approximately 500 billion dollars at the end
of 2011.1 Recent work has found that convertible bonds are attractively priced at issuance to
induce institutional investors and hedge funds to hold them (Choi, Getmansky, and Tookes,
2009; Choi, Getmansky, Henderson, and Tookes, 2010). Arbitrageurs purchase convertible
bonds and typically hedge the equity component of their value by shorting the firm’s stock
(Agarwal, Fung, Loon, and Naik, 2011; Brown, Grundy, Lewis, and Verwijmeren, 2012). As
long as these dedicated investors are not capital-constrained, convertible bonds trade quite
close to their fundamental value.2
Studying the dislocations of the market caused by the financial crisis, Mitchell and Pul-
vino (2012) show that between October 2008 and March 2009 the average yield of 65 busted
(trading at less than par) convertible bonds’ closing prices based on weekly dealer quotes
were below the prices implied by straight debt. Such large and persistent arbitrage opportu-
nities are often attributed to funding concerns and slow-moving capital (Mitchell, Pedersen,
and Pulvino, 2007; Duffie, 2010; Mitchell and Pulvino, 2012; Fleckenstein, Longstaff, and
Lustig, 2013). The main contribution of this paper is to clearly identify trading situations in
which the impact of funding liquidity is virtually absent and show that market segmentation
is an additional and aggravating source of arbitrage crashes.
Using intra-day transactions from July 2002 to December 2011, which are superior to
weekly quotes that may not be firm, we show that many convertible bonds trade at yields
that are significantly above those of comparable straight bonds for large portions of their
lives, implying the existence of negatively-priced equity call options. In particular, we find
that in about 7% of matched trades, convertible bonds were bought at yields that were
higher than those of comparable non-convertible bonds trading at the same time. In a
1Source: Credit Suisse.2Chan and Chen (2007) find that convertible bond underpricing relative to exercise value based on the
underlying stock price resolves within two years of issuance.
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cross-sectional analysis, we find that illiquidity and most bond characteristics only partially
explain the level and probability of mispricing. In general, mispricing is more prevalent if
the convertibility option is out of the money.
We posit that the severe underpricing of convertible bonds during arbitrage crashes is
exacerbated by the existence of different clienteles in the bond market for straight and con-
vertible bonds, as an example insurance companies did not change their buying behavior of
straight bonds during the crashes. Our analysis of the simultaneous purchases of convert-
ible and straight bonds of the same issuer effectively controls for credit risk and funding
problems, thus enabling us to better isolate the contribution of market segmentation. Even
in the presence of impediments to arbitrage, straight bond yields should be higher than
convertible bond yields because one can always sell the low-yielding straight bond to buy
the other bond. Also, investors should not have continued buying the straight bonds; they
should have bought the (otherwise identical) convertible bonds.
Our findings are different from the cheapness of convertible bonds documented by Mitchell
and Pulvino (2012), which they attribute to lack of capital. We show that convertible bonds
were not just cheap; they were a steal. In many cases, market participants forwent free equity
call options by purchasing straight bonds that were strictly dominated by their convertible
counterparts. Moreover, the breaking of the law of one price that we document cannot be
due to funding liquidity alone since the buyers of these straight bonds had already obtained
funding to buy them and could have used these funds to buy the mispriced convertible bonds
instead.
If two distinct clienteles are unable to exchange closely related securities, could a so-
phisticated investor with enough capital to meet margin requirements take advantage of the
underpricing of convertible bonds? To answer this question we match convertible bond trades
taking place at the ask with surrounding non-convertible bond trades at the bid. We verify
that a positive difference exists for many trades and implement a trading strategy that uses
this positive yield spread as a signal for starting long-short positions. We close the positions
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if the yield/prices converge, which can happen in three ways. First, the convertible bid yield
goes below the non-convertible ask yield, thus fully accounting for round-trip transaction
costs. Second, the bonds mature. Third, the issuer files for bankruptcy.
It could be argued that this long-short strategy is not feasible because of capital require-
ments. We note, however, that an investor holding a comparable straight bond would need
no additional capital since she would sell the existing bond and use the proceeds to buy the
underpriced convertible bond. Moreover, the combined long-short position would not incur
margin calls if cross-margining was allowed. The position only requires small injections of
capital to cover the difference in the accrued interest received on the convertible bond and
the interest paid on the straight bond since straight bonds tend to have larger coupons.
Our trading strategy is profitable, generating unconditional and risk-adjusted returns of
more than 1% on a monthly basis. We obtain abnormal returns by regressing the monthly
returns generated by the strategy on the three factors proposed by Fama and French (1992)
and the momentum factor (Carhart, 1997). Since our strategy fully accounts for bid-ask
spreads, the reported alpha is not inflated by transaction costs.
Various limits to arbitrage could explain the mispricing and the profit opportunities that
we identify. Shleifer and Vishny (1997) attribute limits to arbitrage to the principal-agent
problem between the providers of equity capital (principal) and the dedicated arbitrageurs
(agents) who are supposed to take advantage of mispricings. In the presence of fundamental
risk, investors cannot perfectly distinguish temporary negative returns associated with arbi-
trage opportunities from lack of skill of the arbitrageur and, as a result, may fail to provide
capital. Liu and Mello (2011) argue that fragile capital structures, coupled with risk of early
redemptions from nervous investors, prevent dedicated arbitrageurs (i.e. hedge funds) from
fully deploying the cash needed to correct price deviations from fundamentals.
More closely related to the current study, failure of convertible arbitrage hedge funds to
raise and allocate capital to take advantage of convertible bonds trading at fire sale prices
resulted in long periods of depressed bond valuations. In fact, these hedge funds faced
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large redemptions from capital investors that further depressed convertible bond valuations,
especially the valuations of those bonds held by the more capital constrained single strategy
funds (Mitchell, Pedersen, and Pulvino, 2007). These large price discrepancies are finally
resolved once new capital (Duffie, 2010) or new natural “liquid” investors (Duffie, Garleanu,
and Pedersen, 2007) become available to fund the appropriate arbitrage strategies.
While limits to arbitrage did play an important role in the convertible arbitrage crashes,
our findings bring new complexity to the existing explanations. The fact that convertible
bonds were trading at yields that were higher than those of comparable straight bonds par-
tially rules out the slow-moving capital explanation; the capital was already there. Moreover,
if convertible bond prices decline enough, straight bond investors can be seen as the new
natural convertible bond investors. But these investors failed to realize their new potential
role and used their funds to buy strictly dominated securities.
Overall our findings indicate that the mix of explanations for the dislocations of the
convertible bond market should include a strong segmentation within the corporate bond
market. This segmentation might be due to very inattentive straight bond investors,3 reg-
ulatory impediments, or to the perverse effects of existing marking-to-market rules that do
not allow a busted convertible bond holder to disregard the conversion option part of the
security and use comparable straight-bond prices for accounting purpose. We provide evi-
dence that some trading did shift from the straight-bond segment of the market toward the
convertible bond segment, thus partially refuting the lack of attention explanation. Finally,
regulatory impediments also seem unlikely to be driving convertible bond mispricings since
haircuts and insurance companies’ capital requirements are the same for both straight and
busted convertible bonds.
Our paper is related to other work which has found persistent arbitrage opportunities in
the fixed income market. For example, Fleckenstein, Longstaff, and Lustig (2013) find that
3This hypotheses is also consistent with the investor recognition hypothesis of Merton (1987). Facingincomplete information on security characteristics, investors only hold securities whose risk and returnscharacteristics with which they are familiar.
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TIPS tend to be very cheap relative to treasury bonds and that an arbitrage opportunity ex-
ists. They find that the mispricing is related to availability of collateral and to treasury debt
issuance. Mitchell and Pulvino (2012) and Duffie (2010) show that arbitrage opportunities
exist between corporate bonds and credit default swaps. Bai and Collin-Dufresne (2011)
study the cross-sectional determinants of the (negative) CDS-Bond basis, which signal these
arbitrage opportunities. Finally, looking at three comparable bonds of RJR Nabisco Hold-
ings Corporation, Dammon, Dunn, and Spatt (1993) documented substantial underpricing
in the slightly more complex bond that lasted for more than two years. Our findings also
suggest a discount for complexity.
2 Data
The bond trading data used in this study is from the enhanced TRACE database. Maintained
by FINRA, the Financial Industry Regulatory Authority, TRACE reports real-time over-the-
counter (OTC) corporate bond trades. TRACE was introduced in July of 2002. Variables
reported include date, time of execution, price, yield, volume, and whether the reported
transaction represents a customer buy, sell, or inter-dealer trade. TRACE provides data on
OTC trades on more than 99% of the US corporate bond market.
The bond characteristics are from Mergent Fixed Income Securities Database (FISD),
which provides detailed information, at issuance and ongoing, and covers more than 140,000
corporate, U.S. agency and U.S. treasury debt. Mergent provides issuing and maturity dates,
coupon rates, and characteristics of the bond contract.
Although TRACE reports both price and yields for every transaction, approximately
10% of the the yields is missing. Moreover, the yields reported are not yields to maturity.
To make appropriate comparisons, we compute the yields to maturity of both convertible
bonds and straight bonds. We verify that the yield to maturity are often identical to the
yield to worst (between maturity and call date) reported in TRACE.
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2.1 The sample
Using FISD, we collect bonds from firms that have at least one straight bond (medium term
notes or corporate debentures) and one convertible bond outstanding during the sample
period. This sample period ranges from July 2002 to December 2011. We exclude 144A
bonds and floating rate bonds and bonds with less than $1,000,000 initial offering amount.
We also require that the convertible bond is at least as senior as the straight bond. We
match this sample of bonds by 9-letter cusip with TRACE data.
Table 1 presents bond characteristics for the bonds that form the starting sample of this
study. To obtain this sample, we select all TRACE-eligible bonds that are also in FISD. For
each convertible bond, we look for a match among the straight bonds of the same issuer with
similar time to maturity, and equal or worse seniority. Bonds have similar maturity if their
maturity dates are less than one year apart if the closest maturity date is before December
2012, or less than two years otherwise. We allow straight bonds to have worse seniority than
convertible bonds because straight bond yields should be even higher in this case.
As can be seen from Table 1, the issue size of the matched bonds is quite similar. The
median issue size is well over $300,000,000 for each category. On average the convertible
bond coupon rate is half the straight bonds’ coupon rate, which is to be expected given
that convertible bonds have a valuable embedded option. By and large, the bonds in the
sample tend to be senior unsecured. The proportion of callable bonds is higher among non-
convertible bonds, which should make violations much harder to find, given that callability
generally increases yields. Putability, which makes bonds more expensive, is extremely
rare among non-convertible bonds, but not among convertible bonds, which also makes
violations much harder to detect. Finally, we notice that about ten percent of the bonds
have experienced bankruptcy at some point during their life. We make sure that we do not
compare yields to maturity after the issuer has filed for bankruptcy, since the conversion
option becomes worthless.
