Arbitrage crashes: Slow-moving capital or market segmentation?∗ Jens Dick-Nielsen Copenhagen Business School [email protected]

Marco Rossi University of Notre Dame [email protected]

December 6, 2013

Abstract The predominant explanation for arbitrage crashes is a lack of investor capital to exploit mispricing. This paper shows that slow moving capital is only partially responsible for the 2005 and 2008 arbitrage crashes in the convertible bond market. Even when convertible bonds where underpriced, investors were still buying strictly dominated straight bonds from the same issuers. This finding suggests that market segmentation exaggerated the convertible arbitrage crashes. Furthermore, it is possible to exploit the market segmentation with a long/short trading strategy providing positive abnormal returns. The strategy is profitable even after accounting for transaction cost. 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 the FDIC Conference (2011), Indiana State Finance Conference (2011), and the Copenhagen Business School FRIC and Notre Dame seminars for their helpful comments. Special thanks to Sophie Shive for her precious help with an earlier version of this paper. Jens Dick-Nielsen gratefully acknowledges support from the Center for Financial Frictions (FRIC), grant no. DNRF102.

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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 Pulvino (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 opportunities 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 1

Source: Credit Suisse. Chan and Chen (2007) find that convertible bond underpricing relative to exercise value based on the underlying stock price resolves within two years of issuance. 2

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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 convertible 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 convertible 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 sophisticated 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 requirements. 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 arbitrage 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, Gˆarleanu, 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 partially 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 regulatory 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 evidence 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 3 This hypotheses is also consistent with the investor recognition hypothesis of Merton (1987). Facing incomplete information on security characteristics, investors only hold securities whose risk and returns characteristics with which they are familiar.

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TIPS tend to be very cheap relative to treasury bonds and that an arbitrage opportunity exists. 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 Holdings 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.

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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-thecounter (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 nonconvertible 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 ∗ M AD(p, k) + g,

(1)

where g is a granularity parameter which we set equal to $1, and med(p, k), and M AD(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.

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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.

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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, Pedersen, 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 4

The 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. Instead 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 violation 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 specification 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

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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 observation 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 maximum 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 construction 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: • yts − ytcb > 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 0 W X)−1 (X 0 W R),

(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

References Agarwal, Vikas, William H Fung, Yee Cheng Loon, and Narayan Y Naik, 2011, Risk and return in convertible arbitrage: Evidence from the convertible bond market, Journal of Empirical Finance 18, 175–194. Amihud, Yakov, 2002, Illiquidity and stock returns: cross-section and time-series effects, Journal of Financial Markets 5, 31–56. Asquith, Paul, Andrea S. Au, Thomas Covert, and Parag A. Pathak, 2013, The market for borrowing corporate bonds, Journal of Financial Economics 107, 155 – 182. Bai, Jennie, and Pierre Collin-Dufresne, 2011, The cds-bond basis during the financial crisis of 2007-2009, Available at SSRN 1785756. Bessembinder, Hendrik, Kathleen M. Kahle, William F. Maxwell, and Danielle Xu, 2009, Measuring Abnormal Bond Performance, Review of Financial Studies 22, 4219–4258. Brown, Stephen J, Bruce D Grundy, Craig M Lewis, and Patrick Verwijmeren, 2012, Convertibles and hedge funds as distributors of equity exposure, Review of Financial Studies 25, 3077–3112. Carhart, Mark M, 1997, On persistence in mutual fund performance, The Journal of finance 52, 57–82. Chan, Alex, and Nai-fu Chen, 2007, Convertible bond underpricing: Renegotiable covenants, seasoning and convergence, Management Science 53, 1793–1814. Choi, Darwin, Mila Getmansky, Brian Henderson, and Heather Tookes, 2010, Convertible bond arbitrageurs as suppliers of capital, Review of financial studies 23, 2492–2522. Choi, Darwin, Mila Getmansky, and Heather Tookes, 2009, Convertible bond arbitrage, liquidity externalities, and stockprices, Journal of Financial Economics 91, 227–251. Dammon, Robert M, Kenneth B Dunn, and Chester S Spatt, 1993, The relative pricing of highyield debt: The case of rjr nabisco holdings capital corporation, The American Economic Review pp. 1090–1111. Dick-Nielsen, Jens, 2009, Liquidity biases in trace, Journal of Fixed Income 19, 43. , Peter Feldhutter, and David Lando, 2012, Corporate bond market liquidity before and after the onset of the subprime crisis, Journal of Financial Economics 103, 471–492. Downing, Chris, Shane Underwood, and Yuhang Xing, 2009, The relative informational efficiency of stocks and bonds: an intraday analysis, Journal of financial and quantitative analysis 44, 1081–1102.

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Duffie, Darrell, 2010, Presidential address: Asset price dynamics with slow-moving capital, The Journal of finance 65, 1237–1267. , Nicolae Gˆ arleanu, and Lasse Heje Pedersen, 2007, Valuation in over-the-counter markets, Review of Financial Studies 20, 1865–1900. Edwards, Amy K., Lawrence E. Harris, and Michael S. Piwowar, 2007, Corporate bond market transaction costs and transparency, Journal of Finance 62, 1421–1451. Erens, Brad, and Timothy Hoffman, 2010, Are the claims of convertible debt holders at risk in bankruptcy?, Pratt’s Journal of Bankruptcy Law 6, 575–592. Fama, Eugene F, and Kenneth R French, 1992, The cross-section of expected stock returns, the Journal of Finance 47, 427–465. Feldhutter, Peter, 2012, The same bond at different prices: Identifying search frictions and selling pressures, Review of Financial Studies 25, 1155–1206. , Edith Hotchkiss, and Oguzhan Karakas, 2013, The impact of creditor control on corporate bond pricing and liquidity, Working paper. Fleckenstein, Matthias, Francis A Longstaff, and Hanno Lustig, 2013, The tips-treasury bond puzzle, The Journal of Finance. Liu, Xuewen, and Antonio S. Mello, 2011, The fragile capital structure of hedge funds and the limits to arbitrage, Journal of Financial Economics 102, 491 – 506. Merton, Robert C, 1987, A simple model of capital market equilibrium with incomplete information, The Journal of Finance 42, 483–510. Mitchell, Mark, Lasse Pedersen, and Todd Pulvino, 2007, Slow moving capital, The American Economic Review 97, 215–220. Mitchell, Mark, and Todd Pulvino, 2012, Arbitrage crashes and the speed of capital, Journal of Financial Economics 104, 469–490. Rossi, Marco, 2010, Realized volatility, liquidity, and corporate yield spreads, Notre Dame Working Paper. Shleifer, Andrei, and Robert W Vishny, 1997, The limits of arbitrage, The Journal of Finance 52, 35–55.

