**3. Methodology**

#### **3.1 Short-term return analysis**

In this section, we assess the short-term performance of IPO ETFs. In this respect, we compute the first day or initial return of ETFs. The first-day return does not necessarily refer to the return on the launch day of ETFs but refers to the return on the first trading day with no-zero volume because an ETF may have started actual trading on the days that followed its listing on the stock exchange.

Three alternative types of initial returns are computed. The first one refers to the absolute return of ETFs, which, based on [38], is defined as the gain or the loss on a portfolio achieved over a certain period without being compared to a reference portfolio or another benchmark. First-day absolute return is computed in percentage terms using the following formula:

$$JAR\_{l,t=1} = \frac{CTP\_{l,t=1} - OPEN\_{i,t=1}}{OPTN\_{i,t=1}} \tag{1}$$

where IAR*i,t* = 1 refers to the percentage absolute return of the *i*th ETF on its first trading day, CTPi,t = 1 refers to the close trade price of the ETF on its first trading day and OPEN*i,t* = 1 refers to the open trade price of this ETF on the same day.

#### *IPO ETFs: An Alternative Way to Enter the Initial Public Offering Business DOI: http://dx.doi.org/10.5772/intechopen.90269*

The second type of initial return computed is the benchmark-adjusted return of ETFs, which, following [7], is computed as the difference between the initial absolute return of the *i*th ETF and the corresponding return of the benchmark. The firstday benchmark-adjusted return of ETFs is shown in the following formula:

$$\text{BAIR}\_{i,t=1} = \text{IR}\_{i,t=1} \text{-BR}\_{t=1} \tag{2}$$

where BAIR*i,t* = 1 refers to percentage benchmark-adjusted return of the *i*th ETF on its first trading day, IR*i,t* = 1 is defined as above and BR*<sup>t</sup>* = 1 concerns the return of the market index on ETF's first trading day.

In our estimations of benchmark-adjusted returns, we employ two alternative stock indices to serve as benchmarks. The first one is the S&P 500 Index, which consists of the 500 largest companies in terms of market capitalization listed on the NYSE or NASDAQ. The second benchmark used is the S&P 600 Small Cap Index, which covers the small-cap range of US stocks. According to [39], indices that consist mostly of small cap companies are better benchmarks when assessing the performance of smaller stocks or portfolios. The S&P 600 Small Cap Index is used because the ETFs that have been selected to be studied are rather small-cap ETFs and, consequently, a small-cap index may be a more appropriate benchmark.<sup>1</sup>

In order to calculate the return of the index, which will correspond to ETF's firstday return, we use formula (1) for indices too. This means that given that the trading history of the selected benchmarks is much longer than the history of the sample's ETFs, we calculate the return of indices on ETF's first trading day by subtracting the open price of the index on the day which relates to ETF's first trading day from its close price on the same day and we divide by the open price.

The third type of initial return estimated is the abnormal return obtained with the usage of the market model. In order to estimate abnormal returns of ETFs, we follow the approach of [40]. More specifically, so as to estimate the abnormal returns of ETFs, we first need to estimate the time series market model expressed in Eq. (3), via which the return of ETFs is successively regressed on the return of the selected market indices:

$$R\_i = a\_i + \beta\_i R\_m + \varepsilon\_i \tag{3}$$

where *Ri* stands for the daily return of the *i*th ETF, *Rm* represents the return of the market index, namely the return of the S&P 500 Index or the S&P 600 Small Cap Index. We estimate market model to obtain the alpha and beta coefficients of each ETF, which we will then use to compute abnormal returns with the following model:

ð1Þ

[21] provides evidence that the initial returns and the long-run performance of IPOs were negatively related during the period 1960–1969. Ritter [7] finds that IPO stocks significantly underperform a set of comparable companies over the 3 years after going public. Rajan and Servaes [22] reveal that over a 5-year period after going public, companies' underperformance relative to the market benchmarks ranges from 17% to 47.1%. Carter et al. [23] estimate an average underperformance of US IPOs over a three-year period after the initial offering of 19.92%. Gompers and Lerner [24] examine the performance for up to 5 years after listing of nearly 3661 IPOs in the US during the period 1935–1972 and find some evidence of underperformance when event time buy-and-hold abnormal returns are used but underperformance disap-

