_{1}

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I examine convertible bond arbitrageurs’ long-run impact on convertible bond issuers’ stock prices. I find a negative relation between arbitrage activity around convertible bond issues and convertible bond issuers’ long-run stock returns. Average three-year holding period return of convertible bond issuers with no-arbitrage activity around their convertible bond issues is two times larger than that of convertible bond issuers with arbitrage activity around their convertible bond issues. Overall, I show that convertible bond arbitrageurs’ price impact is not limited to short-term [1], but it also has a long-term component.

A convertible bond (CB) is a hybrid security that resembles to regular bond in that it makes fixed coupon payments, and equity in that it gives the bondholder the option to convert the bond into issuer’s stock. CB market in the U.S. has been growing fast. CB issues increased from $15.1 billion in 1993 to $61.6 billion in 2007 [

^{1}Shkilko et al. [

The arbitrageurs’ short selling around CB issues may cause short-term and long-term price pressure.1 The short-lived price pressure caused by arbitrage related short selling is studied extensively in the literature [

By analyzing the returns of convertible debt issuers for 3-year period, I find that holding period returns (HPR) of CB issuers that experience arbitrage activity around their CB issues are 7.80%, 20.32% and 34.83% in 1-, 2-, and 3-year horizons.2 On the other hand, HPRs of CB issuers that do not experience arbitrage activity around their CB issues are 40.22%, 61.07% and 70.03% in 1-, 2-, and 3-year horizons. Average three-year HPR of CB issuers with no-arbitrage activity around their CB issues is two times larger than that of CB issuers with arbitrage activity around their CB issues.3 A wealth relative comparison also shows that, except 6-month horizon, the no-arbitrage sample’s stock returns outperform the arbitrage sample’s stock returns from 1^{st} month of issue to 36^{th} month.

In a multivariate analysis, I examine the relation between the CB arbitrage activity and future stock price movements of CB issuers. Interestingly, I find a negative relation between CB issuers’ stock returns and CB arbitrage activity in long-run. The coefficients of the CB arbitrage proxies are (−0.098), (−0.0806), (−0.0669), (−0.0666), and (−0.0551) in 1-, 2-, 6-, 12-, and 18-month periods in multivariate analysis. The magnitudes of the coefficients are decreasing in time. CB arbitrage proxy has a marginally significant negative impact in 24-month period and after 24 months impact completely disappears.

^{2}Following Choi et al. [

^{3}From here on, I refer CB issuers with (no-)arbitrage activity around their CB issues as (no-) arbitrage sample.

A possible explanation for the long-run price impact of CB arbitrage activity on CB issuers’ stock prices is the following. As Choi et al. [

This study contributes to short selling, convertible bond, and convertible bond arbitrage literature. One line of research documents that short sellers’ actions predict short-run stock returns [

The paper proceeds as follows. Section 2 presents hypothesis development and related literature. Section 3 describes data and sample selection. Section 4 explains the long-run price performance measures. Section 5 presents and discusses the findings of paper. Section 6 concludes.

Arbitrage related short selling around CB issues creates price pressure. For example, due to arbitrage induced short selling CB issuers experience negative abnormal stock returns around CB issues [

^{4}Convertible bond arbitrage has two phases, in the first phase hedge funds buy convertible bond at issue and short the underlying stock. In the second phase, arbitrageurs adjust their positions by shorting the stock if prices go up and buy it if prices go down [

Hypothesis 1: Arbitrage induced short selling around convertible bond offerings have negative long-run impact on CB issuers’ stock prices.

The sample consists of all convertible bond issues (public, private, and Rule 114a) by U.S. publicly traded firm from Jan-2006 to Dec-2012.5 I obtain accounting data from the Compustat Fundamentals Annual database, stock price related data from the Center for Research in Security Prices and convertible bond offerings from the Securities Data Corporation Database. Choi et al. [_{t}, which is the change in short interest (number of shares) during the period t, scaled by total shares outstanding in period t − 1. The change in short interest is the difference between short interest in month t and short interest during month t − 1.

