4-1 Research Design
The research is carried out in three parts, as follows. In the first, we examine matched TDRs’ stock performances after they listed, and compare the stock performances of matched TDRs with those of the matched stocks listed on the TWSE. Following previous studies26, we use seven indicators that are commonly used by financial analysts and investors to measure financial performance, as described in the following section. We perform a matching procedure to compare the indicators of TDRs and those of their counterparts. We match each TDR with a listed firm in the same industry (based on the industry classification system of the Taiwan Economic Journal) at the end of the year prior to listing (defined as year -1) in order to control for potential operating risks. We then match the sample firms belonging to the same total assets quintile in year -1 to control for potential size effects. Finally, a TDR is matched with its counterpart according to the closest net income in year -1 to control for profitability across firms.
In the second part, we examine the stock performance of full TDRs sample after they listed, and compare it with that of the market.
In the third part, we examine the relation between TDRs’ operating performance and earnings management from year -2 to year 2. The indices of operating performance are return on assets and return on equity, and the index of earnings management is the cross-sectional Jones (1991) model adjusted for lagged return on assets (Kothari 2005), which is used to estimate discretionary accruals.
26 Sharpe (1966), Treynor and Black (1973), Jensen (1968), and Treynor (1966).
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4-2 Measurement Indices
We use seven indices to measure stock performance for our sample firms, which include the standard deviation, Sharpe ratio, beta, information ratio, Jensen’s alpha, Treynor ratio and abnormal returns. Moreover, we use two indices to measure operating performance, which are return on assets and return on equity. Finally, to examine the earnings management of the TDRs, we use a performance-matched modified Jones model (Kothari 2005) to estimate discretionary accruals. We annualize each index in our research, and these are explained in more detail, as follows:
Standard Deviation (SD)
The standard deviation (SD) is a common indicator to measure risk, and it shows how much variation or dispersion there is from the average value. A low standard deviation indicates that the data tend to be close to the mean, while a high standard deviation indicates that the data are spread out over a large range of values. With regard to stock returns, when the standard deviation is higher, then this means that the variation in stock returns in good and bad conditions is bigger, and the risk related to the stocks is greater. The SD is calculated using equation (1).
𝜎𝜎𝑖𝑖 = �∑(𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅����)𝚤𝚤𝑖𝑖 2
𝑛𝑛 − 1 (1)
Where 𝜎𝜎𝑖𝑖 refers to SD for portfolio i. 𝑅𝑅𝑖𝑖𝑖𝑖 represents monthly stock returns of portfolio i in period t, and 𝑅𝑅���� means the average past twelve-month stock returns of 𝚤𝚤𝑖𝑖 portfolio i in period t.
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Sharpe Ratio
The Sharpe ratio is an indicator to measure risk-adjusted performance, first developed by William Sharpe in 1966. This ratio measures the stock returns’ excess risk-free rate per unit of deviation in an investment asset or a portfolio. If the Sharpe ratio is positive, this means that the stock returns are higher than the risk-free rate. In contrast, if the Sharpe ratio is negative, it means that the stock returns are lower than the risk-free rate. The Sharpe ratio is calculated by subtracting the risk-free rate from the stock returns of the portfolio, and dividing the result by the standard deviation of its stock returns, as shown in equation (2).
Sharpe Ratio =𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖
𝜎𝜎𝑖𝑖𝑖𝑖 (2)
Where 𝑅𝑅𝑖𝑖𝑖𝑖 represents the yearly stock returns of portfolio i in period u, and 𝑅𝑅𝑓𝑓𝑖𝑖 represents the risk-free rate in period u. We use the one-year certificate of deposit rate in the Bank of Taiwan as the risk-free rate. 𝜎𝜎𝑖𝑖𝑖𝑖 refers to standard deviation of portfolio i over the period u.
Beta
The beta is an indicator to evaluate the systematic risk of stocks, and it indicates the degree to which investments and broad market conditions are related. Positive betas mean that the returns on investments are positively correlated, while negative betas mean that there is a negative relationship between them. We calculate beta using equation (3).