Outside the United Sates, in Australia, How et al. [25] compare the long-run performance of companies going public that payed a dividend and similarly matched firms, which did not pay a dividend revealing strong evidence that the paying firms perform significantly better than the nonpaying firms for a period up to 5 years after the dividend initiation date. Moshirian et al. [26] indicate that in China, Hong Kong, Japan, Korea, Malaysia, and Singapore, whilst there is initial underpricing in Asian IPOs, the existence of long-run underperformance depends on the methodology used. In Japan, Kirkulak [27] reports a three-year underperformance of �18.3% for the stocks listed between 1998 and 2001. In Canada, Kooli and Suret [28] find that investors who buy stocks immediately after their listing and hold these shares for a period of 3 years will incur a loss of about 20%. When a five-year buy-and-hold strategy is considered, underperformance amounts to �26.5%. In the United Kingdom, a number of studies such as those of [17, 29–31] have documented the existence of IPOs' long-run overpricing. Other studies on European IPOs, such as those of [32–34] for Germany, [35] for Austria, [36] for Spain, [18] for Italy, and [37] for France, also reveal significant long-run overpricing of IPOs. Overpricing is evidenced by their poor long-term performance compared to the performance of relevant market indices or reference stock portfolios. Based on these findings, IPOs would not be

In this section, we assess the short-term performance of IPO ETFs. In this respect, we compute the first day or initial return of ETFs. The first-day return does not necessarily refer to the return on the launch day of ETFs but refers to the return on the first trading day with no-zero volume because an ETF may have started actual trading on the days that followed its listing on the stock exchange.

Three alternative types of initial returns are computed. The first one refers to the absolute return of ETFs, which, based on [38], is defined as the gain or the loss on a portfolio achieved over a certain period without being compared to a reference portfolio or another benchmark. First-day absolute return is computed in percent-

where IAR*i,t* = 1 refers to the percentage absolute return of the *i*th ETF on its first trading day, CTPi,t = 1 refers to the close trade price of the ETF on its first trading day and OPEN*i,t* = 1 refers to the open trade price of this ETF on the same day.

pears when cumulative abnormal returns are utilized.

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

suitable for long-term buy-and-hold trading strategies.

**3. Methodology**

**100**

**3.1 Short-term return analysis**

age terms using the following formula:

<sup>1</sup> As we will explain in a following section, each IPO ETF has its own benchmark and, thus, one could wonder why we do not use each ETF's own benchmark to estimate their benchmark-adjusted performance. We do not do so, for two reasons. The first one is that the majority of ETFs worldwide and IPO ETFs in particular are passively managed and, thus, the tracking error of these funds, that is the difference in returns between ETFs and underlying indices, is expected to be low. (We will see in **Table 1** that the tracking error of the sample's ETFs is indeed low.) Therefore, a new ETF's price will also generally remain in line with the price of the underlying basket of securities and an "underpricing" pattern like that observed in IPOs of ordinary stocks is not expected to be the case. The second reason is that we try to identify whether IPO ETFs can be an alternative investing tool of investors seeking returns, which will be better than the average market returns, with the market returns being usually represented by indices such as the two used in our analysis.

$$AR\_{\ell; t=1} = R\_{i, \iota=1} - \hat{\alpha}\_i - \hat{\beta}\_i R\_{m, \iota=1} \tag{4}$$

each ETF (as above). The buy-and-hold return is estimated in percentage terms using a formula similar to formula (5). The key difference between the two calculations concerns the estimation window. This means that, for instance, in the case of the first 6-month period, buy-and-hold return is computed by considering the percentage difference in the close trade prices of the *i*th ETF between the first and the 126th trading day after the month of ETF's listing on the stock exchange, in the case of the 12-month period, buy-and-hold return is computed by considering the percentage difference in the close trade price of the *i*th ETF between the first and the 252nd trading day after the month of ETF's listing, and so on. A last note is that, similarly to cumulative returns, we estimate the buy-and-hold return in its absolute,