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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 each issuer, we match each convertible bond to the non-convertible bonds with similar maturity and the same or worse seniority. Note that one convertible bond might be matched to more non-convertible bonds. Seniority goes 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 dummies indicating whether the bond is callable, putable, or has experienced bankruptcy during its life. The other variables are self-explanatory.

Mean Issue Size ($MIO) 590.39 Coupon 3.23 Seniority 2.34 Maturity at Issuance 11.22 Callable 0.60 Putable 0.38 Bankruptcy 0.11

Convertible (N=190) P1 Median 17.87 0.00 2.00 2.77 0.00 0.00 0.00

375.00 3.13 2.00 7.22 1.00 0.00 0.00

28

P90

Mean

2711.9 10.00 4.00 30.02 1.00 1.00 1.00

404.81 7.10 2.01 10.67 0.82 0.03 0.10

Non-convertible (N=226) P1 Median P90 6.00 2.20 1.00 3.01 0.00 0.00 0.00

310.00 6.95 2.00 9.92 1.00 0.00 0.00

1300.0 12.50 3.00 30.02 1.00 1.00 1.00

29

All pairs Violations

Panel C: 2008 Arbitrage Crash

All pairs Violations

Panel B: 2005 Arbitrage Crash

All pairs Violations

Panel A: Full Sample

9,423 1,668

1,073 64

32,867 2,884

Obs.

-6.318 1.243

-4.094 5.887

-5.900 1.590

Mean

-19.39 0.012

-14.51 0.086

-19.83 0.008

P1

-17.21 0.048

-8.740 0.199

-15.13 0.047

P5

-14.62 0.067

-8.110 0.302

-12.33 0.076

P10

-11.65 0.266

-6.111 1.014

-9.076 0.274

P25

-6.132 0.750

-4.221 5.588

-5.352 0.820

P50

-0.510 1.511

-1.832 9.265

-1.944 1.873

P75

0.624 2.351

-1.104 12.578

-0.134 3.635

P90

1.386 3.693

0.333 14.463

0.658 6.520

P95

3.012 9.143

11.511 16.962

3.295 10.101

P99

This table presents the empirical distribution of the yield differentials between convertible and comparable non-convertible bonds of the same firm for the full sample and two subperiods. The distribution is for all pairs and conditional on violations occurring. The two subperiods are for the 2005 convertible bond arbitrage crash and for the 2008 arbitrage crash. The first period is defined to run from 2004Q4 to 2005Q3, which spans the early part of the 2005 crash. The second period is defined from 2008Q2 to 2009Q4 which spans the peak of the subprime crisis. The yield differentials are measured in percentage points.

Table 2: Distribution of Violations

Table 3: Explanatory Variables This table presents the explanatory variables used in the cross-sectional analysis of the probability and the level of mispricing. Log Issue Size is the natural logarithm of the convertible bonds’ offering amount;Issue Size Spread is the difference between the convertible and the matched straight bonds’ offering amount; Years Old (or Age) is the time (in years) since the convertible bonds’ issuance; Age Spread is the difference in age of the matched bonds; Years to Maturity is the time to maturity of the convertible bonds’ (expressed in years); Maturity Spread is the difference in the time to maturity of the matched bonds; Rating is a numerical variable ranging from 1 (AAA) to 25 (D, or default) and is set to missing if the bond is not rated; Price Pressure 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 the stock return of the issuer in the previous month; Log Moneyness is the natural logarithm of the moneyness of the conversion option embedded in the convertible bond; Volatility is the issuer’s stock return volatility in the 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 DickNielsen, Feldhutter, and Lando (2012) and available at feldhutter.com; Term Spread is the difference between the 10-year and 2-year constant maturity treasury yields; TED Spread is the difference between the 30-day Eurodollar and treasury rate; Vix is the implied volatility of options written on the S&P500. The last three macro variables are available at the daily frequency.

Log Issue Size Issue Size Spread Years Old Age Spread Years to Maturity Maturity Spread Rating Price Pressure Liquidity Spread Return (1m) Log Moneyness Volatility Log Assets Market Leverage Mkt Liquidity (D) Term Spread TED Spread Vix

N

Mean

STD

P1

P25

Median

P75

P99

14,706 14,706 14,706 14,706 14,706 14,706 14,561 12,028 11,787 13,390 11,865 13,390 13,640 11,865 114 2,263 2,245 2,264

13.52 0.48 1.52 -2.36 4.70 0.00 11.95 -0.00 -0.57 0.04 -0.51 0.04 9.87 0.42 0.06 0.02 0.01 21.29

0.80 0.88 1.36 3.53 3.00 1.15 4.65 0.01 1.04 0.20 0.72 0.02 1.00 0.22 1.24 0.01 0.01 10.27

11.79 -1.20 0.00 -14.51 1.16 -1.92 4.00 -0.03 -2.83 -0.40 -2.35 0.01 6.63 0.06 -1.20 -0.00 0.00 10.31

13.02 -0.24 0.59 -4.25 3.32 -0.88 9.00 -0.01 -1.25 -0.07 -1.15 0.02 9.11 0.20 -0.72 0.00 0.00 14.29

13.46 0.57 1.19 -1.95 4.07 0.33 12.00 -0.00 -0.67 0.02 -0.33 0.03 10.05 0.39 -0.34 0.02 0.00 18.55

14.03 1.13 2.11 -0.33 5.24 0.92 16.00 0.00 0.05 0.12 -0.00 0.05 10.45 0.62 0.32 0.02 0.01 24.88

14.73 1.90 5.18 4.99 19.19 1.97 20.00 0.03 2.75 0.75 0.79 0.10 12.18 0.78 4.75 0.03 0.04 62.98

30

31

Pseudo R2 N. viol. N. non-viol.