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𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖 = 𝛼𝛼𝑖𝑖 + 𝛽𝛽𝑖𝑖�𝑅𝑅𝑚𝑚𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖� + 𝜀𝜀𝑖𝑖𝑖𝑖 (3) Where 𝑅𝑅𝑖𝑖𝑖𝑖 represents the monthly stock returns of portfolio i in period t, and 𝑅𝑅𝑓𝑓𝑖𝑖 is the monthly risk-free rate (computed from the one-year certificate of deposit rate in the Bank of Taiwan). 𝑅𝑅𝑚𝑚𝑖𝑖 is the monthly returns of the market in period t. 𝛼𝛼𝑖𝑖 is the intercept, 𝜀𝜀𝑖𝑖𝑖𝑖 is the residual error, and 𝛽𝛽𝑖𝑖 is the beta of portfolio i.
Information ratio (IR)
The widely used information ratio (IR) was developed by Treynor and Black (1973), and measures whether the stock returns exceed an appropriate benchmark relative to the standard deviation of the excess returns. We use industrial stocks as a benchmark in order to effectively eliminate industrial risk, leaving only risk in relation to the management.
Therefore, the IR shows how a manager has performed per unit of active risk. When it is positive, this means the managers outperform the other firms in the same industry. In contrast, if it is negative this means that the managers underperform the other firms in the same industry. It is computed as the stock returns minus the industrial returns, and divided by the standard deviation of those excess returns, using the formula in equation (4).
Information ratio =∑(𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑠𝑠𝑖𝑖)
𝜎𝜎(𝑅𝑅𝑖𝑖𝑖𝑖−𝑅𝑅𝑠𝑠𝑖𝑖) (4)
Where 𝑅𝑅𝑖𝑖𝑖𝑖 represents the monthly stock returns of portfolio i in period t, and 𝑅𝑅𝑠𝑠𝑖𝑖
is the average industrial returns. 𝜎𝜎(𝑅𝑅𝑖𝑖𝑖𝑖−𝑅𝑅𝑠𝑠𝑖𝑖) refers to the standard deviation of those excess returns.
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Jensen’s alpha
Jensen’s alpha was defined by Michael Jensen (1968), and is used to determine the excess returns of securities over the theoretical returns. A positive Jensen’s alpha means the manager’s skill or privileged information has made a positive contribution to a portfolio’s excess returns. This indicator is calculated using equation (5).
𝛼𝛼𝑖𝑖 = 𝑅𝑅���� − �𝑅𝑅𝚤𝚤𝑖𝑖 𝑓𝑓𝑖𝑖+ 𝛽𝛽𝑖𝑖�𝑅𝑅����� − 𝑅𝑅𝑚𝑚𝑖𝑖 𝑓𝑓𝑖𝑖�� (5)
Where 𝑅𝑅���� represents average stock returns computed from past twelve months of 𝚤𝚤𝑖𝑖 portfolio i in period t, and 𝑅𝑅𝑓𝑓𝑖𝑖 is the average monthly risk-free return rate (computed from the one-year certificate of deposit rate in the Bank of Taiwan). 𝑅𝑅����� is the average 𝑚𝑚𝑖𝑖 monthly market returns from the past twelve months in period t. 𝛽𝛽𝑖𝑖 is the weighted-average systematic risk of portfolio i. 𝛼𝛼𝑖𝑖 is Jensen’s alpha.
Treynor Ratio (TR)
The Treynor ratio named after Jack L. Treynor (1966), and is defined as the excess return of stocks per unit of weighted-average systematic risk (beta), the weight of each risk loading being the value of the corresponding risk premium. A higher TR represents better performance by the stocks under analysis. This is calculated using equation (6).
𝑇𝑇𝑅𝑅𝑖𝑖𝑖𝑖 = 𝑅𝑅𝑖𝑖𝑖𝑖− 𝑅𝑅𝑓𝑓𝑖𝑖
𝛽𝛽𝑖𝑖𝑖𝑖 (6)
Where 𝑇𝑇𝑅𝑅𝑖𝑖𝑖𝑖 represents the Treynor ratio of portfolio i in period u. 𝑅𝑅𝑖𝑖𝑖𝑖 means the
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yearly stock returns, while 𝑅𝑅𝑓𝑓𝑖𝑖 means the yearly risk-free rate (the one-year certificate of deposit rate in Bank of Taiwan). 𝛽𝛽𝑖𝑖𝑖𝑖 is the weighted-average systematic risk of portfolio i in period u.
Abnormal Returns (CAPM)
The widely-used single factor capital asset pricing model (CAPM) was developed by Michael Jensen (1968), and is often used to measure the performance of mutual funds and other portfolios, based on a time-series regression to obtain abnormal returns. This is calculated using equations (7) and (8).