Specifically, I obtain monthly short interest data of convertible debt issuers from the Compustat Supplemental Short Interest Files from Jan-2006 to Dec-2012. Following Choi et al. [^{th} of each month), I match the issue date with short interest for that month. Otherwise, the short-interest data for the next month is matched to the issue month. Since September 2007 short interest data is reported twice in month, I adjust my algorithm to bi-monthly reporting starting that month. I normalize the change in short interest by the number of shares outstanding measured on trading date-20 relative to the convertible bond issue date.

_{t}) is positive then the firm is included in arbitrage sample, otherwise firm is included in non-arbitrage sample.

The long-run price performance measures are calculated following Ritter [

^{5}This is the period I have access to the short-interest data.

Monthly market adjusted returns are calculated as the monthly raw return on a stock minus the monthly CRSP value-weighted market index for the corresponding

Issue year | Number of issues | Change in short interest | Shares outstanding | ||
---|---|---|---|---|---|

Year | N | Mean | Std. Dev. | Mean | Std. Dev. |

2006 | 69 | 0.8853 | 3.3365 | 182,111.68 | 387,055.46 |

2007 | 79 | 2.0595 | 3.2143 | 115,093.06 | 214,482.7 |

2008 | 67 | 1.2382 | 2.6363 | 176,394.45 | 357,651.76 |

2009 | 78 | 1.9771 | 2.7208 | 251,544.17 | 776,325.63 |

2010 | 59 | 0.8251 | 5.2471 | 638,575.61 | 1,838,559.92 |

2011 | 57 | 1.9653 | 2.1677 | 627,543.61 | 3,836,712.22 |

2012 | 60 | 1.6867 | 2.3589 | 139,105.15 | 211,435.88 |

This table represents number of convertible debt issues per year from 2006 to 2012. N is the number of issuers. Change in short interest is calculated by following Choi et al. [

21-trading-day period. The market adjusted return for stock i in month t is defined as:

a r i , t = r i , t − r m , t , (1)

where r i , t is raw return of the firm i month t and r m , t is the CRSP value-weighted market return in month t.

The average market-adjusted return on a portfolio of n stocks for month t is the equally-weighted arithmetic average of the market-adjusted returns:

A R t = 1 n ∑ i = 1 n ( r i , t − r m a r k e t , t ) , (2)

where r i , t is the total return on the issuer firm in event month t, and r m a r k e t , t is the return on CRSP value-weighted market portfolio. The t-statistics are calculated as A R t * n t / S d t , where AR_{t} is the average market adjusted return for month t.

The cumulative market adjusted returns from month q to month s is the summation of the average market-adjusted returns:

C A R q , s = ∑ t = q s A R t (3)

Following Ritter [

H P R t = ∏ t = 1 n ( 1 + r i , t ) − 1 , (4)

where r i , t is the daily return on stock i.

To have a clear interpretation of holding period return, in the spirit of Ritter [

W R t = 1 + average t month total return of no arbitrage firms 1 + average t mont htotal return of arbitrage firms . (5)

A wealth relative greater (less) than 1.00 can be interpreted as no-arbitrage sample outperforms (underperforms) relative to the arbitrage sample.

The results in

Next, I divide the sample into arbitrage and no-arbitrage subsamples and compare the performances of the two subsamples. I calculate the performance measures following Ritter [

Ritter [

Month of CB issuing | AR | t-stat. | Number of issuers | CAR |
---|---|---|---|---|