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2.2 Construction of Yield Spreads
We clean the TRACE data following Dick-Nielsen (2009). Even after removing cancelled
trades and revising modified ones, graphical inspection of the data reveals the presence of
outliers which manifest themselves as large price reversals. Removing price reversals of 20%
(see, e.g., Bessembinder, Kahle, Maxwell, and Xu (2009)) is often insufficient to eliminate
outliers. Therefore, we further filter the data using the methodology of Rossi (2010). The
filter requires bond prices to satisfy the following condition for inclusion:
|p−med(p, k)| ≤ 5 ∗MAD(p, k) + g, (1)
where g is a granularity parameter which we set equal to $1, and med(p, k), and MAD(p, k)
are respectively the centered rolling median, and median absolute deviations of the price p
using k observations (we set k = 20).
We would like to test whether convertible bonds are priced below comparable straight
bonds, thus at yields higher than comparable straight bonds. However, Edwards, Harris, and
Piwowar (2007) show that transaction costs for bonds can vary greatly and, since we have
trade prices which embed bid-ask spreads, we do not want transaction costs to contaminate
our results. Thus we compare only bond purchases in the main analysis of the paper. The
trading strategy is even more restrictive; we compare convertible bond purchases (dealer sells
to customer) to straight-bond sales (dealer buys from customer) when we open the arbitrage
position; we compare convertible bond sales to straight-bond purchases when we close the
position.
Finally, yield spreads are computed as the difference between the convertible bond yields
and comparable non-convertible bond yields issued by the same firm. For most of our
analysis, we compare only customer buys and require that the straight bond trades take
place within three hours of the convertible bond trades.
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2.3 Yield Spreads
Figure 1 reports the distribution of yield spreads. The law of one price requires the empirical
distribution of yields spreads to have negative support, but there are at least 7% of spreads
that are positive. We find a similar proportion if we require the trades to take place within
one hour of each other. Note that slightly negative spreads might also indicate convertible
bond cheapness, but they do not indicate the presence of arbitrage opportunities per se.
Table 2 presents the distribution of yield spreads over the entire sample and for the two
subsamples coinciding with the arbitrage crashes. The first subsample is the arbitrage crash
of 2005. According to Mitchell, Pedersen, and Pulvino (2007) convertible bond arbitrage
funds faced large redemptions by institution investors in early 2005 which already began
in late 2004. Hence, we let the arbitrage crash of 2005 range from 2004Q1 to 2005Q3.
The underpricing of convertible bonds stretched even longer than this date but we limit the
period to contain only the start of the crash. The second subperiod spans the subprime crisis
from 2008Q2 to 2009Q4. Again, this period only covers part of the crisis but brackets the
peak of the 2008 arbitrage crash in the convertible bond market. Table 2 shows that most
of the violations occur in the second arbitrage crash during the subprime crisis. However,
judging on the median size of the violations, the first arbitrage crash had larger violations.
Expanding the period of the first crash would capture a larger part of the violations, but the
conclusion would still be the same, that the first crash saw fewer but larger violations than
the subprime crisis arbitrage crash.
Figure 2a and 2b present the proportion of violations over time by issue and issuer. For
all matched bond pair within a given month we register whether there is at least one violation
during that month or not. Figure 2a shows that during the peak of the 2008 crisis after the
default of Lehman Brothers more than 80% of the matched bond pairs trading in that month
had at least one violation. While violations were more likely during the recent financial crisis,
the figure shows that mispricing occurred during other periods as well. Furthermore, the
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violations are not concentrated in a few bond pairs. Rather they occur for large parts of the
market. Figure 2b shows in the same way that the violations are not just concentrated to
the bonds of a small number of issuers. Outside the arbitrage crashes we still see violations
in the bonds of around 20% of the issuers in many of the months.
Figure 3a provides information on the level of mispricing over time. As can be seen,
the financial crisis and the arbitrage crash of 2005 were periods characterized by very low
convertible bond prices, so much as to make average and median spreads very close to zero,
or even positive. Focusing on the violations alone (Figure 3b), the average yield spread
exceeded 30% at the peak of the crisis.
3 A First Look at the Segmentation Hypothesis
To get a first idea of the nature of the two arbitrage crashes in 2005 and 2008 we plot
the monthly customer buying volume (dealer selling volume) in the two bond groups over
time. Figure 6a shows the aggregated buying volume across all bonds in each group. The
arbitrage crashes are usually explained by slow moving capital or a lack of capital from
potential investors (see Mitchell, Pedersen, and Pulvino (2007) and Mitchell and Pulvino
(2012)). Hence, we would expect the buying volume in the non-convertible bonds to die
out during the crashes. This should happen because the matched non-convertible bonds are
strictly dominated by the convertible bonds during the crashes. It was possible to buy the
convertible bonds cheaper than the non-convertible bonds and not only get the option part
for free but actually get the bond part for a discount. However, we do not see the buying
volume in the non-convertible bonds vanishing. Investors are still buying these bonds as can
be seen from Figure 6a. Volumes in the two samples are very close together both in the first
and in the second crash. The buying volume does decrease for the non-convertible bonds
during the 2008 crisis but it closely follows the trend from the convertible sample.
The substantial buying volume of dominated straight bonds during the crisis is the first
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rough indication of a market segmentation. Of course, during arbitrage crashes Sharpe ratios
can get so high that investors from completely different areas of finance should move into
the crashed market. This could also have been true for the convertible bonds and would also
be a form of market segmentation if it did not happen. But our analysis shows evidence of
within market segmentation where investors are still buying a completely dominated asset.
Therefore, the crash is not only a matter of slow moving capital, but also a matter of market
segmentation since a group of “natural” investors did have the capital to invest in convertible
bonds but chose not to do it, which probably exaggerated the arbitrage crash.
Figure 6b shows the dealer inventory levels in the two samples over time. The dealer
inventories are constructed by subtracting total dealer sells from total dealer buying each
month in each sample. This gives us the dealer inventory change (caused by trading) in
each market segment. We then get the inventory level by cumulating the changes over time.
Hence, the level is measured relative to a starting point of zero at the beginning of the sample
period. When we implicitly construct the inventory level in this way we do not account for
primary market activities or changes caused by bond price movements. What we want to
see in this graph is whether dealers were net sellers or buyers during the arbitrage crashes.
In the two crash periods dealers seem to be just matching buyers and sellers. Hence, they do
not really build up inventory, if anything they are net sellers and decrease their inventory.
This ensures that when we later on in the analysis focus on customer buys we do cover the
entire universe of agents that are net buyers. Focusing only on customer buys and thus
excluding potential dealers building up inventory could distort the picture. However, since
dealers are not building up inventory, this will not be a problem.
Having the fundamental value of convertible bonds being different from quoted prices is
not in itself evidence of an arbitrage opportunity. The bond could be so illiquid that financial
frictions make it impossible to realize this theoretical arbitrage. The low prices of convertible
bonds could just be caused by lower liquidity in this sample compared to our matched sample.
We will control for this later on in the analysis but we can get a first impression that this
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is not the case from figure 5. Figure 5 shows the (low frequency) Amihud Illiq measure
(Amihud, 2002) for each of the two samples. The Amihud measure is first calculated on a
monthly basis for each bond by dividing the daily return (using a daily average price) by
total daily trading volume in millions of dollars. The monthly measure is then averaged
within each market segment across time. The figure shows that the convertible bonds as a
group is in fact more liquid than the matched sample. Hence, a difference in liquidity is not
the main reason why convertibles bonds were cheaper than the matched bonds during the
arbitrage crashes.
One group of investors which we are able to identify in the transaction data is insurance
companies. The NAIC database provides information on all buys and sells carried out by
this investor group. Figure 7 shows the fraction of the total customer buying volume which
was executed by insurance companies. Notice that straight bonds and busted convertible
bonds have the same capital requirements for the insurance companies and that insurance
companies are also allowed to hold speculative grade bonds although these bonds have higher
capital requirement than investment grade bonds. 7a shows that insurance companies as a
fraction of the total market buying in the straight bonds used in our sample were more active
during the two arbitrage crashes. The fraction spikes in late 2004 and again during the 2008
credit crisis. In the latter case insurance companies accounted for around 30 percent of the
market. However, as seen earlier the total market buying volume also decreased at the same
time, hence the absolute trading activity by insurance companies is more or less unaffected.
As a comparison 7b shows the fraction for convertible bonds. Here insurance companies
accounts for a much smaller fraction of the overall trading. Interestingly, the fraction does
spike during the arbitrage crashes showing that some insurance companies do in fact shift
over. Again, part of the spikes are caused by other investors dropping out of the market
while the insurance companies stayed in. So the spikes are not actual evidence of a change
in behavior. Especially, because the straight bond buying is more or less unaffected by the
crashes, insurance companies seem to be an investor group which contribute to the market
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segmentation.
Thus far, we have provided suggestive evidence on an aggregated level. In the following
sections we refine the analysis and compare bonds on a much finer basis.
4 Which factors explain the yield gap?
In this section, we explore potential determinants of the frequency and severity of mispricing.
These can be market conditions, characteristics of the underlying firm, those of the bonds
themselves, or the publicly traded stock of the firm.
4.1 Financial asset characteristics
Characteristics of the bonds can make them more or less desirable to investors, and may
affect the extent of mispricing. We include the age of the bond, the (log) issue size, and
the time to maturity in years, as well as its rating. The appendix (Section A) presents the
bond rating codes and the S&P and Moody’s ratings they are equivalent to. The rating is
numerical and is lower for higher quality bonds.
We also include moneyness at the time of the matched transaction pair observation as
the ratio of stock price divided by conversion price. The conversion price is provided by
the Mergent database and the stock price by CRSP. Moneyness may be important for two
reasons. First, moneyness of the conversion option determines how much one can hedge the
convertible bond with the firm’s stock. Second, Downing, Underwood, and Xing (2009) show
that returns on out of the money convertible bond generally lag the returns on the firm’s
stock more than do returns on closer-to-the-money-convertibles. Thus, moneyness can be
related to efficiency of the market for the convertible bond. Furthermore, moneyness is a
rough measure of the value of the conversion option. In normal times we would expect yield
differentials between matched pairs to be explained by the value of the option. Hence, the
yield differential should be negatively related to moneyness with a normally lower yield on
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the convertible bond than on the matched straight bond.
For all bonds, we can calculate an effective daily bid-ask spread as the relative price
difference between buy and sell side transactions as in Feldhutter, Hotchkiss, and Karakas
(2013). Using institutional sized trades (above $100,000 nominal value) we thus calculate:
bid-ask =Pask − Pbid
Pask
where Pask and Pbid are daily bond specific averages. Part of the convertible bond mispricing
could be explained by a difference in liquidity. If one of the two bonds in a pair is more costly
to trade then that could distort the theoretical price relationship. We try to capture this
effect by including a liquidity spread calculated as the difference in effective bid-ask spreads.
Finally, we include a bond selling pressure measure. Both the convertible bond arbitrage
crash of 2005 and 2008 were initiated by fire sales of the convertible bonds (Mitchell, Peder-
sen, and Pulvino (2007) and Mitchell and Pulvino (2012)). In order to capture the effect of
selling pressure we add the selling pressure measure from Feldhutter, Hotchkiss, and Karakas
(2013) motivated by the search model in Feldhutter (2012). For each bond we calculate the
relative difference between average daily prices of small Psmall and large Plarge transactions:
selling pressure =Psmall − Plarge
Plarge
we then aggregate the measure from being bond specific to firm specific by averaging over all
outstanding issues from the firm. According to the model of Feldhutter (2012), the measure
will decrease (have lower values) in times of selling pressure. We use the firm level measure
instead of the bond specific measure in order to get a more robust measure. Also, selling
pressure seems to be related to the firm’s collective bond portfolio in our sample rather than
the convertible bonds alone.