E(𝑅𝑅𝑖𝑖𝑖𝑖) = 𝛼𝛼𝑖𝑖+ 𝑅𝑅𝑓𝑓𝑖𝑖+ 𝛽𝛽𝑖𝑖[𝐸𝐸(𝑅𝑅𝑚𝑚𝑖𝑖) − 𝑅𝑅𝑓𝑓𝑖𝑖] (7)
Abnormal Returns = 𝑅𝑅𝑖𝑖𝑖𝑖− E(𝑅𝑅𝑖𝑖𝑖𝑖) (8)
Equation (7) states that the expected returns of portfolio i in period t E(𝑅𝑅𝑖𝑖𝑖𝑖) , using the average value for companies in the same industry as the benchmark, equals the Jensen’s alpha plus risk-free rate (the one-year certificate of deposit rate in the Bank of Taiwan) 𝑅𝑅𝑓𝑓𝑖𝑖, plus the portfolio’s market beta 𝛽𝛽𝑖𝑖, multiplied by the expected excess returns of the market over the risk-free rate 𝑅𝑅𝑓𝑓𝑖𝑖, as [𝐸𝐸(𝑅𝑅𝑚𝑚𝑖𝑖) − 𝑅𝑅𝑓𝑓𝑖𝑖]. In equation (8), the abnormal returns equal the actual stock returns of portfolio i in period t 𝑅𝑅𝑖𝑖𝑖𝑖 minus the expected returns of portfolio i in period t E(𝑅𝑅𝑖𝑖𝑖𝑖).
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Return on assets (ROA)
Return on assets (ROA) measures how profitable a company is using its total assets.
Companies can use both debt and equity to acquire their assets, and ROA determines how effectively companies turn their funding into earnings. A higher ROA is better, as it means that a company is using its assets more efficiently. We calaulate ROA using equation (9).
ROA =COI + IE × (1 − 𝑇𝑇𝑇𝑇𝑇𝑇)
Asset × 100% (9)
Where ROA refers to return on assets (TEJ item: 0101), COI is continuing operating income (TEJ item: 3920), IE represents interest expenses (TEJ item: 3510), TAX is the tax rate, which is 25% and 17% before and after 2010, respectively. Asset represents average total assets (TEJ item: 0010).
Return on equity (ROE)
Return on equity (ROE) measures the rate of return on the equity of the common stock owners, and it assesses how efficeintly a company can generate profits from the funds that stockholders have invested. A higher ROE is better, as it means that a company is using its these funds more efficiently. We calaulate ROE using equation (10).
ROE = COI
Equity × 100% (10)
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Where ROE refers to return on equity (TEJ item: 0103), COI is continuing operating income (TEJ item: 3920), and Equity represents average stockholders’ equity (TEJ item:
2000).
The Performance-matched Modified Jones Model (2005)
Kothari et al (2005) developed a model of discretionary accruals plus an additional discretionary accrual measurement including return on assets (ROA), as show in equation (11). The prediction error from equation (11) serves as the proxy for discretionary accruals in year t. Nondiscretionary accruals are the difference between total accruals and discretionary accruals.
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖𝑡𝑡
𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡 = 𝛼𝛼1 1
𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡+ 𝛼𝛼2𝑃𝑃𝑃𝑃𝐸𝐸𝑖𝑖𝑖𝑖𝑡𝑡
𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡+ 𝛼𝛼3∆𝑅𝑅𝐸𝐸𝑅𝑅𝑖𝑖𝑖𝑖𝑡𝑡
𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡 + 𝛼𝛼4𝑅𝑅𝑅𝑅𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡
𝑇𝑇𝑖𝑖−1,𝑖𝑖𝑡𝑡 + 𝜀𝜀𝑖𝑖𝑖𝑖𝑡𝑡 (11)
Where TAtij is total accruals in year t of the firm i in the industry j, measured as the difference between income before extraordinary items (TEJ item: 3930) and cash flow from operations (TEJ item: 7210) in year t. At−1,ij is total assets (TEJ item: 0010) at the beginning of year t of firm i in the industry j. PPEtij means gross property, plant, and equipment at the end of the year t of firm i in industry j. We compute PPEtij using net property, plant, and equipment (TEJ item: 0400) minus accumulated depreciation on property, plant, and equipment (TEJ item: 0486). ∆𝑅𝑅𝐸𝐸𝑅𝑅𝑖𝑖𝑖𝑖𝑡𝑡 is revenue (TEJ item: 3100) in year t less revenues in year t-1 of firm i in industry j, and ROAt−1,ij is lagged return on assets (TEJ item: 0101) at year t-1 of firm i in industry j. , , and represent the parameters to be estimated, and represents discretionary accruals.