*IPO ETFs: An Alternative Way to Enter the Initial Public Offering Business*

The risk-adjusted performance of IPO ETFs is evaluated in this section with the usage of an augmented Fama and French model. This model is based on the model developed by [42] to which the [43] Momentum factor, a Conservative Minus Aggressive factor and a Robust Minus Weak factor have been added. The model is

where *Ri* and *Rm* are defined as above, *Rf* is the risk-free rate expressed by the 1 month US Treasury bill rate, SMB (Small Minus Big) is the average return on nine small cap portfolios minus the average return on nine big cap portfolios, HML (high minus low) is the average return on two value portfolios (in book-to-market equity terms) minus the average return on two growth portfolios, UMD is the average of the returns on two (big and small) high prior return portfolios minus the average of the returns on two low prior return portfolios,<sup>2</sup> CMA (Conservative Minus Aggressive) is the average return on two conservative portfolios minus the average return on two aggressive portfolios and RMW (Robust Minus Weak) is the average return on two robust operating profitability portfolios minus the average return on 2-weak

In the [42] model, the size effect implies that small cap firms exhibit returns that are superior to those of large firms. Theoretical explanations for the small size effect suggest that the stocks of small firms are less liquid and trading in them generates greater transaction costs; there is also less information available on small companies and, thus, the monitoring cost of a portfolio with small stocks is generally greater

The book-to-market equity ratio effect captured by the HML factor implies that the average returns on stocks with a high book-value to market-value equity ratio must be greater than the returns on stocks with a low book-value to market-value equity ratio. The high book-value firms are considered to be underpriced by the market and, therefore, they constitute appealing buy-and-hold targets, as their

<sup>2</sup> Big means that a firm is above the median market cap on the NYSE at the end of the previous day while

<sup>3</sup> The historical daily data of the risk-free rate, the Fama and French three factors, the Carhart momentum factor, the robust minus weak factor and the conservative minus aggressive factor are available on the website of Kenneth French (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/

 <sup>þ</sup> *<sup>β</sup><sup>2</sup>*,*iSMB* <sup>þ</sup> *<sup>β</sup><sup>3</sup>*,*iHML* <sup>þ</sup> *<sup>β</sup><sup>4</sup>*,*iUMD* <sup>þ</sup> *<sup>β</sup><sup>5</sup>*,*iCMA* þ *β<sup>6</sup>*,*iRMW* þ *ε<sup>i</sup>* (7)

benchmark-adjusted and abnormal forms.

*DOI: http://dx.doi.org/10.5772/intechopen.90269*

**3.3 Risk-adjusted performance analysis**

shown in Eq. (7):

*Ri* � *Rf* ¼ *α<sup>i</sup>* þ *β<sup>1</sup>*,*<sup>i</sup> Rm* � *Rf*

operating profitability portfolios.<sup>3</sup>

than the cost of a portfolio of large firms.

small firms are below the median NYSE market cap.

data\_library.html).

**103**

where *ARi,t* = 1 is the abnormal return of the *ith* ETF on the first trading day, computed as the difference between the actual absolute return of ETF and the expected return based on the market model on the first trading day, *α*^*<sup>i</sup>* and *β*^ *<sup>i</sup>* are the parameters obtained from the market model. The estimation window of Eq. (4) covers the entire trading history of each ETF up to October 31, 2016.