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4.2 Differences in treatment at bankruptcy
The straight bonds and convertible bonds in each pair in our study are also matched on
seniority. Furthermore, the bonds have the same rating or the straight bonds have a lower
rating. According to Erens and Hoffman (2010), “..historically, it has been accepted that the
amount of a bankruptcy claim arising from a convertible debt instrument equals the amount
of funds loaned under the instrument.” The paper goes on to describe one exception of the
2007 SONICblue bankruptcy, where straight bondholders raised an objection that the senior
claim should be reduced by the amount of the option value at issuance because the option
is equity which is junior to bonds. According to Erens and Hoffman (2010), no reported
cases have ruled on this issue. We are not aware of any bankruptcy where senior convertible
bondholders did not receive equal treatment to senior straight bondholders.
Inspection of the data reveals that convertible and straight bond prices generally converge
upon bankruptcy. Figure 4a compares the yields and the prices of two matched bonds issued
by Delta Airlines, which filed for bankruptcy in 2005 before the credit crisis. As can be seen,
the prices converge after the filing date. Focusing on another bankruptcy taking place after
the credit crisis, Figure 4b shows that bond prices of AMR, the parent company of American
Airlines, also converged after the filing date.
Note that, even if the bonds are still trading after bankruptcy, we do not compute yields to
maturity so as to not attribute a would-be zero spread to mispricing. Since after bankruptcy
there is no longer optionality in a convertible bond, the yield spread are rightly close to zero.
4.3 Uncertainty of timing of cash flows
Due to the possibility of conversion, the timing of cash flows is uncertain for convertible
bonds. However, since the holder chooses whether to convert to his or her advantage, this
timing uncertainty should not decrease the value of the convertible bonds. Nevertheless,
we examine callability of the bonds by the issuer and putability of the bonds by the bond
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holders. Callability might not matter much during the 2008 crisis, since it was difficult for
firms to raise capital and they might not have been able to finance a call of the bonds.
4.4 Firm characteristics
Firm characteristics such as size could affect the mispricing, both because they are related
to the probability of bankruptcy and recovery, and because the underlying stock is often
used to hedge positions in the convertible. We use Log(Assets), the log of the firm’s assets.
In untabulated results, the book to market ratio of the firm is not a significant explanatory
variable for the mispricing. We also include market leverage for the firm and the one month
stock return.
4.5 Market conditions
We use several measures that vary with market conditions and which could potentially
explain a time series variation in the frequency and size of the violations. We include the TED
spread, the Term spread and the Vix index. Finally, we include the corporate bond market
illiquidity factor4 from Dick-Nielsen, Feldhutter, and Lando (2012). The illiquidity measure
is calculated as a monthly average of four bond specific normalized illiquidity measures,
the high-frequency Amihud measure (Amihud (2002)), the unique round trip cost measure
(Feldhutter (2012)) and the standard deviations of these two. The bond specific measures
are then aggregated to a market wide measure by weighting each bond measure with the
issuance size. Higher values of the aggregated measure indicates a more illiquid market.
Another possibly relevant market condition to include is one of short sales constraints.
However, Asquith, Au, Covert, and Pathak (2013) document that the market for borrowing
bonds is similar to the market for borrowing stocks, with borrowing costs of between 10 and
20 basis points per year, and that the market did not suffer much from the financial crisis.
The arbitrage in this case would rely on borrowing straight debt, which is fairly liquid in
4The monthly measure is available from feldhutter.com.
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these firms.
5 Analysis
We want to analyze the cross-sectional determinants of convertible bond underpricing. In-
stead of defining bond underpricing using a theoretical models as in Mitchell, Pedersen,
and Pulvino (2007) and Mitchell and Pulvino (2012), we use yield spreads and define as
mispricings those observations with a non-negative spread. Unlike the theoretical approach,
our matching approach requires transaction on both convertible and similar non-convertible
bonds issued by the same firm. However, relatively to the model-based approach, a vio-
lation in our model-free approach identifies more clearly a strictly dominated investment
opportunity.
In Table 3, we take a first look at the explanatory variables broken down into percentiles.
A notable feature of the convertible bonds in the sample is that they are quite young,
with the median bonds being 1.19 years old. Moreover, the convertible bonds tend to be
approximately two years younger than straight bonds. The fact the the convertible bonds
in our sample are younger and that they are also larger (as indicated by Issue Size Spread)
suggests that they are not less liquid than the matched straight bonds.
5.1 Probability of Mispricing
We model the probability of a transaction pair being a violation with a logistic regression.
Table 4 shows estimates from various specifications of the logistic regression. The first spec-
ification includes bond characteristics and differences between bond characteristics within
each pair. The other models are augmented with firm-level and macro variables. In Model 4
and 5 we weight observations differently, giving more weight to matched trades that happen
closer in time.
Violations happen naturally more often in larger convertible bond issues since these issues
16
see more trading on average. In contrast to earlier studies, violations are more common in
older issues and are thus not restricted to underpricing around issuance. Bond pairs with
shorter time to maturity are more likely to be violations. As the rating deteriorates, i.e.
the rating variable goes up, violations are more likely. This could be because lower rated
bonds have a more uncertain valuation and investors are not able to do a proper valuation.
However, since the convertible bond strictly dominates the straight bond uncertainty should
not matter. Another explanation could be that investors just want to get rid of the lower
rated bonds and are willing to do this in a fire sale where they do not care about fair
valuation. But that is only a partial explanation since few of the bonds are actually close to
default. Most bonds also trade in a default and even in this case there should not be any
violations. Hence, a low rating cannot explain why we see a violation even if we do see more
violations in lower rated bonds.
The coefficient for selling pressure in the bonds of the issuer have the right sign in that
a lower value indicates more selling pressure. More selling pressure could be associated with
fire sales and in the end violations. However, in the first specification of the logistic regression
selling pressure is not significant. Financial frictions for the convertible bond is a natural
candidate that could account for the violations. If the convertible bond is less liquid than
the straight bond then transaction costs and search frictions would increase the yield of the
convertible bond making it more likely to see violations. This effect does exist as can be
seen in Table 4. Violations are more frequent in bond pairs where the liquidity spread is
positive meaning that the convertible bond is less liquid than the straight bond. However,
the average convertible bond is actually more liquid than the average straight bond and even
though the R2 is quite high, the liquidity spread is not the sole determinant of the violations.
In Model 2, we add firm specific variables. The bond characteristics remain almost
unchanged except for the selling pressure variable which now becomes significant. Violations
are more likely for smaller firms with low market leverage. So violations are not very likely for
large firms primarily financed by debt. One potential explanation for this result is that high
17
leverage increases both yields through a credit risk channel, but lowers just convertible bond
yields through an (increased) equity volatility channel, thus making violations less likely.
Finally, the moneyness of the convertible bond, i.e. the ratio of stock price to conversion
price, is significant indicating that violations are less likely for convertible bonds which are
more in the money. This is quite intuitive in that higher moneyness implies a higher value
of the conversion option. When the convertible bond is in the money it is obvious that it is
worth more than the straight bond. As the option value approaches zero the bonds should
be identical and smaller price differences can more easily constitute a violation. However,
the time series behavior of the violations indicates that the violations are not just noise.
In Model 3, we add variables that proxy for market conditions. It is no secret that our
sample period contains the worst financial crisis since the great depression. To allow the
included factors to pick up more than just the subprime crisis, we have included a crisis
dummy in all the specifications. The dummy is especially important for the market wide
variables. All the time series variables spike during the crisis and, without the dummy, they
would just mechanically pick up the crisis where we also see most violations. Of course that
would be consistent with our sample behavior, but it would not give any idea of the impact
of the variables outside the crisis. In a later section we do a robustness check and repeat
the analysis without the crisis. Market illiquidity and the Vix are not significant whereas
the TED and term spread are significant. All the four variables are positively correlated so
excluding one would shift the explanatory weight towards the others. This makes it hard to
specifically interpret the effects. However, the overall conclusion is that market conditions
do matter over and above the dummy effect of the crisis.
In Model 4 and 5, we repeat the two former regressions but now we weight each observa-
tion of a transaction pair with the time gap between the observations in the pair. The longer
the transactions are spaced in time the more likely it is that new information has arrived
in the market which could impact the valuation. Hence, what we call violations could just
be market movements. To alleviate this possible bias we employ the weighting scheme. The
18
only variable that decreases in significance is bond age, all other variables remain significant
and with the proper sign. The results seem very robust to the weighting scheme so the max-
imum time gap set to three hours does eliminate the arrival of new information on average.
It is primarily market conditions that become more economically important when we weight
with the time gap. The increase in significance is driven by an increase in violations with
low time gap during bad market conditions, primarily the subprime crisis. Outside the crisis
the time gap is larger for transaction pairs with violations.
5.2 Level of Mispricing
Whereas the former section looked at determinants of the frequency of violations this section
looks at determinants of the size of the violation.
Apriori we expect the value of the conversion option to be the main determinant of any
price differential between the convertible bond and the matched straight bond. Panel A
of Table 6 shows that both moneyness and equity volatility are significant in most of the
specifications. When the convertible bond has higher moneyness or the equity volatility is
higher, making it more likely that the stock could realize high increases, the yield differential
becomes larger (more negative) with the convertible bond being more valuable. When adding
more explanatory variables to the regression for the admissible trades we can see that they
do become statistically significant but economically small. The bond pairs are not matched
on issuance size or bond age and a size or age difference does matter, but not by much. The
size effect could be a liquidity difference in that larger issues usually are considered more
liquid. To account for such an effect we have included the liquidity spread as well which
is not significant. The bond pairs are matched on time to maturity which by construction
bounds the difference. Still, the maturity spread does become significant, but depending on
the specification the sign of the difference flips, showing that the effect is not very robust.
Finally, there is a difference in the spread caused by the callability feature, particularly for
the case when one of the bonds is callable and the other is not. If one bond is callable and
19
the other is not, there could be uncertainty as to what the actual maturity date is.
The above effects were all for admissible trades, i.e. transaction pairs without violations.
For those trades it is possible to explain large parts of the yield differentials. Looking at
panel B of table 6 we can see that for the violations we do not get the same effects. The
value of the conversion option does not moderate or explain any yield differential for the
violations. There are two reasons for this; first, as we saw in the logistic regression most
violations occur for convertible bonds where the option value is low. Second, anecdotally
in the fire sales during the arbitrage crashes investors were more focused on selling than on
getting a fair price. Whereas differences in characteristics were statistically significant if not
economically significant for the admissible pairs, there is no evidence that they should matter
at all for the violations. Again, callability is significant but the sign flips depending on the
specification. The overall conclusion is that whereas we are in fact able to explain yield
differentials for the admissible trades with conversion option value as the main determinant,
we are not able to explain the size of the violations. This finding supports the view that
the violations are real violations and not systematically caused by, for example, the usual
financial market frictions.
