*3.2. Performance Index*

The market model was used to measure the short- and long-term performances after the announcement of convertible bonds. OLS was adopted to establish the regression model of individual securities on the market portfolio.

$$R\_{i,t} = \alpha\_i + \beta\_l R\_{m,t} + \varepsilon\_{i,t} \tag{3}$$

where *Ri,t* is the rate of return of the stock of company *i* in day (month) *t*; *Rm,t* is the rate of return of the market portfolio in day (month) *t* regarding the daily (monthly) rate of return of the Taiwan weighted stock index; *α* and *β* are regression coefficients; and *ε* is the error term.

The date (month) of the announcement of the convertible bonds was regarded as the event day (month); 30 days after the announcement was set as the short-term event period; and 60 months after the announcement was regarded as the long-term event period. The period from 31 days to 210 days before the announcement was considered the short-term estimating period and the period from 12 months to 60 months was regarded as the long-term estimating period. A total of 180 days and 49 months comprised the observation period.

Abnormal returns (ARs) was calculated with the actual return in event period minus the expected return estimated by the market model. Mean ARs refers to the mean value of the ARs of all sample companies. The short-term (long-term) cumulative abnormal returns *SCAR0\_t* (*LCAR0\_t*) denote the accumulated AR by company *i* from the day (month) of announcement of convertible bonds, 0, to day (month) *t*. The cumulative mean ARs represent the cumulative value of the mean ARs from the day (month) of announcement of convertible bonds 0 to day (month).

<sup>2</sup> The index measuring the degree of companies' financial constraints were widely used, including by Lamont et al. (2001), Baker et al. (2003), Chen et al. (2007), and Hennessy et al. (2007). In following Whited and Wu (2006), the WW index was included to measure whether a company has financial constraints. The result is consistent with the empirical results.