Term Spread

TED Spread

Vix

Mkt Liquidity (D)

Market Leverage

Log Assets

Return (1m)

Log Moneyness

Liquidity Spread

Price Pressure

Rating

Years to Maturity

Years Old

Log Issue Size

Crisis

0.187 666 9,088

4.715 (29.78)∗∗∗ 0.406 (4.91)∗∗∗ 0.920 (15.39)∗∗∗ -0.795 (-16.81)∗∗∗ 0.285 (18.21)∗∗∗ -5.334 (-1.11) 0.926 (18.97)∗∗∗

(1)

0.246 615 8,290

4.173 (19.31)∗∗∗ 0.415 (3.20)∗∗∗ 0.513 (4.77)∗∗∗ -0.898 (-12.32)∗∗∗ 0.310 (9.69)∗∗∗ -37.52 (-6.06)∗∗∗ 0.880 (13.52)∗∗∗ -3.532 (-16.03)∗∗∗ -0.585 (-2.04)∗∗ -0.764 (-4.91)∗∗∗ -14.62 (-14.56)∗∗∗

(2)

0.248 613 8,264

4.081 (10.81)∗∗∗ 0.286 (2.10)∗∗ 0.649 (5.77)∗∗∗ -0.868 (-11.72)∗∗∗ 0.290 (8.43)∗∗∗ -42.16 (-6.45)∗∗∗ 0.812 (12.05)∗∗∗ -3.668 (-15.86)∗∗∗ -0.431 (-1.43) -1.102 (-6.29)∗∗∗ -15.21 (-14.37)∗∗∗ 0.013 (0.06) 0.012 (0.74) 21.266 (1.68)∗ 63.414 (4.10)∗∗∗

Model (3)

0.252 615 8,290

5.241 (17.45)∗∗∗ 1.266 (7.41)∗∗∗ 0.305 (2.17)∗∗ -1.155 (-12.80)∗∗∗ 0.359 (8.87)∗∗∗ -77.97 (-10.21)∗∗∗ 1.395 (13.88)∗∗∗ -3.567 (-12.05)∗∗∗ -1.293 (-3.98)∗∗∗ -1.612 (-7.88)∗∗∗ -15.63 (-11.02)∗∗∗

(4)

0.255 613 8,264

5.144 (9.69)∗∗∗ 0.830 (4.35)∗∗∗ 0.736 (4.51)∗∗∗ -1.144 (-11.93)∗∗∗ 0.346 (7.69)∗∗∗ -95.16 (-10.84)∗∗∗ 1.236 (11.54)∗∗∗ -3.900 (-11.98)∗∗∗ -0.894 (-2.59)∗∗∗ -1.936 (-8.52)∗∗∗ -17.15 (-10.55)∗∗∗ 0.036 (0.14) 0.007 (0.34) 54.289 (3.26)∗∗∗ 79.383 (4.32)∗∗∗

(5) 17.3 [ 5.9] 1.6 [ 0.5] 3.6 [ 1.1] -3.1 [ -1.0] 1.1 [ 0.4] -21.0 [ -6.6] 3.6 [ 1.2]

(1) 10.9 [ 0.5] 1.0 [ 0.1] 1.2 [ 0.1] -2.1 [ -0.1] 0.7 [ 0.0] -89.0 [ -4.9] 2.1 [ 0.1] -8.4 [ -0.5] -1.4 [ -0.1] -1.8 [ -0.1] -34.7 [ -1.9]

10.5 [ 0.4] 0.7 [ 0.0] 1.5 [ 0.1] -2.0 [ -0.1] 0.7 [ 0.0] -99.3 [ -4.0] 1.9 [ 0.1] -8.6 [ -0.4] -1.0 [ -0.0] -2.6 [ -0.1] -35.8 [ -1.5] 0.0 [ 0.0] 0.0 [ 0.0] 50.1 [ 2.0] 149.3 [ 6.1]

10.7 [ 0.2] 2.1 [ 0.0] 0.5 [ 0.0] -1.9 [ -0.0] 0.6 [ 0.0] -127.9 [ -2.9] 2.3 [ 0.1] -5.9 [ -0.1] -2.1 [ -0.0] -2.6 [ -0.1] -25.7 [ -0.6]

Overall Marginal Effects (%) (2) (3) (4)

10.1 [ 0.1] 1.4 [ 0.0] 1.2 [ 0.0] -1.9 [ -0.0] 0.6 [ 0.0] -156.7 [ -2.0] 2.0 [ 0.0] -6.4 [ -0.1] -1.5 [ -0.0] -3.2 [ -0.0] -28.2 [ -0.4] 0.1 [ 0.0] 0.0 [ 0.0] 89.4 [ 1.1] 130.7 [ 1.7]

(5)

This table presents coefficient estimated and marginal effects from five logistic regression models. Overall (average) marginal effects are on the right (median effects in parenthesis). In models 4 and 5 observations for which the time gap between matched transactions is higher are weighted less. The dependent variable is binary: one if the yield spread is positive and zero otherwise. The regressors are defined in Table 3.

Table 4: Probability of Mispricing

32

Pseudo R2 N. viol. N. non-viol.