5.3 Robustness
To test the robustness of the findings regarding violation frequency and violation size we
do two robustness tests. First, we use the “worst” possible yield differential measure which
we call the max yield spread approach. Whenever a convertible trade is matched with
multiple straight-bond trades, instead of selecting the closest trade in time, we select the
trade with the highest yield. This approach makes violations much harder to find. The
second robustness test is to exclude the 2008 subprime crisis from the analysis. We do this
by repeating the analysis with only the pre-crisis period up to mid 2008. Since the 2008 crisis
weights heavily in the analysis it is interesting to see if the determinants remain unchanged
for the pre-crisis period alone.
20
When we use the maximum yield approach we get almost identical results. The construc-
tion of the yield differential for the matched transaction pairs is very robust. Whether we
select closest in time or highest yields make no difference, the traded prices for institutional
trades are very close together within the time interval of 3 hours that we use for selecting
pairs. Again, the interval seems sufficiently small to not allow new information to arrive. If
new information had been a problem we would most likely have seen a difference between the
two approaches. Table 6 and table 9 are very similar in terms of estimates and significance.
Also table 4 and 8 are very close. Both the analysis of size and frequency of the violations
are robust to the maximum yield specification.
Looking at the pre-crisis alone gives us an idea of the ability of the determinants to pick
up a general effect rather than a subprime crisis effect. We do see more violations during
the subprime crisis and almost all time series variables and firm accounting variables spike
in some way at that time as well. With this in mind, it could be that the analysis is only
valid for the 2008 crisis and not outside this crisis. However, tables 4 and 5 are very similar.
The analysis of the frequency of the violations seems to be robust to the subprime crisis.
Still, this does not mean that the 2008 crisis was not special, since we did include a subprime
crisis dummy in the former analysis. But is does indicate that the dummy was successful
in accounting for most of the special circumstances of the crisis. The main difference is in
the variables for the market conditions. Here the Vix has now replaced the Term spread in
being significant. Market conditions does matter outside the crisis and Vix has more time
series variation in this period than does the Term spread which is why it is able to pick up
more significance. When looking at the size of the spread table 6 and 7 are also very close
for the admissible trades. The value of the conversion option is still the main determinant.
However, there are minor differences for the violations. In the full sample analysis we find
very few significant determinants which indicates a complete fire sale where the fair value
has little impact. Before the crisis more variables are significant but with no clear tendency
across the specifications. Only when including issuer dummies or time dummies do we get
21
these extra variables to be significant. For example, then the liquidity difference within the
bond pair matters. However, given the smaller number of violations outside the crisis (only
1/3 of the full sample) it may be too much to condition on issuer and time. The residual
effect may not be systematic in nature. Especially, the signs are not robust and intuitive
when we start to condition on issuer and time series effects in the pre-crisis sample.
6 Trading Strategy
It is straightforward to identify violations of the law of one price. Figure 8a shows bond
prices/yields that are consistent with the law of one price. As can be seen, the convertible
bid ask yield is always below the straight bond bid yield, so there is never room to start
an arbitrage trade. On the other hand, Figure 8b shows that, after the collapse of Lehman
Brothers, some convertible bonds experienced a sharp decrease in price which gave rise to
arbitrage opportunities. We next describe how to take advantage of these opportunities.
6.1 A Long/Short Trading Strategy
This strategy requires selling short the low-yielding instrument, i.e. the straight bond,
and using the funds from the short proceeds to buy the high-yielding convertible bonds.
The position would be closed upon convergence of the bond prices, which can happen in
three ways. First, the convertible bid yield goes below the non-convertible ask yield (fully
accounting for round-trip transaction costs). Second, the bonds mature. Lastly, the issue
files for bankruptcy. To sum up, the steps are:
1. Mispricing Identification (“The signal”). For every convertible bond, identify
a convertible bond trade taking place at a yield that is equal or higher than that of a
comparable straight bond.
2. “Carry-Trade” Transaction. Sell straight bonds short and use the proceeds to
buy convertible bonds. The accrued interest is typically higher for the short position.
22
The difference between the coupon rates on the straight bond and the convertible bond
represents a negative cash flow. The cost of carry is therefore given by (cs− cl), where
the cs and cl are the coupon rates on the shorted and purchased bond respectively.
3. Close Position. Close the short and long position if any of the following is true:
• yst − ycbt > k ≥ 0
• one of the two bonds reaches maturity
• the issuer files for bankruptcy
• τ days have passed without full convergence having occurred.
Because profit opportunities are higher during arbitrage crashes and dedicated investors
do not have the capital to eliminate relative value mispricing, the number of positions open
over time will vary as a result. Figure 9 plots the number of open positions (y-axis) during any
given month (x-axis). Each plot represents a different combination of the parameters of the
strategy. HP represents the maximum holding period allowed for any position; YS represent
the yield spread signals for respectively opening and closing a position. For instance, the
parameters of the northwest box indicate that a position can be opened if the the yield spread
is zero and closed if the straight bond yield is 50 basis points bigger than the convertible
bond yield; if convergence does not happen within 90 days, then the position is closed using
prevailing prices. Next, we analyze the returns generated by these strategies.
6.2 Empirical Performance
We analyze the monthly returns generated by the trading strategy. Monthly returns are
obtained by cumulating the daily returns of the long leg and the short leg of the strategy
and then taking the difference. Figure 10 reports the monthly returns for the different
versions of the strategy. These returns are obtained by averaging the returns generated by
each position (i.e. bond pair). Using the monthly returns, Figure 11 shows the growth in the
23
value of one dollar invested on day zero. As can be seen, there is a remarkable draw done in
the cumulative returns corresponding to the two convertible bonds arbitrage crashes.
Table 10 reports the annualized mean, standard deviation (SD), and Sharpe ratio (SR)
of the returns generated by the long-short trading strategy. Moreover, the table reports
the coefficients estimates and R2 of the four-factor model of monthly returns. The strategy
generates high average returns, both unconditionally and after adjusting for risk. As can be
seen from the high standard deviation and the low R2 the strategy has a lot of idiosyncratic
risk. The source of systematic risk that matters the most is momentum, followed by market
risk. The risk-adjusted performance (α) of more than 1% on a monthly basis is high. With
only statistical significance at the 10% level for the one-year horizon, statistical significance
might seem weak. However, a trader would likely see these high abnormal returns as a
great opportunity with relatively little risk, especially considering that these returns already
account for transaction costs.
One of the main reasons behind the weak statistical significance is the relatively small
and time-varying sample size of the bond pairs involved in the strategy. As can be seen
from Figure 9, the number of positions is relatively low in the first part of the sample and
peaks during the financial crisis. It can easily be shown that, everything else equal, average
returns from one or two bond pairs are less reliable in a statistical sense than averages
obtained from over ten bond pairs. To incorporate this source of heteroscedasticity in the
estimation process of the four-factor model, we employ a Generalized Least Squares (GLS)
approach, which ends up being a weighted least squares estimation. Specifically, we estimate
the vector β with the intercept and factor loading as:
β = (X ′WX)−1(X ′WR), (2)
where R is the strategy return vector, X is a matrix of ones and risk factors, and W is a
diagonal weighting matrix. The weights are given by 1/nt, where nt is equal to the size of
24
the cross-section of bond pairs at time t. Ordinary Least Squares (OLS) estimation assumes
that the number of observations over time is constant, i.e. n1 = n2 = . . . nT .
Table 11 replicates Table 10, with the difference that the factor models intercept and
factor loadings are estimated with Equation (2). The table shows that giving more weights
to observations that are based on more bond pairs result in substantially more statistical
significance with respect to α and somewhat less significance for the factor loadings. For
holding periods longer that 180 days, at least one specification of the strategy gives α that
is statistically significant at the 5% level. Momentum is still important and its impact is
consistent across strategy specifications, whereas the impact of the market factor is not
constant across specifications.
7 Conclusion
We study how often convertible bonds trade at prices (yields) that are too low (high) relative
to those of comparable straight bonds issued by the same firm and find that this happens
for more than 7% of the matched trades . The trading situations that we identify represent
arbitrage opportunities as they imply negatively priced equity call options. These violations
occur most frequently, but not exclusively, during the 2008 credit crisis and are evidence of
market segmentation between convertible debt and straight debt.
Large price deviations from fundamentals are often attributed to market frictions. By
construction, our matching procedure controls for funding liquidity and slow moving capital
because we look at instances in which straight bond buyers evidently already have secured
funding to buy strictly dominated securities. Moreover, the funding/capital requirements
for busted convertible bonds and straight bonds are identical. Our findings suggest that, in
addition to slow moving capital, the existence of clienteles within the corporate bond market
is a concurrent and aggravating determinant of arbitrage crashes.
25
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27
Table 1: Bond Characteristics
This table presents bond characteristics for the starting sample of convertible and non-convertible bonds.To determine the starting sample, we select all the TRACE-eligible bonds that are also in FISD. For eachissuer, we match each convertible bond to the non-convertible bonds with similar maturity and the same orworse seniority. Note that one convertible bond might be matched to more non-convertible bonds. Senioritygoes from one to five, indicating in increasing order whether a bond is senior secured (1), senior unsecured,senior subordinate, subordinate, and junior subordinate (5). Callable, Putable, and Bankruptcy are dummiesindicating whether the bond is callable, putable, or has experienced bankruptcy during its life. The othervariables are self-explanatory.
Convertible (N=190) Non-convertible (N=226)Mean P1 Median P90 Mean P1 Median P90
Issue Size ($MIO) 590.39 17.87 375.00 2711.9 404.81 6.00 310.00 1300.0Coupon 3.23 0.00 3.13 10.00 7.10 2.20 6.95 12.50Seniority 2.34 2.00 2.00 4.00 2.01 1.00 2.00 3.00Maturity at Issuance 11.22 2.77 7.22 30.02 10.67 3.01 9.92 30.02Callable 0.60 0.00 1.00 1.00 0.82 0.00 1.00 1.00Putable 0.38 0.00 0.00 1.00 0.03 0.00 0.00 1.00Bankruptcy 0.11 0.00 0.00 1.00 0.10 0.00 0.00 1.00
28
Table
2:
Dis
trib
uti
on
of
Vio
lati
ons
Th
ista
ble
pre
sents
the
emp
iric
ald
istr
ibu
tion
of
the
yie
ldd
iffer
enti
als
bet
wee
nco
nver
tib
lean
dco
mp
ara
ble
non
-conve
rtib
leb
on
ds
of
the
sam
efi
rmfo
rth
efu
llsa
mp
lean
dtw
osu
bp
erio
ds.
Th
ed
istr
ibu
tion
isfo
rall
pair
san
dco
nd
itio
nal
on
vio
lati
on
socc
urr
ing.
Th
etw
osu
bp
erio
ds
are
for
the
2005
conve
rtib
leb
ond
arb
itra
gecr
ash
and
for
the
2008
arb
itra
ge
crash
.T
he
firs
tp
erio
dis
defi
ned
toru
nfr
om
2004Q
4to
2005Q
3,
wh
ich
span
sth
eea
rly
par
tof
the
2005
cras
h.
Th
ese
con
dp
erio
dis
defi
ned
from
2008Q
2to
2009Q
4w
hic
hsp
an
sth
ep
eak
of
the
sub
pri
me
cris
is.
The
yie
ldd
iffer
enti
als
are
mea
sure
din
per
centa
gep
oints
.