After calculating the three types of ETFs' initial return, we then compute the average short-term returns of longer periods. More specifically, we compute the average daily returns of ETFs over the first 2, 3, 4, 5, 21 (i.e., 1 month), and 63 (i.e., 3 months) of trading. Similarly to the initial returns, we first calculate the absolute return of each ETF as follows:

$$AR\_{\bar{l},t} = \frac{CTP\_{i,t} - CT\_{i,t-1}}{CTP\_{i,t-1}} \tag{5}$$

where *ARi,t* refers to percentage absolute return of the *i*th ETF on day *t* and CTPi, <sup>t</sup> refers to the close trade price of the ETF on the same day. Afterward, we estimate the benchmark-adjusted and abnormal returns of ETFs using the framework described in formulas (2), (3) and (4) above.

#### **3.2 Long-term return analysis**

The long-run performance of IPO ETFs is assessed in this section. Two types of long-run performance measures are employed in the analysis; cumulative average returns and buy-and-hold returns. The cumulative average return is calculated as in [41]. More specifically, we calculate the average daily return of each ETF for each calendar month during its entire trading history excluding the launch month of ETF and starting from the month that follows the initial trading of the fund. Following [30], we do so to allow for the possibility of price support in the first few trading days. The cumulative average return starting on the first trading day of the month following the listing of the *ith* ETF and extending to T months after the listing is the summation of the average returns in each month:

$$CAR\_l = \sum\_{t=2}^{T} MARR\_t \tag{6}$$

where CARi refers to the cumulative average return of the *i*th ETF and AMRt is the average daily return of the fund in month *t*.

We note that we calculate three alternative types of cumulative returns, which are the cumulative absolute return, the cumulative benchmark-adjusted return and the cumulative abnormal return following the framework described in the previous section. Again, two benchmarks are used; the S&P 500 Index and the S&P 600 Small Cap Index. Moreover, we compute cumulative returns over the first 6 months (i.e., 126 trading days), 12 months (i.e., 252 trading days), 18 months (i.e., 378 trading days), and 24 months (i.e., 504 trading days) of the trading history of each ETF as well as over its entire trading history up to October 31, 2016.

In order to calculate the buy-and-hold return of ETFs, we assume that an investor buys ETF shares on their listing day and holds them up to a specific time interval, which, in our case, ranges from 6 months to the entire trading history of

*IPO ETFs: An Alternative Way to Enter the Initial Public Offering Business DOI: http://dx.doi.org/10.5772/intechopen.90269*

each ETF (as above). The buy-and-hold return is estimated in percentage terms using a formula similar to formula (5). The key difference between the two calculations concerns the estimation window. This means that, for instance, in the case of the first 6-month period, buy-and-hold return is computed by considering the percentage difference in the close trade prices of the *i*th ETF between the first and the 126th trading day after the month of ETF's listing on the stock exchange, in the case of the 12-month period, buy-and-hold return is computed by considering the percentage difference in the close trade price of the *i*th ETF between the first and the 252nd trading day after the month of ETF's listing, and so on. A last note is that, similarly to cumulative returns, we estimate the buy-and-hold return in its absolute, benchmark-adjusted and abnormal forms.

## **3.3 Risk-adjusted performance analysis**

ð4Þ

*<sup>i</sup>* are the

ð5Þ

ð6Þ

where *ARi,t* = 1 is the abnormal return of the *ith* ETF on the first trading day, computed as the difference between the actual absolute return of ETF and the expected return based on the market model on the first trading day, *α*^*<sup>i</sup>* and *β*^

parameters obtained from the market model. The estimation window of Eq. (4)

After calculating the three types of ETFs' initial return, we then compute the average short-term returns of longer periods. More specifically, we compute the average daily returns of ETFs over the first 2, 3, 4, 5, 21 (i.e., 1 month), and 63 (i.e., 3 months) of trading. Similarly to the initial returns, we first calculate the absolute

where *ARi,t* refers to percentage absolute return of the *i*th ETF on day *t* and CTPi, <sup>t</sup> refers to the close trade price of the ETF on the same day. Afterward, we estimate the benchmark-adjusted and abnormal returns of ETFs using the framework