Term Spread

TED Spread

Vix

Mkt Liquidity (D)

Market Leverage

Log Assets

Return (1m)

0.065 251 7,953

-0.197 (-1.97)∗∗ Years Old 0.715 (9.96)∗∗∗ Years to Maturity -0.603 (-10.61)∗∗∗ Rating 0.242 (13.14)∗∗∗ Price Pressure -15.42 (-2.07)∗∗ Liquidity Spread 0.794 (13.79)∗∗∗ Log Moneyness

Log Issue Size

(1)

0.126 215 7,178

0.713 (3.53)∗∗∗ 0.031 (0.22) -1.013 (-9.97)∗∗∗ 0.262 (5.82)∗∗∗ -63.22 (-5.73)∗∗∗ 0.577 (6.30)∗∗∗ -3.140 (-11.40)∗∗∗ -1.620 (-3.64)∗∗∗ -1.112 (-4.75)∗∗∗ -15.12 (-11.93)∗∗∗

(2)

0.129 213 7,152

0.132 (0.53) 0.430 (2.41)∗∗ -0.896 (-8.22)∗∗∗ 0.255 (5.51)∗∗∗ -64.73 (-5.81)∗∗∗ 0.516 (5.19)∗∗∗ -3.346 (-11.01)∗∗∗ -1.470 (-3.28)∗∗∗ -1.039 (-4.23)∗∗∗ -14.18 (-10.09)∗∗∗ 0.264 (0.63) 0.041 (1.43) 214.09 (4.33)∗∗∗ 43.703 (1.57)

Model (3)

0.177 215 7,178

1.295 (4.93)∗∗∗ -0.303 (-1.51) -1.343 (-8.52)∗∗∗ 0.378 (5.95)∗∗∗ -129.2 (-8.69)∗∗∗ 1.232 (7.58)∗∗∗ -3.639 (-9.26)∗∗∗ -1.964 (-4.39)∗∗∗ -1.734 (-5.39)∗∗∗ -19.38 (-10.44)∗∗∗

(4)

0.179 213 7,152

0.775 (1.85)∗ -0.016 (-0.05) -1.319 (-7.09)∗∗∗ 0.392 (6.07)∗∗∗ -134.3 (-8.82)∗∗∗ 1.105 (6.30)∗∗∗ -3.878 (-8.72)∗∗∗ -1.824 (-3.79)∗∗∗ -1.565 (-4.55)∗∗∗ -19.69 (-9.06)∗∗∗ 0.371 (0.59) 0.083 (1.96)∗∗ 180.97 (2.42)∗∗ -18.37 (-0.46)

(5)

This Table mimics Table 4, but uses only observations before the credit crisis (up to 2008Q2).

-0.6 [ -0.3] 2.2 [ 0.9] -1.9 [ -0.8] 0.8 [ 0.3] -47.9 [ -20.2] 2.5 [ 1.0]

(1)

Table 5: Probability of Mispricing (Pre-Crisis)

1.1 [ 0.1] 0.0 [ 0.0] -1.6 [ -0.2] 0.4 [ 0.0] -97.1 [ -10.9] 0.9 [ 0.1] -4.8 [ -0.5] -2.5 [ -0.3] -1.7 [ -0.2] -23.2 [ -2.6]

0.2 [ 0.0] 0.6 [ 0.0] -1.3 [ -0.1] 0.4 [ 0.0] -92.5 [ -6.9] 0.7 [ 0.1] -4.8 [ -0.4] -2.1 [ -0.2] -1.5 [ -0.1] -20.3 [ -1.5] 0.4 [ 0.0] 0.1 [ 0.0] 305.9 [ 22.9] 62.4 [ 4.7]

1.3 [ 0.0] -0.3 [ -0.0] -1.3 [ -0.0] 0.4 [ 0.0] -126.3 [ -3.8] 1.2 [ 0.0] -3.6 [ -0.1] -1.9 [ -0.1] -1.7 [ -0.1] -18.9 [ -0.6]

Overall Marginal Effects (%) (2) (3) (4)

0.7 [ 0.0] -0.0 [ -0.0] -1.1 [ -0.0] 0.3 [ 0.0] -116.8 [ -2.2] 1.0 [ 0.0] -3.4 [ -0.1] -1.6 [ -0.0] -1.4 [ -0.0] -17.1 [ -0.3] 0.3 [ 0.0] 0.1 [ 0.0] 157.4 [ 3.0] -16.0 [ -0.3]

(5)

Table 6: Regression Analysis This table presents OLS regression of the yield spreads on several explanatory variables (defined in Table 3). The top panel uses only negative spreads; the bottom panel uses non-negative spreads. Panel A: Admissible Trades Return (1m) Log Moneyness Volatility

0.0016 (0.09) -.0292 (-1.82)∗ -.9551 (-4.58)∗∗∗

0.0066 (0.29) -.0391 (-4.78)∗∗∗ -.6848 (-3.13)∗∗∗ -.0095 (-2.01)∗ 0.0027 (1.92)∗ -.0122 (-2.37)∗∗ 0.0216 (1.87)∗ 0.0257 (2.12)∗∗ 0.0012 (0.60)

0.0040 (0.20) -.0169 (-1.56) -.0136 (-0.07) -.0088 (-2.21)∗∗ -.0012 (-1.08) 0.0047 (2.71)∗∗∗ -.0074 (-0.47) 0.0214 (3.64)∗∗∗ -.0025 (-1.45)

-.0097 (-0.61) -.0613 (-7.88)∗∗∗ -1.533 (-6.79)∗∗∗ -.0046 (-0.87) 0.0028 (2.47)∗∗ -.0049 (-1.67) 0.0377 (2.66)∗∗ 0.0510 (4.43)∗∗∗ 0.0039 (2.34)∗∗

-.0102 (-0.75) -.0334 (-7.48)∗∗∗ -.4486 (-1.99)∗ -.0097 (-1.44) -.0013 (-1.35) 0.0051 (4.32)∗∗∗ -.0374 (-3.73)∗∗∗ -.0181 (-0.93) -.0006 (-0.61)

0.24 10,837

0.45 8,535

0.79 8,535

0.63 8,535

0.87 8,535

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs.