Ob
s.M
ean
P1
P5
P10
P25
P50
P75
P90
P95
P99
Pan
elA
:F
ull
Sam
ple
All
pai
rs32
,867
-5.9
00
-19.8
3-1
5.1
3-1
2.3
3-9
.076
-5.3
52
-1.9
44
-0.1
34
0.6
58
3.2
95
Vio
lati
ons
2,88
41.
590
0.0
08
0.0
47
0.0
76
0.2
74
0.8
20
1.8
73
3.6
35
6.5
20
10.1
01
Pan
elB
:20
05A
rbit
rage
Cra
sh
All
pai
rs1,
073
-4.0
94
-14.5
1-8
.740
-8.1
10
-6.1
11
-4.2
21
-1.8
32
-1.1
04
0.3
33
11.5
11
Vio
lati
ons
645.
887
0.0
86
0.1
99
0.3
02
1.0
14
5.5
88
9.2
65
12.5
78
14.4
63
16.9
62
Pan
elC
:20
08A
rbit
rage
Cra
sh
All
pai
rs9,
423
-6.3
18
-19.3
9-1
7.2
1-1
4.6
2-1
1.6
5-6
.132
-0.5
10
0.6
24
1.3
86
3.0
12
Vio
lati
ons
1,66
81.
243
0.0
12
0.0
48
0.0
67
0.2
66
0.7
50
1.5
11
2.3
51
3.6
93
9.1
43
29
Table 3: Explanatory Variables
This table presents the explanatory variables used in the cross-sectional analysis of the probability and thelevel of mispricing. Log Issue Size is the natural logarithm of the convertible bonds’ offering amount;IssueSize Spread is the difference between the convertible and the matched straight bonds’ offering amount; YearsOld (or Age) is the time (in years) since the convertible bonds’ issuance; Age Spread is the difference in ageof the matched bonds; Years to Maturity is the time to maturity of the convertible bonds’ (expressed inyears); Maturity Spread is the difference in the time to maturity of the matched bonds; Rating is a numericalvariable ranging from 1 (AAA) to 25 (D, or default) and is set to missing if the bond is not rated; PricePressure is the relative difference between average daily prices of small Psmall and large Plarge transactions;Liquidity Spread is the difference in the log of the bid-ask spreads of the matched bonds; Return (1m) is thestock return of the issuer in the previous month; Log Moneyness is the natural logarithm of the moneynessof the conversion option embedded in the convertible bond; Volatility is the issuer’s stock return volatility inthe previous six months; Log Assets is the natural logarithm of the issuer’s total assets (AT, in Compustat);Market Leverage is defined (with Compustat notation) as dltt+dlc+bast
lt+mktcap , where mktcap is the issuer’s equity
market capitalization; Mkt Liquidity (D) is the monthly corporate bond market illiquidity factor from Dick-Nielsen, Feldhutter, and Lando (2012) and available at feldhutter.com; Term Spread is the differencebetween the 10-year and 2-year constant maturity treasury yields; TED Spread is the difference between the30-day Eurodollar and treasury rate; Vix is the implied volatility of options written on the S&P500. Thelast three macro variables are available at the daily frequency.
N Mean STD P1 P25 Median P75 P99
Log Issue Size 14,706 13.52 0.80 11.79 13.02 13.46 14.03 14.73Issue Size Spread 14,706 0.48 0.88 -1.20 -0.24 0.57 1.13 1.90Years Old 14,706 1.52 1.36 0.00 0.59 1.19 2.11 5.18Age Spread 14,706 -2.36 3.53 -14.51 -4.25 -1.95 -0.33 4.99Years to Maturity 14,706 4.70 3.00 1.16 3.32 4.07 5.24 19.19Maturity Spread 14,706 0.00 1.15 -1.92 -0.88 0.33 0.92 1.97Rating 14,561 11.95 4.65 4.00 9.00 12.00 16.00 20.00Price Pressure 12,028 -0.00 0.01 -0.03 -0.01 -0.00 0.00 0.03Liquidity Spread 11,787 -0.57 1.04 -2.83 -1.25 -0.67 0.05 2.75Return (1m) 13,390 0.04 0.20 -0.40 -0.07 0.02 0.12 0.75Log Moneyness 11,865 -0.51 0.72 -2.35 -1.15 -0.33 -0.00 0.79Volatility 13,390 0.04 0.02 0.01 0.02 0.03 0.05 0.10Log Assets 13,640 9.87 1.00 6.63 9.11 10.05 10.45 12.18Market Leverage 11,865 0.42 0.22 0.06 0.20 0.39 0.62 0.78Mkt Liquidity (D) 114 0.06 1.24 -1.20 -0.72 -0.34 0.32 4.75Term Spread 2,263 0.02 0.01 -0.00 0.00 0.02 0.02 0.03TED Spread 2,245 0.01 0.01 0.00 0.00 0.00 0.01 0.04Vix 2,264 21.29 10.27 10.31 14.29 18.55 24.88 62.98
30
Table
4:
Pro
babil
ity
of
Mis
pri
cing
Th
ista
ble
pre
sents
coeffi
cien
tes
tim
ated
and
marg
inal
effec
tsfr
om
five
logis
tic
regre
ssio
nm
od
els.
Ove
rall
(aver
age)
marg
inal
effec
tsare
on
the
right
(med
ian
effec
tsin
par
enth
esis
).In
mod
els
4an
d5
ob
serv
ati
on
sfo
rw
hic
hth
eti
me
gap
bet
wee
nm
atc
hed
tran
sact
ion
sis
hig
her
are
wei
ghte
dle
ss.
Th
ed
epen
den
tva
riab
leis
bin
ary:
one
ifth
eyie
ldsp
read
isp
osi
tive
an
dze
rooth
erw
ise.
Th
ere
gre
ssors
are
defi
ned
inT
ab
le3.
Mod
elO
vera
llM
arg
inal
Eff
ects
(%)
(1)
(2)
(3)
(4)
(5)
(1)
(2)
(3)
(4)
(5)
Cri
sis
4.71
54.
173
4.0
81
5.2
41
5.1
44
17.3
10.9
10.5
10.7
10.1
(29.
78)∗∗∗
(19.
31)∗∗∗
(10.8
1)∗∗∗
(17.4
5)∗∗∗
(9.6
9)∗∗∗
[5.9
][
0.5
][
0.4
][
0.2
][
0.1
]L
ogIs
sue
Siz
e0.
406
0.41
50.2
86
1.2
66
0.8
30
1.6
1.0
0.7
2.1
1.4
(4.9
1)∗∗∗
(3.2
0)∗∗∗
(2.1
0)∗∗
(7.4
1)∗∗∗
(4.3
5)∗∗∗
[0.5
][
0.1
][
0.0
][
0.0
][
0.0
]Y
ears
Old
0.92
00.
513
0.6
49
0.3
05
0.7
36
3.6
1.2
1.5
0.5
1.2
(15.
39)∗∗∗
(4.7
7)∗∗∗
(5.7
7)∗∗∗
(2.1
7)∗∗
(4.5
1)∗∗∗
[1.1
][
0.1
][
0.1
][
0.0
][
0.0
]Y
ears
toM
atu
rity
-0.7
95-0
.898
-0.8
68
-1.1
55
-1.1
44
-3.1
-2.1
-2.0
-1.9
-1.9
(-16
.81)∗∗∗
(-12
.32)∗∗∗
(-11.7
2)∗∗∗
(-12.8
0)∗∗∗
(-11.9
3)∗∗∗
[-1
.0]
[-0
.1]
[-0
.1]
[-0
.0]
[-0
.0]
Rat
ing
0.28
50.
310
0.2
90
0.3
59
0.3
46
1.1
0.7
0.7
0.6
0.6
(18.
21)∗∗∗
(9.6
9)∗∗∗
(8.4
3)∗∗∗
(8.8
7)∗∗∗
(7.6
9)∗∗∗
[0.4
][
0.0
][
0.0
][
0.0
][
0.0
]P
rice
Pre
ssu
re-5
.334
-37.
52-4
2.1
6-7
7.9
7-9
5.1
6-2
1.0
-89.0
-99.3
-127.9
-156.7
(-1.
11)
(-6.
06)∗∗∗
(-6.4
5)∗∗∗
(-10.2
1)∗∗∗
(-10.8
4)∗∗∗
[-6
.6]
[-4
.9]
[-4
.0]
[-2
.9]
[-2
.0]
Liq
uid
ity
Sp
read
0.92
60.
880
0.8
12
1.3
95
1.2
36
3.6
2.1
1.9
2.3
2.0
(18.
97)∗∗∗
(13.
52)∗∗∗
(12.0
5)∗∗∗
(13.8
8)∗∗∗
(11.5
4)∗∗∗
[1.2
][
0.1
][
0.1
][
0.1
][
0.0
]L
ogM
oney
nes
s-3
.532
-3.6
68
-3.5
67
-3.9
00
-8.4
-8.6
-5.9
-6.4
(-16
.03)∗∗∗
(-15.8
6)∗∗∗
(-12.0
5)∗∗∗
(-11.9
8)∗∗∗
[-0
.5]
[-0
.4]
[-0
.1]
[-0
.1]
Ret
urn
(1m
)-0
.585
-0.4
31
-1.2
93
-0.8
94
-1.4
-1.0
-2.1
-1.5
(-2.
04)∗∗
(-1.4
3)
(-3.9
8)∗∗∗
(-2.5
9)∗∗∗
[-0
.1]
[-0
.0]
[-0
.0]
[-0
.0]
Log
Ass
ets
-0.7
64-1
.102
-1.6
12
-1.9
36
-1.8
-2.6
-2.6
-3.2
(-4.
91)∗∗∗
(-6.2
9)∗∗∗
(-7.8
8)∗∗∗
(-8.5
2)∗∗∗
[-0
.1]
[-0
.1]
[-0
.1]
[-0
.0]
Mar
ket
Lev
erag
e-1
4.62
-15.2
1-1
5.6
3-1
7.1
5-3
4.7
-35.8
-25.7
-28.2
(-14
.56)∗∗∗
(-14.3
7)∗∗∗
(-11.0
2)∗∗∗
(-10.5
5)∗∗∗
[-1
.9]
[-1
.5]
[-0
.6]
[-0
.4]
Mkt
Liq
uid
ity
(D)
0.0
13
0.0
36
0.0
0.1
(0.0
6)
(0.1
4)
[0.0
][
0.0
]V
ix0.0
12
0.0
07
0.0
0.0
(0.7
4)
(0.3
4)
[0.0
][
0.0
]T
ED
Sp
read
21.2
66
54.2
89
50.1
89.4
(1.6
8)∗
(3.2
6)∗∗∗
[2.0
][
1.1
]T
erm
Sp
read
63.4
14
79.3
83
149.3
130.7
(4.1
0)∗∗∗
(4.3
2)∗∗∗
[6.1
][
1.7
]
Pse
ud
oR
20.
187
0.24
60.2
48
0.2
52
0.2
55
N.
vio
l.66
661
5613
615
613
N.
non
-vio
l.9,
088
8,29
08,2
64
8,2
90
8,2
64
31
Tab
le5:
Pro
babil
ity
of
Mis
pri
cing
(Pre
-Cri
sis)
Th
isT
able
mim
ics
Tab
le4,
bu
tu
ses
only
obse
rvati
on
sb
efore
the
cred
itcr
isis
(up
to2008Q
2).