1 | −0.2297** | −2.17 | 467 | −0.2297 |

2 | −0.1928** | −2.40 | 467 | −0.4225 |

3 | −0.1812** | −2.10 | 466 | −0.6037 |

4 | −0.1090 | −1.60 | 466 | −0.7127 |

5 | −0.0936* | −1.82 | 466 | −0.8063 |

6 | −0.1623* | −1.76 | 466 | −0.9686 |

7 | −0.1152* | −1.70 | 465 | −1.0838 |

8 | −0.0757 | −0.93 | 465 | −1.1595 |

9 | −0.1214* | −1.93 | 465 | −1.2809 |

10 | −0.1388** | −2.28 | 459 | −1.4197 |

11 | −0.0734 | −0.67 | 457 | −1.4931 |

12 | −0.1918** | −2.28 | 457 | −1.6849 |

13 | −0.1494** | −2.42 | 455 | −1.8343 |

14 | −0.0590 | −0.81 | 447 | −1.8933 |

15 | −0.1181* | −1.96 | 439 | −2.0114 |

16 | 0.0533 | 0.22 | 433 | −1.9581 |

17 | −0.0830* | −1.79 | 421 | −2.0411 |

18 | −0.1249* | −1.78 | 421 | −2.1660 |

19 | 0.1435 | 0.49 | 403 | −2.0225 |

20 | −0.1685** | −2.26 | 396 | −2.1910 |

21 | −0.1219** | −2.20 | 388 | −2.3129 |

22 | 0.9515 | 0.92 | 381 | −1.3614 |

23 | −0.1253* | −1.74 | 376 | −1.4867 |

24 | −0.1499** | −1.99 | 375 | −1.6366 |

26 | 0.5233 | 0.78 | 372 | −1.1133 |

27 | −0.1591 | −1.60 | 368 | −1.2724 |

28 | −0.1169 | −1.55 | 364 | −1.3893 |

29 | −0.1267 | −1.53 | 359 | −1.5160 |

30 | −0.0598* | −1.85 | 358 | −1.5758 |

31 | −0.0418 | −1.09 | 355 | −1.6176 |

32 | −0.0384 | −0.98 | 348 | −1.6560 |

33 | −0.0923 | −1.09 | 339 | −1.7483 |

34 | −0.0803 | −1.59 | 331 | −1.8286 |

35 | −0.1196** | −1.98 | 325 | −1.9482 |

36 | −0.1333** | −2.03 | 312 | −2.0815 |

Average market-adjusted returns (AR) and cumulative average return (CAR), in percent, with associated t-statistics for the 36 months after issuing the convertible debt. A R t = 1 n ∑ i = 1 n ( r i , t − r m a r k e t , t ) , where r i , t is the total return on the issuer firm in event month t, and r m a r k e t , t is the return on CRSP value-weighted market portfolio. The t-statistics are calculated as A R t * n t / S d t , where AR_{t} is the average market adjusted return for month t, n is the number of observations in month t, and Sd_{t} is the cross-sectional standard deviations of the adjusted returns in month t. CAR is the cumulative average adjusted returns in month t. ***, **, and * represent significance at 1%, 5%, and 10% level, respectively.

Month of issuing | No arbitrage sample | Arbitrage sample | Wealth Relative |
---|---|---|---|

1-month | 0.0998 | −0.0128 | 1.1141 |

3-month | 0.0297 | −0.0253 | 1.0564 |

6-month | 0.0769 | 0.1296 | 0.9533 |

9-month | 0.2520 | 0.1036 | 1.1345 |

12-month | 0.4022 | 0.078 | 1.3007 |

15-month | 0.2790 | 0.1647 | 1.0981 |

18-month | 0.3245 | 0.1966 | 1.1069 |

21-month | 0.3180 | 0.1869 | 1.1105 |

24-month | 0.6107 | 0.2032 | 1.3387 |

27-month | 0.6282 | 0.2298 | 1.3240 |

30-month | 0.7131 | 0.2493 | 1.3712 |

33-month | 0.6623 | 0.3245 | 1.2550 |

36-month | 0.7003 | 0.3483 | 1.2611 |

For each time period holding period return is calculated as H P R t = ∏ t = 1 n ( 1 + r i , t ) − 1 , where r i , t is the daily return on stock i. Arbitrage sample is the sample of firms that change in short interest (∆SI) is positive, in the no arbitrage sample ∆SI is negative or equals to zero. Wealth relative is calculated, following Ritter [

I also examine the impact of CB arbitrageurs on CB issuers’ stock prices in a multivariate setting. Similar to Ritter [

Return i = b 0 + b 1 Δ S I i + b 2 log ( volume i ) + b 3 market _ r e t i + ε i , (6)

where Return_{i} is the raw return of CB issuer in a given period, measured by using 21 trading days in a given month. ∆SI_{i} the change in short interest (proxy for arbitrage activity) is calculated by following Choi et al. [_{i} is total number of shares traded daily in a given month. Market ret_{i} is the return on the CRSP value weighted market index.