Panel B: Violations Return (1m) Log Moneyness Volatility

-.0242 (-5.44)∗∗∗ -.0035 (-0.48) 0.3005 (1.67)

-.0265 (-4.49)∗∗∗ 0.0019 (0.22) 0.2179 (0.91) -.0078 (-1.29) -.0005 (-0.41) 0.0065 (1.74) -.0199 (-1.31) -.0191 (-3.09)∗∗∗ 0.0002 (0.21)

-.0184 (-2.77)∗∗ 0.0271 (1.43) 0.6972 (1.38) -.0063 (-2.04)∗ -.0015 (-0.56) 0.0029 (0.45) 0.0102 (0.63) 0.0056 (0.21) 0.0011 (1.21)

0.0101 (0.95) -.0094 (-1.34) -.0988 (-0.48) 0.0041 (0.78) -.0013 (-1.08) -.0001 (-0.03) 0.0111 (0.65) 0.0137 (1.18) 0.0031 (1.86)∗

0.0202 (2.38)∗∗ -.0049 (-0.45) -.2006 (-0.58) -.0008 (-0.13) -.0043 (-2.96)∗∗ -.0013 (-0.42) 0.0422 (6.22)∗∗∗ 0.0557 (4.90)∗∗∗ 0.0022 (1.74)

0.15 718

0.18 631

0.31 631

0.71 631

0.75 631

Issuer

Yr-Mon

Both

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs. Fixed Effects

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) Log Moneyness Volatility

0.0102 (0.45) -.0395 (-2.39)∗∗ -1.640 (-4.39)∗∗∗

0.0171 (0.67) -.0500 (-5.39)∗∗∗ -1.307 (-6.87)∗∗∗ -.0095 (-2.16)∗∗ 0.0027 (2.04)∗∗ -.0088 (-2.13)∗∗ 0.0237 (2.17)∗∗ 0.0364 (3.12)∗∗∗ 0.0035 (2.03)∗∗

0.0117 (0.52) -.0172 (-1.21) -.3862 (-3.43)∗∗∗ -.0109 (-2.28)∗∗ -.0018 (-2.03)∗∗ 0.0048 (5.06)∗∗∗ 0.0012 (0.10) 0.0120 (5.44)∗∗∗ -.0006 (-0.41)

-.0097 (-0.53) -.0663 (-7.58)∗∗∗ -1.926 (-6.57)∗∗∗ -.0051 (-1.10) 0.0032 (2.90)∗∗∗ -.0038 (-1.35) 0.0367 (2.68)∗∗ 0.0551 (4.67)∗∗∗ 0.0045 (2.56)∗∗

-.0054 (-0.30) -.0323 (-6.51)∗∗∗ -.5963 (-3.93)∗∗∗ -.0090 (-1.27) -.0017 (-2.09)∗∗ 0.0051 (6.68)∗∗∗ -.0273 (-2.64)∗∗ -.0089 (-0.53) 0.0004 (0.39)

0.29 8,823

0.53 7,394

0.83 7,394

0.66 7,394

0.89 7,394

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs.

Panel B: Violations Return (1m) Log Moneyness Volatility

-.0088 (-0.64) -.0011 (-0.17) 0.6439 (16.39)∗∗∗

-.0005 (-0.09) 0.0154 (1.55) -.1372 (-0.19) -.0225 (-4.37)∗∗∗ 0.0024 (0.63) 0.0258 (1.09) -.0912 (-0.93) -.0408 (-1.29) 0.0026 (1.56)

0.0130 (1.92)∗ 0.0450 (1.52) -1.724 (-5.69)∗∗∗ 0.0875 (2.98)∗∗ -.0462 (-2.36)∗∗ -.1215 (-2.67)∗∗ 0.8001 (2.61)∗∗ 0.3608 (2.20)∗ 0.0077 (3.70)∗∗∗

0.0098 (0.71) -.0523 (-2.43)∗∗ -2.785 (-2.80)∗∗ -.0233 (-1.99)∗ -.0019 (-1.74) -.0070 (-1.45) -.0002 (-0.03) 0.0366 (2.25)∗ 0.0348 (2.07)∗

0.0098 (0.71) -.0523 (-2.43)∗∗ -2.785 (-2.80)∗∗ -.0233 (-1.99)∗ -.0019 (-1.74) -.0070 (-1.45) -.0002 (-0.03) 0.0366 (2.25)∗ 0.0348 (2.07)∗

0.13 251

0.44 218

0.68 218

0.82 218

0.82 218

Issuer

Yr-Mon

Both

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs. Fixed Effects

34

35

Pseudo R2 N. viol. N. non-viol.

Term Spread

TED Spread

Vix

Mkt Liquidity (D)

Market Leverage

Log Assets

Return (1m)

Log Moneyness

Liquidity Spread

Price Pressure

Rating

Years to Maturity

Years Old

Log Issue Size

Crisis

0.182 616 9,138

4.690 (29.66)∗∗∗ 0.334 (3.95)∗∗∗ 0.878 (14.56)∗∗∗ -0.765 (-15.99)∗∗∗ 0.252 (16.26)∗∗∗ -3.696 (-0.76) 0.974 (19.46)∗∗∗

(1)

0.233 565 8,340

3.974 (18.51)∗∗∗ 0.387 (2.83)∗∗∗ 0.394 (3.46)∗∗∗ -0.805 (-10.72)∗∗∗ 0.234 (6.88)∗∗∗ -31.84 (-5.23)∗∗∗ 0.973 (14.61)∗∗∗ -3.541 (-15.43)∗∗∗ -0.049 (-0.17) -0.764 (-4.67)∗∗∗ -14.33 (-13.78)∗∗∗

(2)

0.236 563 8,314

3.867 (10.40)∗∗∗ 0.289 (2.02)∗∗ 0.515 (4.38)∗∗∗ -0.777 (-10.09)∗∗∗ 0.209 (5.74)∗∗∗ -37.70 (-5.84)∗∗∗ 0.906 (13.15)∗∗∗ -3.700 (-15.21)∗∗∗ 0.177 (0.57) -1.102 (-5.86)∗∗∗ -14.97 (-13.65)∗∗∗ 0.002 (0.01) 0.009 (0.55) 28.473 (2.25)∗∗ 56.975 (3.53)∗∗∗