The long-run performance of IPO ETFs is assessed in this section. Two types of long-run performance measures are employed in the analysis; cumulative average returns and buy-and-hold returns. The cumulative average return is calculated as in [41]. More specifically, we calculate the average daily return of each ETF for each calendar month during its entire trading history excluding the launch month of ETF and starting from the month that follows the initial trading of the fund. Following [30], we do so to allow for the possibility of price support in the first few trading days. The cumulative average return starting on the first trading day of the month following the listing of the *ith* ETF and extending to T months after the listing is the

where CARi refers to the cumulative average return of the *i*th ETF and AMRt is

We note that we calculate three alternative types of cumulative returns, which are the cumulative absolute return, the cumulative benchmark-adjusted return and the cumulative abnormal return following the framework described in the previous section. Again, two benchmarks are used; the S&P 500 Index and the S&P 600 Small Cap Index. Moreover, we compute cumulative returns over the first 6 months (i.e., 126 trading days), 12 months (i.e., 252 trading days), 18 months (i.e., 378 trading days), and 24 months (i.e., 504 trading days) of the trading history of each

In order to calculate the buy-and-hold return of ETFs, we assume that an inves-

ETF as well as over its entire trading history up to October 31, 2016.

tor buys ETF shares on their listing day and holds them up to a specific time interval, which, in our case, ranges from 6 months to the entire trading history of

covers the entire trading history of each ETF up to October 31, 2016.

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

return of each ETF as follows:

**3.2 Long-term return analysis**

described in formulas (2), (3) and (4) above.

summation of the average returns in each month:

the average daily return of the fund in month *t*.

**102**

The risk-adjusted performance of IPO ETFs is evaluated in this section with the usage of an augmented Fama and French model. This model is based on the model developed by [42] to which the [43] Momentum factor, a Conservative Minus Aggressive factor and a Robust Minus Weak factor have been added. The model is shown in Eq. (7):

$$\begin{aligned} R\_i - R\_f &= a\_i + \beta\_{1,i} (R\_m - R\_f) + \beta\_{2,i} \text{SMB} + \beta\_{3,i} \text{HML} + \beta\_{4,i} \text{UMD} + \beta\_{5,i} \text{CMA} \\ &+ \beta\_{6,i} \text{RMW} + \varepsilon\_i \end{aligned} \tag{7}$$

where *Ri* and *Rm* are defined as above, *Rf* is the risk-free rate expressed by the 1 month US Treasury bill rate, SMB (Small Minus Big) is the average return on nine small cap portfolios minus the average return on nine big cap portfolios, HML (high minus low) is the average return on two value portfolios (in book-to-market equity terms) minus the average return on two growth portfolios, UMD is the average of the returns on two (big and small) high prior return portfolios minus the average of the returns on two low prior return portfolios,<sup>2</sup> CMA (Conservative Minus Aggressive) is the average return on two conservative portfolios minus the average return on two aggressive portfolios and RMW (Robust Minus Weak) is the average return on two robust operating profitability portfolios minus the average return on 2-weak operating profitability portfolios.<sup>3</sup>

In the [42] model, the size effect implies that small cap firms exhibit returns that are superior to those of large firms. Theoretical explanations for the small size effect suggest that the stocks of small firms are less liquid and trading in them generates greater transaction costs; there is also less information available on small companies and, thus, the monitoring cost of a portfolio with small stocks is generally greater than the cost of a portfolio of large firms.

The book-to-market equity ratio effect captured by the HML factor implies that the average returns on stocks with a high book-value to market-value equity ratio must be greater than the returns on stocks with a low book-value to market-value equity ratio. The high book-value firms are considered to be underpriced by the market and, therefore, they constitute appealing buy-and-hold targets, as their

<sup>2</sup> Big means that a firm is above the median market cap on the NYSE at the end of the previous day while small firms are below the median NYSE market cap.

<sup>3</sup> The historical daily data of the risk-free rate, the Fama and French three factors, the Carhart momentum factor, the robust minus weak factor and the conservative minus aggressive factor are available on the website of Kenneth French (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ data\_library.html).

price is expected to rise later. This anomaly undermines the semi-strong form efficiency of the stock market.