^{6}For robustness I also conduct a risk adjusted return analysis of four factor model, Fama and French [

The first finding of

Variable | Coeff. | t-stat | Variable | Coeff. | t-stat | ||
---|---|---|---|---|---|---|---|

1-month | Intercept | −4.2545*** | −6.80 | 18-month | Intercept | −2.7181*** | −4.02 |

Delta SI. | −0.0978*** | −2.97 | Delta SI. | −0.0551*** | −2.70 | ||

Volume | 0.4057*** | 6.68 | Volume | 0.1591*** | 3.98 | ||

Market ret. | −0.6556 | −0.29 | Market ret. | 2.0396* | 1.76 | ||

R-Square | 0.0997 | R-Square | 0.0576 | ||||

N | 468 | N | 413 | ||||

2-month | Intercept | −4.3042*** | −5.79 | 24-month | Intercept | −4.2256*** | −5.94 |

Delta SI. | −0.0806*** | −3.39 | Delta SI. | −0.0349* | −1.65 | ||

Volume | 0.2520*** | 5.74 | Volume | 0.2460*** | 5.82 | ||

Market ret. | −0.8206 | −0.58 | Market ret. | 0.6817 | 0.63 | ||

R-Square | 0.0852 | R-Square | 0.0902 | ||||

N | 467 | N | 375 | ||||

6-month | Intercept | −4.9289*** | −5.81 | 30-month | Intercept | −2.0104*** | −6.58 |

Delta SI. | −0.0669** | −2.44 | Delta SI. | 0.0056 | 0.62 | ||

Volume | 0.2896*** | 5.77 | Volume | 0.1152*** | 6.36 | ||

Market ret. | 2.9198* | 1.77 | Market ret. | 1.6019*** | 3.38 | ||

R-Square | 0.0811 | R-Square | 0.1279 |

N | 466 | N | 358 | ||||
---|---|---|---|---|---|---|---|

12-month | Intercept | −4.9138*** | −6.26 | 31-month | Intercept | −1.9411*** | −5.27 |

Delta SI. | −0.0666*** | −2.69 | Delta SI. | 0.0021 | 0.20 | ||

Volume | 0.2862*** | 6.16 | Volume | 0.1127*** | 5.15 | ||

Market ret. | 2.2155 | 1.58 | Market ret. | 1.6552*** | 2.76 | ||

R-Square | 0.0933 | R-Square | 0.0868 | ||||

N | 458 | N | 355 |

The regression model is Return i = b 0 + b 1 Δ S I i + b 2 log ( volume i ) + b 3 market _ r e t i + ε i . Return i is the raw return of CB issuers in a given period, measured by using 21 trading days in a given month. ∆SI_{i} the change in short interest is calculated by following Choi et al. [

I examine CB dynamic arbitrageurs’ impacts on CB issuers’ stock prices in long-run. I proxy for arbitrage activity around convertible bond issues applying proxy developed by Choi et al. [

My findings extend short selling literature by documenting that CB arbitrage related short selling can have long-term impacts on stock returns. Hence, examining types of short-sellers can improve our understanding of short-selling activities. I also add to the convertible bond literature by showing that the CB arbitrage activity has a negative long-term effect on stock CB issuers’ stock prices. Finally, my findings contribute to the convertible bond arbitrate literature by documenting that price impact of CB arbitrageurs is not limited to short-term, but it also has a long-term component.

Yildiz, S. (2018) Dynamic Arbitrageurs’ Long-Run Impacts on Convertible Bond Issuers’ Stock Prices. Theoretical Economics Letters, 8, 1553-1564. https://doi.org/10.4236/tel.2018.89099