Model (3)

0.237 565 8,340

4.323 (17.58)∗∗∗ 1.073 (6.88)∗∗∗ -0.065 (-0.51) -1.062 (-13.45)∗∗∗ 0.258 (6.68)∗∗∗ -47.97 (-7.14)∗∗∗ 1.311 (15.55)∗∗∗ -3.552 (-13.53)∗∗∗ 0.265 (0.86) -1.229 (-6.28)∗∗∗ -14.67 (-11.84)∗∗∗

(4)

0.242 563 8,314

4.369 (9.77)∗∗∗ 0.790 (4.62)∗∗∗ 0.317 (2.22)∗∗ -0.994 (-11.90)∗∗∗ 0.208 (4.75)∗∗∗ -69.37 (-8.77)∗∗∗ 1.135 (12.81)∗∗∗ -3.883 (-13.90)∗∗∗ 0.755 (2.26)∗∗ -1.736 (-7.82)∗∗∗ -15.63 (-11.56)∗∗∗ -0.125 (-0.54) 0.011 (0.62) 67.684 (4.71)∗∗∗ 100.87 (5.37)∗∗∗

(5) 15.9 [ 4.6] 1.2 [ 0.3] 3.2 [ 0.9] -2.8 [ -0.8] 0.9 [ 0.3] -13.6 [ -3.8] 3.6 [ 1.0]

(1) 9.8 [ 0.4] 0.9 [ 0.0] 0.9 [ 0.0] -1.8 [ -0.1] 0.5 [ 0.0] -70.1 [ -3.3] 2.1 [ 0.1] -7.8 [ -0.4] -0.1 [ -0.0] -1.7 [ -0.1] -31.5 [ -1.5]

9.4 [ 0.2] 0.6 [ 0.0] 1.1 [ 0.0] -1.7 [ -0.1] 0.5 [ 0.0] -83.0 [ -2.7] 2.0 [ 0.1] -8.1 [ -0.3] 0.4 [ 0.0] -2.4 [ -0.1] -33.0 [ -1.1] 0.0 [ 0.0] 0.0 [ 0.0] 62.7 [ 2.1] 125.4 [ 4.1]

9.3 [ 0.3] 1.9 [ 0.1] -0.1 [ -0.0] -1.9 [ -0.1] 0.5 [ 0.0] -85.6 [ -3.0] 2.3 [ 0.1] -6.3 [ -0.2] 0.5 [ 0.0] -2.2 [ -0.1] -26.2 [ -0.9]

Overall Marginal Effects (%) (2) (3) (4)

9.2 [ 0.1] 1.5 [ 0.0] 0.6 [ 0.0] -1.8 [ -0.0] 0.4 [ 0.0] -128.7 [ -2.4] 2.1 [ 0.0] -7.2 [ -0.1] 1.4 [ 0.0] -3.2 [ -0.1] -29.0 [ -0.5] -0.2 [ -0.0] 0.0 [ 0.0] 125.5 [ 2.3] 187.1 [ 3.5]

(5)

Same as Table 4, but with different matching procedure. For every convertible bond trade we consider all the straight bond trades happening within three hours and select the trade with the highest yield to maturity.

Table 8: Probability of Mispricing (With Maximum Yield)

Table 9: Regression Analysis (With Maximum Yield) Same as Table 6, but with different matching procedure. For every convertible bond trade we consider all the straight bonds trades happening within three hours and select the trade with the highest yield to maturity. Panel A: Admissible Trades Return (1m) Log Moneyness Volatility

0.0013 (0.08) -.0287 (-1.76)∗ -.9669 (-4.58)∗∗∗

0.0055 (0.25) -.0387 (-4.73)∗∗∗ -.6903 (-3.13)∗∗∗ -.0099 (-2.06)∗∗ 0.0027 (1.96)∗ -.0126 (-2.43)∗∗ 0.0219 (1.88)∗ 0.0264 (2.20)∗∗ 0.0012 (0.60)

0.0035 (0.18) -.0157 (-1.42) -.0127 (-0.06) -.0084 (-1.94)∗ -.0012 (-0.94) 0.0045 (2.57)∗∗ -.0067 (-0.41) 0.0225 (3.91)∗∗∗ -.0025 (-1.42)

-.0094 (-0.61) -.0604 (-7.89)∗∗∗ -1.530 (-6.80)∗∗∗ -.0050 (-0.94) 0.0028 (2.46)∗∗ -.0053 (-1.80)∗ 0.0381 (2.67)∗∗ 0.0511 (4.41)∗∗∗ 0.0039 (2.33)∗∗

-.0098 (-0.76) -.0326 (-7.34)∗∗∗ -.4432 (-1.99)∗ -.0095 (-1.43) -.0013 (-1.28) 0.0047 (4.22)∗∗∗ -.0370 (-3.68)∗∗∗ -.0186 (-0.96) -.0006 (-0.57)

0.24 10,888

0.45 8,585

0.79 8,585

0.64 8,585

0.87 8,585

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs.