Mod
elO
vera
llM
arg
inal
Eff
ects
(%)
(1)
(2)
(3)
(4)
(5)
(1)
(2)
(3)
(4)
(5)
Log
Issu
eS
ize
-0.1
970.
713
0.1
32
1.2
95
0.7
75
-0.6
1.1
0.2
1.3
0.7
(-1.
97)∗∗
(3.5
3)∗∗∗
(0.5
3)
(4.9
3)∗∗∗
(1.8
5)∗
[-0
.3]
[0.1
][
0.0
][
0.0
][
0.0
]Y
ears
Old
0.71
50.
031
0.4
30
-0.3
03
-0.0
16
2.2
0.0
0.6
-0.3
-0.0
(9.9
6)∗∗∗
(0.2
2)(2
.41)∗∗
(-1.5
1)
(-0.0
5)
[0.9
][
0.0
][
0.0
][
-0.0
][
-0.0
]Y
ears
toM
atu
rity
-0.6
03-1
.013
-0.8
96
-1.3
43
-1.3
19
-1.9
-1.6
-1.3
-1.3
-1.1
(-10
.61)∗∗∗
(-9.
97)∗∗∗
(-8.2
2)∗∗∗
(-8.5
2)∗∗∗
(-7.0
9)∗∗∗
[-0
.8]
[-0
.2]
[-0
.1]
[-0
.0]
[-0
.0]
Rat
ing
0.24
20.
262
0.2
55
0.3
78
0.3
92
0.8
0.4
0.4
0.4
0.3
(13.
14)∗∗∗
(5.8
2)∗∗∗
(5.5
1)∗∗∗
(5.9
5)∗∗∗
(6.0
7)∗∗∗
[0.3
][
0.0
][
0.0
][
0.0
][
0.0
]P
rice
Pre
ssu
re-1
5.42
-63.
22-6
4.7
3-1
29.2
-134.3
-47.9
-97.1
-92.5
-126.3
-116.8
(-2.
07)∗∗
(-5.
73)∗∗∗
(-5.8
1)∗∗∗
(-8.6
9)∗∗∗
(-8.8
2)∗∗∗
[-2
0.2
][
-10.9
][
-6.9
][
-3.8
][
-2.2
]L
iqu
idit
yS
pre
ad0.
794
0.57
70.5
16
1.2
32
1.1
05
2.5
0.9
0.7
1.2
1.0
(13.
79)∗∗∗
(6.3
0)∗∗∗
(5.1
9)∗∗∗
(7.5
8)∗∗∗
(6.3
0)∗∗∗
[1.0
][
0.1
][
0.1
][
0.0
][
0.0
]L
ogM
oney
nes
s-3
.140
-3.3
46
-3.6
39
-3.8
78
-4.8
-4.8
-3.6
-3.4
(-11
.40)∗∗∗
(-11.0
1)∗∗∗
(-9.2
6)∗∗∗
(-8.7
2)∗∗∗
[-0
.5]
[-0
.4]
[-0
.1]
[-0
.1]
Ret
urn
(1m
)-1
.620
-1.4
70
-1.9
64
-1.8
24
-2.5
-2.1
-1.9
-1.6
(-3.
64)∗∗∗
(-3.2
8)∗∗∗
(-4.3
9)∗∗∗
(-3.7
9)∗∗∗
[-0
.3]
[-0
.2]
[-0
.1]
[-0
.0]
Log
Ass
ets
-1.1
12-1
.039
-1.7
34
-1.5
65
-1.7
-1.5
-1.7
-1.4
(-4.
75)∗∗∗
(-4.2
3)∗∗∗
(-5.3
9)∗∗∗
(-4.5
5)∗∗∗
[-0
.2]
[-0
.1]
[-0
.1]
[-0
.0]
Mar
ket
Lev
erag
e-1
5.12
-14.1
8-1
9.3
8-1
9.6
9-2
3.2
-20.3
-18.9
-17.1
(-11
.93)∗∗∗
(-10.0
9)∗∗∗
(-10.4
4)∗∗∗
(-9.0
6)∗∗∗
[-2
.6]
[-1
.5]
[-0
.6]
[-0
.3]
Mkt
Liq
uid
ity
(D)
0.2
64
0.3
71
0.4
0.3
(0.6
3)
(0.5
9)
[0.0
][
0.0
]V
ix0.0
41
0.0
83
0.1
0.1
(1.4
3)
(1.9
6)∗∗
[0.0
][
0.0
]T
ED
Sp
read
214.0
9180.9
7305.9
157.4
(4.3
3)∗∗∗
(2.4
2)∗∗
[22.9
][
3.0
]T
erm
Sp
read
43.7
03
-18.3
762.4
-16.0
(1.5
7)
(-0.4
6)
[4.7
][
-0.3
]
Pse
ud
oR
20.
065
0.12
60.1
29
0.1
77
0.1
79
N.
vio
l.25
121
5213
215
213
N.
non
-vio
l.7,
953
7,17
87,1
52
7,1
78
7,1
52
32
Table 6: Regression Analysis
This table presents OLS regression of the yield spreads on several explanatory variables (defined in Table3). The top panel uses only negative spreads; the bottom panel uses non-negative spreads.
Panel A: Admissible Trades
Return (1m) 0.0016 0.0066 0.0040 -.0097 -.0102(0.09) (0.29) (0.20) (-0.61) (-0.75)
Log Moneyness -.0292 -.0391 -.0169 -.0613 -.0334(-1.82)∗ (-4.78)∗∗∗ (-1.56) (-7.88)∗∗∗ (-7.48)∗∗∗
Volatility -.9551 -.6848 -.0136 -1.533 -.4486(-4.58)∗∗∗ (-3.13)∗∗∗ (-0.07) (-6.79)∗∗∗ (-1.99)∗
Issue Size Spread -.0095 -.0088 -.0046 -.0097(-2.01)∗ (-2.21)∗∗ (-0.87) (-1.44)
Age Spread 0.0027 -.0012 0.0028 -.0013(1.92)∗ (-1.08) (2.47)∗∗ (-1.35)
Maturity Spread -.0122 0.0047 -.0049 0.0051(-2.37)∗∗ (2.71)∗∗∗ (-1.67) (4.32)∗∗∗
Both Callable 0.0216 -.0074 0.0377 -.0374(1.87)∗ (-0.47) (2.66)∗∗ (-3.73)∗∗∗
Call-NoCall 0.0257 0.0214 0.0510 -.0181(2.12)∗∗ (3.64)∗∗∗ (4.43)∗∗∗ (-0.93)
Liquidity Spread 0.0012 -.0025 0.0039 -.0006(0.60) (-1.45) (2.34)∗∗ (-0.61)
Adj. R2 0.24 0.45 0.79 0.63 0.87Obs. 10,837 8,535 8,535 8,535 8,535
Panel B: Violations
Return (1m) -.0242 -.0265 -.0184 0.0101 0.0202(-5.44)∗∗∗ (-4.49)∗∗∗ (-2.77)∗∗ (0.95) (2.38)∗∗
Log Moneyness -.0035 0.0019 0.0271 -.0094 -.0049(-0.48) (0.22) (1.43) (-1.34) (-0.45)
Volatility 0.3005 0.2179 0.6972 -.0988 -.2006(1.67) (0.91) (1.38) (-0.48) (-0.58)
Issue Size Spread -.0078 -.0063 0.0041 -.0008(-1.29) (-2.04)∗ (0.78) (-0.13)
Age Spread -.0005 -.0015 -.0013 -.0043(-0.41) (-0.56) (-1.08) (-2.96)∗∗
Maturity Spread 0.0065 0.0029 -.0001 -.0013(1.74) (0.45) (-0.03) (-0.42)
Both Callable -.0199 0.0102 0.0111 0.0422(-1.31) (0.63) (0.65) (6.22)∗∗∗
Call-NoCall -.0191 0.0056 0.0137 0.0557(-3.09)∗∗∗ (0.21) (1.18) (4.90)∗∗∗
Liquidity Spread 0.0002 0.0011 0.0031 0.0022(0.21) (1.21) (1.86)∗ (1.74)
Adj. R2 0.15 0.18 0.31 0.71 0.75Obs. 718 631 631 631 631
Fixed Effects Issuer Yr-Mon Both
33
Table 7: Regression Analysis (pre crisis)
Same as Table 6, but just using pre-crisis data (up to 2008Q2).
Panel A: Admissible Trades
Return (1m) 0.0102 0.0171 0.0117 -.0097 -.0054(0.45) (0.67) (0.52) (-0.53) (-0.30)
Log Moneyness -.0395 -.0500 -.0172 -.0663 -.0323(-2.39)∗∗ (-5.39)∗∗∗ (-1.21) (-7.58)∗∗∗ (-6.51)∗∗∗
Volatility -1.640 -1.307 -.3862 -1.926 -.5963(-4.39)∗∗∗ (-6.87)∗∗∗ (-3.43)∗∗∗ (-6.57)∗∗∗ (-3.93)∗∗∗
Issue Size Spread -.0095 -.0109 -.0051 -.0090(-2.16)∗∗ (-2.28)∗∗ (-1.10) (-1.27)
Age Spread 0.0027 -.0018 0.0032 -.0017(2.04)∗∗ (-2.03)∗∗ (2.90)∗∗∗ (-2.09)∗∗
Maturity Spread -.0088 0.0048 -.0038 0.0051(-2.13)∗∗ (5.06)∗∗∗ (-1.35) (6.68)∗∗∗
Both Callable 0.0237 0.0012 0.0367 -.0273(2.17)∗∗ (0.10) (2.68)∗∗ (-2.64)∗∗
Call-NoCall 0.0364 0.0120 0.0551 -.0089(3.12)∗∗∗ (5.44)∗∗∗ (4.67)∗∗∗ (-0.53)
Liquidity Spread 0.0035 -.0006 0.0045 0.0004(2.03)∗∗ (-0.41) (2.56)∗∗ (0.39)
Adj. R2 0.29 0.53 0.83 0.66 0.89Obs. 8,823 7,394 7,394 7,394 7,394
Panel B: Violations
Return (1m) -.0088 -.0005 0.0130 0.0098 0.0098(-0.64) (-0.09) (1.92)∗ (0.71) (0.71)
Log Moneyness -.0011 0.0154 0.0450 -.0523 -.0523(-0.17) (1.55) (1.52) (-2.43)∗∗ (-2.43)∗∗
Volatility 0.6439 -.1372 -1.724 -2.785 -2.785(16.39)∗∗∗ (-0.19) (-5.69)∗∗∗ (-2.80)∗∗ (-2.80)∗∗
Issue Size Spread -.0225 0.0875 -.0233 -.0233(-4.37)∗∗∗ (2.98)∗∗ (-1.99)∗ (-1.99)∗
Age Spread 0.0024 -.0462 -.0019 -.0019(0.63) (-2.36)∗∗ (-1.74) (-1.74)
Maturity Spread 0.0258 -.1215 -.0070 -.0070(1.09) (-2.67)∗∗ (-1.45) (-1.45)
Both Callable -.0912 0.8001 -.0002 -.0002(-0.93) (2.61)∗∗ (-0.03) (-0.03)
Call-NoCall -.0408 0.3608 0.0366 0.0366(-1.29) (2.20)∗ (2.25)∗ (2.25)∗
Liquidity Spread 0.0026 0.0077 0.0348 0.0348(1.56) (3.70)∗∗∗ (2.07)∗ (2.07)∗
Adj. R2 0.13 0.44 0.68 0.82 0.82Obs. 251 218 218 218 218
Fixed Effects Issuer Yr-Mon Both
34
Tab
le8:
Pro
babil
ity
of
Mis
pri
cing
(Wit
hM
axim
um
Yie
ld)
Sam
eas
Tab
le4,
bu
tw
ith
diff
eren
tm
atch
ing
pro
ced
ure
.F
or
ever
yco
nve
rtib
leb
on
dtr
ad
ew
eco
nsi
der
all
the
stra
ight
bon
dtr
ad
esh
ap
pen
ing
wit
hin
thre
eh
ours
and
sele
ctth
etr
ade
wit
hth
eh
igh
est
yie
ldto
matu
rity
.