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4-3 Sample Selection and Descriptive Statistics
The TDR data is obtained from the Taiwan Economic Journal (TEJ) for the period between 1997 and 2012. We choose 1997 as the initial sample year because it is the earliest year for which TEJ provides TDR data. All sample firms need to have all the required data for at least one year before and after secondary listing (year-1, 0, 1). There are 37 TDRs that meet this criterion in our sample.
The reason we use firm-years but not firm-quarters is because there are too many missing values in the TEJ quarterly data for TDRs. We consider year 0 as a pre-listing year, and this approximation regards all TDRs as being listed on the last day of the year.
However, since the actual listings occurred at various points during year 0, the noise due to this approximation is one limitation of our tests.
Table 7 summarizes the sample selection procedure. For the period 1997-2012 there are 271 observations with financial and stock returns merged data available on the TEJ, corresponding to 37 distinct TDR firms. We drop two firm-years (0 TDR firms) because the required financial data are unavailable, reducing the sample size to 269 observations (37 TDR firms). We delete three firm-years (0 TDR firms) for which the samples are in the top and bottom 1% of assets, sales, equity and yearly returns. Next, we remove one TDR firm (four firm-years) with financial data for less than three years (year -1, 0, 1).
This reduces the sample size to 265 firm-years corresponding to 36 TDR firms. We then delete four TDR firms (28 firm-years) because no matching firms could be found. The final sample thus consists of 237 firm-years, corresponding to 32 TDR firms.
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TABLE 7 Sample Selection
Criterion
Number of Firm Years
Number of Distinct Firms Preliminary merged TDRs with financial and stock
returns data available on TEJ (1997-2012)
271 37
Less: observations without the required data (2) (0)
Data available 269 37
Less: the samples in the top and bottom 1% of assets, sales, equity and yearly returns
(3) (0)
Data available 266 37
Less: observations deleted because they have data for less than three years (-1, 0, 1)
(1) (1)
Data available 265 36
Less: control firms unavailable (28) (4)
Final Sample 237 32
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Table 8 presents the distribution of the sample firms across industry (Panel A) and time (Panel B). As the results in Panel A indicate, our sample spans 11 different two digit SIC codes. Among the industries that are well represented are Food (SIC 12) with 27 observations (11.4 percent), Textiles (SIC 14) with eight observations (3.4 percent), Electric Machinery (SIC 15) with seven observations (3.0 percent), Electric Appliances and Cables (SIC 16) with six observations (2.5 percent), Chemical Biotechnology Medicine (SIC 17) with 20 observations (8.4 percent), Iron and Steel (SIC 20) with nine observations (3.8 percent), Rubber (SIC 21) with 12 observations (5.1 percent), Motor Vehicles (SIC 22) with six observations (2.5 percent), Electronics (SIC 23) with 114 observations (48.1 percent), General Merchandise Trade (SIC 29) with six observations (2.5 percent), and Others (SIC 99) with 22 observations (9.3 percent). Panel B presents the distribution of the TDRs over the sample period. The number rose significantly after 2007, and then stabilized. As noted earlier, this rise is mostly likely due to the deregulation with regard to TDR carried out in 2008, with 35 TDRs listed over the period 2009-2011, resulting in an increase in the amount of one- to four-year pre-listing financial data on the TEJ since 2007.
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TABLE 8
Industry and Time Sample Distribution Panel A: Industry Distribution
SIC Code Description Firm Years % of Sample
12 Foods 27 11.4
14 Textiles 8 3.4
15 Electric and Machinery 7 3.0
16 Electric Appliances and Cables 6 2.5
17 Biotechnology and Medical Care 20 8.4
20 Steel and Iron 9 3.8
21 Rubber 12 5.1
22 Automobile 6 2.5
23 Electronics 114 48.1
29 Wholesale and Retail 6 2.5
99 Others 22 9.3
237 100.0
Panel B: Time Distribution
Year Firm Years % of Sample
1997 2 0.8
1998 2 0.8
1999 4 1.7
2000 4 1.7
2001 6 2.5
2002 6 2.5
2003 6 2.5
2004 7 3.0
2005 9 3.8
2006 16 6.8
2007 25 10.5
2008 30 12.7
2009 31 13.1
2010 30 12.7
2011 30 12.7
2012 29 12.2
Total 237 100.0
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