Panel B: Violations Return (1m) Log Moneyness Volatility

-.0271 (-4.37)∗∗∗ -.0046 (-0.78) 0.2888 (1.92)∗

-.0301 (-3.88)∗∗∗ 0.0015 (0.21) 0.2437 (1.24) -.0066 (-1.32) -.0007 (-0.53) 0.0057 (1.78) -.0213 (-1.50) -.0213 (-3.81)∗∗∗ -.0006 (-0.61)

-.0239 (-3.21)∗∗∗ 0.0247 (1.58) 0.6701 (1.77) -.0066 (-2.43)∗∗ -.0005 (-0.25) 0.0050 (1.10) 0.0063 (0.45) -.0043 (-0.24) 0.0001 (0.15)

0.0054 (0.50) -.0060 (-0.96) 0.0096 (0.05) 0.0045 (0.78) -.0013 (-1.14) 0.0000 (0.00) 0.0068 (0.40) 0.0146 (1.28) 0.0021 (1.17)

0.0139 (1.81)∗ -.0041 (-0.33) 0.0705 (0.26) -.0030 (-0.40) -.0038 (-1.52) -.0006 (-0.13) 0.0340 (7.45)∗∗∗ 0.0534 (2.49)∗∗ 0.0012 (0.60)

0.18 667

0.20 581

0.32 581

0.70 581

0.75 581

Issuer

Yr-Mon

Both

Issue Size Spread Age Spread Maturity Spread Both Callable Call-NoCall Liquidity Spread Adj. R2 Obs. Fixed Effects

36

Table 10: Trading Strategy (OLS) This table presents the mean, standard deviation, and Sharpe Ratio of the monthly returns produced by the long-short trading strategy. The table also reports ordinary least squares (OLS) coefficient estimates of the FF three factor model augmented with the momentum factor. Each panel reports strategies with different allowed holding periods. Within each panel, we consider different opening/closing signals for the strategy positions. O/C

Mean

SD

SR

α

βM KT

βHM L

βSM B

βU M D

R2

0.0102 ( 1.32) 0.0103 ( 1.35) 0.0085 ( 1.57) 0.0073 ( 1.40)

0.0994 ( 0.54) 0.1193 ( 0.65) 0.1552 ( 1.14) 0.1360 ( 1.03)

-0.0852 ( -0.25) -0.1124 ( -0.33) 0.0803 ( 0.32) 0.1307 ( 0.55)

0.0982 ( 0.32) 0.0955 ( 0.32) -0.0783 ( -0.36) -0.0752 ( -0.35)

-0.2578 ( -1.78) -0.2594 ( -1.81) -0.2250 ( -2.10) -0.2330 ( -2.24)

0.07

0.0106 ( 1.57) 0.0084 ( 1.18) 0.0077 ( 1.35) 0.0070 ( 1.22)

0.1352 ( 0.81) 0.1198 ( 0.67) 0.1774 ( 1.23) 0.1935 ( 1.32)

0.0328 ( 0.11) -0.0035 ( -0.01) 0.1449 ( 0.55) 0.1337 ( 0.51)

-0.0803 ( -0.29) -0.0855 ( -0.29) -0.2190 ( -0.93) -0.2214 ( -0.93)

-0.2599 ( -1.94) -0.2753 ( -1.91) -0.2245 ( -1.96) -0.2453 ( -2.10)

0.0109 ( 1.78) 0.0100 ( 1.61) 0.0091 ( 1.81) 0.0081 ( 1.59)

0.0715 ( 0.46) 0.0957 ( 0.61) 0.1313 ( 1.00) 0.1440 ( 1.09)

0.0488 ( 0.17) 0.0736 ( 0.26) 0.1183 ( 0.50) 0.1289 ( 0.55)

-0.0471 ( -0.19) -0.0815 ( -0.32) -0.1795 ( -0.85) -0.1796 ( -0.85)

-0.2841 ( -2.32) -0.2844 ( -2.27) -0.2473 ( -2.38) -0.2410 ( -2.30)

0.0066 ( 1.24) 0.0066 ( 1.26) 0.0064 ( 1.30) 0.0058 ( 1.16)

0.1219 ( 0.88) 0.1411 ( 1.04) 0.1589 ( 1.22) 0.1753 ( 1.35)

0.2064 ( 0.84) 0.2146 ( 0.89) 0.2146 ( 0.93) 0.2241 ( 0.97)

-0.1388 ( -0.63) -0.1736 ( -0.80) -0.2272 ( -1.09) -0.2221 ( -1.07)

-0.2725 ( -2.50) -0.2733 ( -2.54) -0.2581 ( -2.51) -0.2597 ( -2.54)

Maximum Holding Period: 90 days 0/0.5

0.0118

0.0719

0.1438

0/1

0.0115

0.0716

0.1406

0.5/0.5

0.0108

0.0551

0.1688

0.5/1

0.0097

0.0538

0.1527

0.07 0.10 0.11

Maximum Holding Period: 180 days 0/0.5

0.0127

0.0675

0.1652

0/1

0.0101

0.0726

0.1194

0.5/0.5

0.0102

0.0594

0.1460

0.5/1

0.0092

0.0605

0.1270

0.07 0.06 0.09 0.10

Maximum Holding Period: 360 days 0/0.5

0.0131

0.0633

0.1845

0/1

0.0122

0.0647

0.1675

0.5/0.5

0.0115

0.0550

0.1823

0.5/1

0.0106

0.0553

0.1641

0.08 0.08 0.09 0.10

Maximum Holding Period: 720 days 0/0.5

0.0092

0.0579

0.1335

0/1

0.0091

0.0574

0.1327

0.5/0.5

0.0090

0.0552

0.1368

0.5/1

0.0085

0.0552

0.1259

37

0.11 0.11 0.12 0.13

Table 11: Trading Strategy (GLS) Same as Table 10, except that the factor model estimates are obtained as β = (X 0 W X)−1 (X 0 W R), 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 on the diagonal are given by 1/nt , where nt is equal to the size of 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 . O/C

Mean

SD

SR

α

βM KT

βHM L

βSM B

βU M D

R2

0.0117 ( 1.19) 0.0117 ( 1.22) 0.0099 ( 1.52) 0.0078 ( 1.24)

0.0280 ( 0.09) 0.0564 ( 0.19) 0.1981 ( 0.88) 0.1164 ( 0.53)

-0.3695 ( -0.78) -0.4008 ( -0.86) 0.0666 ( 0.21) 0.2019 ( 0.64)

0.4042 ( 0.83) 0.4592 ( 0.95) -0.0670 ( -0.20) -0.0417 ( -0.13)