Mod
elO
vera
llM
arg
inal
Eff
ects
(%)
(1)
(2)
(3)
(4)
(5)
(1)
(2)
(3)
(4)
(5)
Cri
sis
4.69
03.
974
3.8
67
4.3
23
4.3
69
15.9
9.8
9.4
9.3
9.2
(29.
66)∗∗∗
(18.
51)∗∗∗
(10.4
0)∗∗∗
(17.5
8)∗∗∗
(9.7
7)∗∗∗
[4.6
][
0.4
][
0.2
][
0.3
][
0.1
]L
ogIs
sue
Siz
e0.
334
0.38
70.2
89
1.0
73
0.7
90
1.2
0.9
0.6
1.9
1.5
(3.9
5)∗∗∗
(2.8
3)∗∗∗
(2.0
2)∗∗
(6.8
8)∗∗∗
(4.6
2)∗∗∗
[0.3
][
0.0
][
0.0
][
0.1
][
0.0
]Y
ears
Old
0.87
80.
394
0.5
15
-0.0
65
0.3
17
3.2
0.9
1.1
-0.1
0.6
(14.
56)∗∗∗
(3.4
6)∗∗∗
(4.3
8)∗∗∗
(-0.5
1)
(2.2
2)∗∗
[0.9
][
0.0
][
0.0
][
-0.0
][
0.0
]Y
ears
toM
atu
rity
-0.7
65-0
.805
-0.7
77
-1.0
62
-0.9
94
-2.8
-1.8
-1.7
-1.9
-1.8
(-15
.99)∗∗∗
(-10
.72)∗∗∗
(-10.0
9)∗∗∗
(-13.4
5)∗∗∗
(-11.9
0)∗∗∗
[-0
.8]
[-0
.1]
[-0
.1]
[-0
.1]
[-0
.0]
Rat
ing
0.25
20.
234
0.2
09
0.2
58
0.2
08
0.9
0.5
0.5
0.5
0.4
(16.
26)∗∗∗
(6.8
8)∗∗∗
(5.7
4)∗∗∗
(6.6
8)∗∗∗
(4.7
5)∗∗∗
[0.3
][
0.0
][
0.0
][
0.0
][
0.0
]P
rice
Pre
ssu
re-3
.696
-31.
84-3
7.7
0-4
7.9
7-6
9.3
7-1
3.6
-70.1
-83.0
-85.6
-128.7
(-0.
76)
(-5.
23)∗∗∗
(-5.8
4)∗∗∗
(-7.1
4)∗∗∗
(-8.7
7)∗∗∗
[-3
.8]
[-3
.3]
[-2
.7]
[-3
.0]
[-2
.4]
Liq
uid
ity
Sp
read
0.97
40.
973
0.9
06
1.3
11
1.1
35
3.6
2.1
2.0
2.3
2.1
(19.
46)∗∗∗
(14.
61)∗∗∗
(13.1
5)∗∗∗
(15.5
5)∗∗∗
(12.8
1)∗∗∗
[1.0
][
0.1
][
0.1
][
0.1
][
0.0
]L
ogM
oney
nes
s-3
.541
-3.7
00
-3.5
52
-3.8
83
-7.8
-8.1
-6.3
-7.2
(-15
.43)∗∗∗
(-15.2
1)∗∗∗
(-13.5
3)∗∗∗
(-13.9
0)∗∗∗
[-0
.4]
[-0
.3]
[-0
.2]
[-0
.1]
Ret
urn
(1m
)-0
.049
0.1
77
0.2
65
0.7
55
-0.1
0.4
0.5
1.4
(-0.
17)
(0.5
7)
(0.8
6)
(2.2
6)∗∗
[-0
.0]
[0.0
][
0.0
][
0.0
]L
ogA
sset
s-0
.764
-1.1
02
-1.2
29
-1.7
36
-1.7
-2.4
-2.2
-3.2
(-4.
67)∗∗∗
(-5.8
6)∗∗∗
(-6.2
8)∗∗∗
(-7.8
2)∗∗∗
[-0
.1]
[-0
.1]
[-0
.1]
[-0
.1]
Mar
ket
Lev
erag
e-1
4.33
-14.9
7-1
4.6
7-1
5.6
3-3
1.5
-33.0
-26.2
-29.0
(-13
.78)∗∗∗
(-13.6
5)∗∗∗
(-11.8
4)∗∗∗
(-11.5
6)∗∗∗
[-1
.5]
[-1
.1]
[-0
.9]
[-0
.5]
Mkt
Liq
uid
ity
(D)
0.0
02
-0.1
25
0.0
-0.2
(0.0
1)
(-0.5
4)
[0.0
][
-0.0
]V
ix0.0
09
0.0
11
0.0
0.0
(0.5
5)
(0.6
2)
[0.0
][
0.0
]T
ED
Sp
read
28.4
73
67.6
84
62.7
125.5
(2.2
5)∗∗
(4.7
1)∗∗∗
[2.1
][
2.3
]T
erm
Sp
read
56.9
75
100.8
7125.4
187.1
(3.5
3)∗∗∗
(5.3
7)∗∗∗
[4.1
][
3.5
]
Pse
ud
oR
20.
182
0.23
30.2
36
0.2
37
0.2
42
N.
vio
l.61
656
5563
565
563
N.
non
-vio
l.9,
138
8,34
08,3
14
8,3
40
8,3
14
35
Table 9: Regression Analysis (With Maximum Yield)
Same as Table 6, but with different matching procedure. For every convertible bond trade we consider all thestraight bonds trades happening within three hours and select the trade with the highest yield to maturity.
Panel A: Admissible Trades
Return (1m) 0.0013 0.0055 0.0035 -.0094 -.0098(0.08) (0.25) (0.18) (-0.61) (-0.76)
Log Moneyness -.0287 -.0387 -.0157 -.0604 -.0326(-1.76)∗ (-4.73)∗∗∗ (-1.42) (-7.89)∗∗∗ (-7.34)∗∗∗
Volatility -.9669 -.6903 -.0127 -1.530 -.4432(-4.58)∗∗∗ (-3.13)∗∗∗ (-0.06) (-6.80)∗∗∗ (-1.99)∗
Issue Size Spread -.0099 -.0084 -.0050 -.0095(-2.06)∗∗ (-1.94)∗ (-0.94) (-1.43)
Age Spread 0.0027 -.0012 0.0028 -.0013(1.96)∗ (-0.94) (2.46)∗∗ (-1.28)
Maturity Spread -.0126 0.0045 -.0053 0.0047(-2.43)∗∗ (2.57)∗∗ (-1.80)∗ (4.22)∗∗∗
Both Callable 0.0219 -.0067 0.0381 -.0370(1.88)∗ (-0.41) (2.67)∗∗ (-3.68)∗∗∗
Call-NoCall 0.0264 0.0225 0.0511 -.0186(2.20)∗∗ (3.91)∗∗∗ (4.41)∗∗∗ (-0.96)
Liquidity Spread 0.0012 -.0025 0.0039 -.0006(0.60) (-1.42) (2.33)∗∗ (-0.57)
Adj. R2 0.24 0.45 0.79 0.64 0.87Obs. 10,888 8,585 8,585 8,585 8,585
Panel B: Violations
Return (1m) -.0271 -.0301 -.0239 0.0054 0.0139(-4.37)∗∗∗ (-3.88)∗∗∗ (-3.21)∗∗∗ (0.50) (1.81)∗
Log Moneyness -.0046 0.0015 0.0247 -.0060 -.0041(-0.78) (0.21) (1.58) (-0.96) (-0.33)
Volatility 0.2888 0.2437 0.6701 0.0096 0.0705(1.92)∗ (1.24) (1.77) (0.05) (0.26)
Issue Size Spread -.0066 -.0066 0.0045 -.0030(-1.32) (-2.43)∗∗ (0.78) (-0.40)
Age Spread -.0007 -.0005 -.0013 -.0038(-0.53) (-0.25) (-1.14) (-1.52)
Maturity Spread 0.0057 0.0050 0.0000 -.0006(1.78) (1.10) (0.00) (-0.13)
Both Callable -.0213 0.0063 0.0068 0.0340(-1.50) (0.45) (0.40) (7.45)∗∗∗
Call-NoCall -.0213 -.0043 0.0146 0.0534(-3.81)∗∗∗ (-0.24) (1.28) (2.49)∗∗
Liquidity Spread -.0006 0.0001 0.0021 0.0012(-0.61) (0.15) (1.17) (0.60)
Adj. R2 0.18 0.20 0.32 0.70 0.75Obs. 667 581 581 581 581
Fixed Effects Issuer Yr-Mon Both
36
Table 10: Trading Strategy (OLS)
This table presents the mean, standard deviation, and Sharpe Ratio of the monthly returns produced by thelong-short trading strategy. The table also reports ordinary least squares (OLS) coefficient estimates of theFF three factor model augmented with the momentum factor. Each panel reports strategies with differentallowed holding periods. Within each panel, we consider different opening/closing signals for the strategypositions.