-0.2770 ( -1.03) -0.2857 ( -1.07) -0.1443 ( -0.73) -0.1734 ( -0.90)

0.04

0.0181 ( 2.32) 0.0110 ( 1.29) 0.0104 ( 1.55) 0.0099 ( 1.43)

0.0347 ( 0.14) -0.0600 ( -0.20) 0.1098 ( 0.48) 0.1307 ( 0.54)

-0.0379 ( -0.10) -0.1610 ( -0.36) 0.2074 ( 0.62) 0.2015 ( 0.60)

0.1301 ( 0.33) 0.2722 ( 0.62) -0.1019 ( -0.29) -0.0928 ( -0.26)

-0.3618 ( -1.63) -0.3637 ( -1.42) -0.1829 ( -0.93) -0.2694 ( -1.27)

0.0192 ( 2.76) 0.0173 ( 2.36) 0.0162 ( 2.73) 0.0165 ( 2.65)

-0.1594 ( -0.69) -0.0981 ( -0.40) -0.0164 ( -0.08) -0.0599 ( -0.28)

0.0524 ( 0.15) 0.0980 ( 0.26) 0.1944 ( 0.65) 0.2307 ( 0.75)

-0.0004 ( -0.00) 0.0254 ( 0.07) -0.1741 ( -0.58) -0.1755 ( -0.57)

-0.3416 ( -1.75) -0.3562 ( -1.72) -0.2833 ( -1.58) -0.3061 ( -1.66)

0.0120 ( 1.82) 0.0125 ( 1.88) 0.0131 ( 2.03) 0.0136 ( 2.02)

0.0596 ( 0.27) 0.0825 ( 0.37) 0.1245 ( 0.58) 0.1169 ( 0.53)

0.2878 ( 0.87) 0.3030 ( 0.91) 0.3541 ( 1.06) 0.3779 ( 1.11)

-0.0643 ( -0.19) -0.1109 ( -0.32) -0.2201 ( -0.64) -0.2162 ( -0.61)

-0.2298 ( -1.25) -0.2450 ( -1.32) -0.2782 ( -1.43) -0.2892 ( -1.47)

Maximum Holding Period: 90 days 0/0.5

0.0118

0.0719

0.1438

0/1

0.0115

0.0716

0.1406

0.5/0.5

0.0108

0.0551

0.1688

0.5/1

0.0097

0.0538

0.1527

0.04 0.04 0.03

Maximum Holding Period: 180 days 0/0.5

0.0127

0.0675

0.1652

0/1

0.0101

0.0726

0.1194

0.5/0.5

0.0102

0.0594

0.1460

0.5/1

0.0092

0.0605

0.1270

0.05 0.03 0.03 0.04

Maximum Holding Period: 360 days 0/0.5

0.0131

0.0633

0.1845

0/1

0.0122

0.0647

0.1675

0.5/0.5

0.0115

0.0550

0.1823

0.5/1

0.0106

0.0553

0.1641

0.06 0.05 0.05 0.05

Maximum Holding Period: 720 days 0/0.5

0.0092

0.0579

0.1335

0/1

0.0091

0.0574

0.1327

0.5/0.5

0.0090

0.0552

0.1368

0.5/1

0.0085

0.0552

0.1259

38

0.04 0.05 0.06 0.06

Figure 1: Distribution of Yields Spreads This figure shows the difference between the yield to maturity between non-convertible bonds and comparable convertible 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). We obtain the yield spreads by matching all the convertible bond buys with the non convertible bonds buys taking place within three hours of the convertible bond trade. The figure does not show the top and bottom 0.1% of yield spreads.

39

(a) by Bond

(b) by Issuer

Figure 2: Frequency of Violations Over Time This figure plots the time series distribution of violations. Panel a shows the monthly fraction of bonds with at least one violation during that month. Panel b shows that monthly fraction of bond issuers with at least one bond with at least one violation.

40

(a) Full Sample

(b) Vuolations

Figure 3: Yield Differential for Bond Pairs This figure plots the average and median yield spread between convertible bonds and their matched straight bonds. 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 Convergence For each of the two panels, this figure shows the convertible bond ask yield versus the matched straight bond bid yield (top left plot) faced by investors opening a long-short position; the top left plot shows the yield associated with the closing trades. The bottom plots report average daily prices for the bond pair.

42

Figure 5: Market Price Impact of Trading This figure shows the monthly Amihud illiq measure for the group of convertible bonds versus the group of matched non-convertible bonds. The Amihud measure is calculated for each bond on a monthly basis using daily returns from daily average prices divided by daily total turnover in millions of dollars. The monthly group 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 Flow This figure shows trading activity in the two samples of convertible bond versus non-convertible matched bonds. 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 constructed by each month subtracting total dealer sells from total dealer buys which gives a monthly dealer inventory change. The monthly inventory changes is then cumulated over time to give the dealer inventory relative to a position of zero at the inception of the graph. Note that we do not know the starting positions of the dealers and we do not account for primary market activities in the graph. The left graphs are the raw data points and the right graphs are a 6-month smoothed version.

44

(a) Straight bonds

(b) Convertible Bonds

Figure 7: Proportion of Buying Activity by Insurers This figure shows trading activity (all buys) by insurance companies (from NAIC) as a proportion of the total 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 scenarios This figure presents the yields (top graphs) and prices (bottom graphs) over time of a convertible bond and its non-convertible match for Ford Motor CO DEL (Panel a) and Medtronic INC (Panel b). The left graphs compare convertible bond asks with straight bond bid (to open positions); the right graphs compare convertible bond bids with straight bond ask (to close positions).

46

Figure 9: Trading Strategy: Open Positions The plots show 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.

47

Figure 10: Trading Strategy: Monthly Returns For each bond pair, individual monthly returns are obtained by cumulating the daily returns of the long leg and short leg of the trade and then taking the difference. Monthly return is cross-sectional average of the individual monthly returns.

48

Figure 11: Trading Strategy: Cumulative Returns Cumulative 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