O/C Mean SD SR α βMKT βHML βSMB βUMD R2
Maximum Holding Period: 90 days
0/0.5 0.0118 0.0719 0.1438 0.0102 0.0994 -0.0852 0.0982 -0.2578 0.07( 1.32) ( 0.54) ( -0.25) ( 0.32) ( -1.78)
0/1 0.0115 0.0716 0.1406 0.0103 0.1193 -0.1124 0.0955 -0.2594 0.07( 1.35) ( 0.65) ( -0.33) ( 0.32) ( -1.81)
0.5/0.5 0.0108 0.0551 0.1688 0.0085 0.1552 0.0803 -0.0783 -0.2250 0.10( 1.57) ( 1.14) ( 0.32) ( -0.36) ( -2.10)
0.5/1 0.0097 0.0538 0.1527 0.0073 0.1360 0.1307 -0.0752 -0.2330 0.11( 1.40) ( 1.03) ( 0.55) ( -0.35) ( -2.24)
Maximum Holding Period: 180 days
0/0.5 0.0127 0.0675 0.1652 0.0106 0.1352 0.0328 -0.0803 -0.2599 0.07( 1.57) ( 0.81) ( 0.11) ( -0.29) ( -1.94)
0/1 0.0101 0.0726 0.1194 0.0084 0.1198 -0.0035 -0.0855 -0.2753 0.06( 1.18) ( 0.67) ( -0.01) ( -0.29) ( -1.91)
0.5/0.5 0.0102 0.0594 0.1460 0.0077 0.1774 0.1449 -0.2190 -0.2245 0.09( 1.35) ( 1.23) ( 0.55) ( -0.93) ( -1.96)
0.5/1 0.0092 0.0605 0.1270 0.0070 0.1935 0.1337 -0.2214 -0.2453 0.10( 1.22) ( 1.32) ( 0.51) ( -0.93) ( -2.10)
Maximum Holding Period: 360 days
0/0.5 0.0131 0.0633 0.1845 0.0109 0.0715 0.0488 -0.0471 -0.2841 0.08( 1.78) ( 0.46) ( 0.17) ( -0.19) ( -2.32)
0/1 0.0122 0.0647 0.1675 0.0100 0.0957 0.0736 -0.0815 -0.2844 0.08( 1.61) ( 0.61) ( 0.26) ( -0.32) ( -2.27)
0.5/0.5 0.0115 0.0550 0.1823 0.0091 0.1313 0.1183 -0.1795 -0.2473 0.09( 1.81) ( 1.00) ( 0.50) ( -0.85) ( -2.38)
0.5/1 0.0106 0.0553 0.1641 0.0081 0.1440 0.1289 -0.1796 -0.2410 0.10( 1.59) ( 1.09) ( 0.55) ( -0.85) ( -2.30)
Maximum Holding Period: 720 days
0/0.5 0.0092 0.0579 0.1335 0.0066 0.1219 0.2064 -0.1388 -0.2725 0.11( 1.24) ( 0.88) ( 0.84) ( -0.63) ( -2.50)
0/1 0.0091 0.0574 0.1327 0.0066 0.1411 0.2146 -0.1736 -0.2733 0.11( 1.26) ( 1.04) ( 0.89) ( -0.80) ( -2.54)
0.5/0.5 0.0090 0.0552 0.1368 0.0064 0.1589 0.2146 -0.2272 -0.2581 0.12( 1.30) ( 1.22) ( 0.93) ( -1.09) ( -2.51)
0.5/1 0.0085 0.0552 0.1259 0.0058 0.1753 0.2241 -0.2221 -0.2597 0.13( 1.16) ( 1.35) ( 0.97) ( -1.07) ( -2.54)
37
Table 11: Trading Strategy (GLS)
Same as Table 10, except that the factor model estimates are obtained as β = (X ′WX)−1(X ′WR), where Ris the strategy return vector, X is a matrix of ones and risk factors, and W is a diagonal weighting matrix.The weights on the diagonal are given by 1/nt, where nt is equal to the size of the cross-section of bond pairsat time t. Ordinary Least Squares (OLS) estimation assumes that the number of observations over time isconstant, i.e. n1 = n2 = . . . nT .
O/C Mean SD SR α βMKT βHML βSMB βUMD R2
Maximum Holding Period: 90 days
0/0.5 0.0118 0.0719 0.1438 0.0117 0.0280 -0.3695 0.4042 -0.2770 0.04( 1.19) ( 0.09) ( -0.78) ( 0.83) ( -1.03)
0/1 0.0115 0.0716 0.1406 0.0117 0.0564 -0.4008 0.4592 -0.2857 0.04( 1.22) ( 0.19) ( -0.86) ( 0.95) ( -1.07)
0.5/0.5 0.0108 0.0551 0.1688 0.0099 0.1981 0.0666 -0.0670 -0.1443 0.04( 1.52) ( 0.88) ( 0.21) ( -0.20) ( -0.73)
0.5/1 0.0097 0.0538 0.1527 0.0078 0.1164 0.2019 -0.0417 -0.1734 0.03( 1.24) ( 0.53) ( 0.64) ( -0.13) ( -0.90)
Maximum Holding Period: 180 days
0/0.5 0.0127 0.0675 0.1652 0.0181 0.0347 -0.0379 0.1301 -0.3618 0.05( 2.32) ( 0.14) ( -0.10) ( 0.33) ( -1.63)
0/1 0.0101 0.0726 0.1194 0.0110 -0.0600 -0.1610 0.2722 -0.3637 0.03( 1.29) ( -0.20) ( -0.36) ( 0.62) ( -1.42)
0.5/0.5 0.0102 0.0594 0.1460 0.0104 0.1098 0.2074 -0.1019 -0.1829 0.03( 1.55) ( 0.48) ( 0.62) ( -0.29) ( -0.93)
0.5/1 0.0092 0.0605 0.1270 0.0099 0.1307 0.2015 -0.0928 -0.2694 0.04( 1.43) ( 0.54) ( 0.60) ( -0.26) ( -1.27)
Maximum Holding Period: 360 days
0/0.5 0.0131 0.0633 0.1845 0.0192 -0.1594 0.0524 -0.0004 -0.3416 0.06( 2.76) ( -0.69) ( 0.15) ( -0.00) ( -1.75)
0/1 0.0122 0.0647 0.1675 0.0173 -0.0981 0.0980 0.0254 -0.3562 0.05( 2.36) ( -0.40) ( 0.26) ( 0.07) ( -1.72)
0.5/0.5 0.0115 0.0550 0.1823 0.0162 -0.0164 0.1944 -0.1741 -0.2833 0.05( 2.73) ( -0.08) ( 0.65) ( -0.58) ( -1.58)
0.5/1 0.0106 0.0553 0.1641 0.0165 -0.0599 0.2307 -0.1755 -0.3061 0.05( 2.65) ( -0.28) ( 0.75) ( -0.57) ( -1.66)
Maximum Holding Period: 720 days
0/0.5 0.0092 0.0579 0.1335 0.0120 0.0596 0.2878 -0.0643 -0.2298 0.04( 1.82) ( 0.27) ( 0.87) ( -0.19) ( -1.25)
0/1 0.0091 0.0574 0.1327 0.0125 0.0825 0.3030 -0.1109 -0.2450 0.05( 1.88) ( 0.37) ( 0.91) ( -0.32) ( -1.32)
0.5/0.5 0.0090 0.0552 0.1368 0.0131 0.1245 0.3541 -0.2201 -0.2782 0.06( 2.03) ( 0.58) ( 1.06) ( -0.64) ( -1.43)
0.5/1 0.0085 0.0552 0.1259 0.0136 0.1169 0.3779 -0.2162 -0.2892 0.06( 2.02) ( 0.53) ( 1.11) ( -0.61) ( -1.47)
38
Figure 1: Distribution of Yields SpreadsThis figure shows the difference between the yield to maturity between non-convertible bonds and comparableconvertible bonds by the same issuer. The vertical line at zero represents the demarcation between regular(negative) spreads and those that represent violations of the law of one price (the positive spreads). Weobtain the yield spreads by matching all the convertible bond buys with the non convertible bonds buystaking place within three hours of the convertible bond trade. The figure does not show the top and bottom0.1% of yield spreads.
39
(a) by Bond
(b) by Issuer
Figure 2: Frequency of Violations Over TimeThis figure plots the time series distribution of violations. Panel a shows the monthly fraction of bonds withat least one violation during that month. Panel b shows that monthly fraction of bond issuers with at leastone bond with at least one violation.
40
(a) Full Sample
(b) Vuolations
Figure 3: Yield Differential for Bond PairsThis figure plots the average and median yield spread between convertible bonds and their matched straightbonds. The top panel includes all observations; the bottom panel includes only positive spreads.
41
(a) Bankruptcy Before Crisis
(b) Bankruptcy After Crisis
Figure 4: Two Examples of Bankruptcy and Price ConvergenceFor each of the two panels, this figure shows the convertible bond ask yield versus the matched straight bondbid yield (top left plot) faced by investors opening a long-short position; the top left plot shows the yieldassociated with the closing trades. The bottom plots report average daily prices for the bond pair.
42
Figure 5: Market Price Impact of TradingThis figure shows the monthly Amihud illiq measure for the group of convertible bonds versus the group ofmatched non-convertible bonds. The Amihud measure is calculated for each bond on a monthly basis usingdaily returns from daily average prices divided by daily total turnover in millions of dollars. The monthlygroup measure is found by taking the median across each sample.
43
(a) Buying Volume
(b) Cumulative Changes in Inventory
Figure 6: Dealer Inventory Vs Customer FlowThis figure shows trading activity in the two samples of convertible bond versus non-convertible matchedbonds. Panel A shows the monthly aggregated customer buying volume (dealers selling to non-dealers).Panel B shows the dealer inventory in the two samples over time. The dealer inventories are constructedby each month subtracting total dealer sells from total dealer buys which gives a monthly dealer inventorychange. The monthly inventory changes is then cumulated over time to give the dealer inventory relativeto a position of zero at the inception of the graph. Note that we do not know the starting positions of thedealers and we do not account for primary market activities in the graph. The left graphs are the raw datapoints and the right graphs are a 6-month smoothed version.
44
(a) Straight bonds
(b) Convertible Bonds
Figure 7: Proportion of Buying Activity by InsurersThis figure shows trading activity (all buys) by insurance companies (from NAIC) as a proportion of thetotal trading volume (buying volume) from TRACE for all matched pairs identified by the study.
45
(a) Normal Relation
(b) Abnormal Relation
Figure 8: Non-Arbitrage Relations: two scenariosThis figure presents the yields (top graphs) and prices (bottom graphs) over time of a convertible bondand its non-convertible match for Ford Motor CO DEL (Panel a) and Medtronic INC (Panel b). The leftgraphs compare convertible bond asks with straight bond bid (to open positions); the right graphs compareconvertible bond bids with straight bond ask (to close positions).
46
Figure 9: Trading Strategy: Open PositionsThe plots show the number of open positions (y-axis) during any given month (x-axis). Each plot represents adifferent combination of the parameters of the strategy. HP represents the maximum holding period allowedfor any position; YS represent the yield spread signals for respectively opening and closing a position. Forinstance, the parameters of the northwest box indicate that a position can be opened if the the yield spreadis zero and closed if the straight bond yield is 50 basis points bigger than the convertible bond yield; ifconvergence does not happen within 90 days, then the position is closed using prevailing prices.
47
Figure 10: Trading Strategy: Monthly ReturnsFor each bond pair, individual monthly returns are obtained by cumulating the daily returns of the long legand short leg of the trade and then taking the difference. Monthly return is cross-sectional average of theindividual monthly returns.
48
Figure 11: Trading Strategy: Cumulative ReturnsCumulative returns are obtained by cumulating the gross monthly returns.
49
A Bond rating codes
Rating Code S&P Moody’s
1 AAA Aaa
2 AA+ Aa1
3 AA Aa, Aa2
4 AA- Aa3
5 A+ A1
6 A A,A2
7 A- A3
8 BBB+ Baa1
9 BBB Baa,Baa2
10 BBB- Baa3
11 BB+ Ba1
12 BB Ba,Ba2
13 BB- Ba3
14 B+ B1
15 B B,B2
16 B- B3
17 CCC+ Caa1
18 CCC Caa, Caa2
19 CCC- Caa3
20 CC Ca
21 C C
25 D -
26 SUSP SUSP
27 NR NR
28 SD -
50