The existence of momentum in asset prices is an anomaly which has not been explained sufficiently by the finance theory. The difficulty in explaining the momentum anomaly is that, as the efficient capital markets theory suggests, an increase in the price of an asset cannot be indicative of a further increase in future prices. Behavioral finance has offered some possible explanations to the existence of the momentum anomaly. In particular, investors are assumed to be irrational and, consequently, they underreact to the release of new information failing to incorporate new information in the prices of their transactions.

**4. The sample**

and outside the US.

**105**

websites of ETFs' managing companies.

*DOI: http://dx.doi.org/10.5772/intechopen.90269*

The sample of the study includes the four IPO ETFs available in the US capital market. **Table 1** presents the profiles of ETFs. Presented in the table are the ticker, name of each ETF, name of tracking index, inception date, age in years, expense ratio, average daily volume in number of traded shares, and the historical tracking error of ETFs, which is the difference in returns between ETF and benchmark based on information on historical performance of ETFs before taxes and benchmark returns from each ETF's inception up to December 31, 2015. The information on ETFs' ticker, name, benchmark, inception date, and expense ratio as well as on the historical performance of ETFs and underlying indices has been found on the

*IPO ETFs: An Alternative Way to Enter the Initial Public Offering Business*

Moreover, **Table 1** reports the trading frequency of ETFs that is calculated as the fraction of trading days with nonzero volume to the total trading history (in days) for each fund, the average intraday volatility computed as the percentage fraction of the highest minus the lowest trade price of each fund on day *t* to its close trade price on the same day, and the fraction of each ETF's intraday volatility to the intraday volatility of the S&P 500 Index and the S&P 600 Small Cap Index, respectively. The last ratios help assessing whether IPO ETFs are more volatile than the market or not. The time series of daily volumes, open, high, low, and close prices of ETFs and the S&P 500 Index have been found on the website of NASDAQ. The historical data of

Regarding the underlying assets of ETFs, we note that the first fund tracks the Renaissance US IPO Index, which reflects approximately the top 80% of newly public firms based on full market capitalization. The second ETF follows the Renaissance International IPO Index, which is a portfolio of the top 80% non-USlisted newly public companies, prior to their inclusion in global core equity portfolios. The third ETF seeks to replicate the return of the IPOX®-100 US Index. This index measures the performance of the top 100 largest, typically best performing and most liquid US IPOs during their first 1000 trading days. The last IPO ETF examined tracks the IPOX International Index, which measures the performance of the 50 largest and typically most liquid companies domiciled outside the US within the IPOX Global Composite Index during their first 1000 trading days. All the indices above are reconstituted and adjusted quarterly and companies that have been public for 2 years (in the case of the Renaissance indices) or 1000 days (in the case of the IPOX®-100 US Index and IPOX International Index) are removed.

The average age of ETFs is equal to 4.42 years with the oldest one being the First Trust US Equity Opportunities ETF, which was launched in April 2006. The rest funds are 3 years old at a maximum indicating that this niche of the ETF market is very young but possibly very prosperous. The average expense ratio is modest being equal to 0.68%. In addition, the ETFs tracking non-US-listed IPOs are more expensive than their domestically allocated peers. This cost superiority of domestic ETFs is not surprising as it has been observed in the case of the "traditional" ETFs both in

Moreover, **Table 1** shows that an average number of about 16,000 ETF shares are traded every day with the First Trust US Equity Opportunities ETF being the more tradable fund in the sample. The concentration of trading to the most aged fund may be the result of the advantage of this ETF in terms of information availability relative to the younger funds and may indicate that investors deem this

Going further, the average raw tracking error of the sample is equal to �0.56%. The negative sign means that the average ETF underperforms its benchmark by 56 basis points (bps). Among the four ETFs in the sample, only one outperforms its

ETF as more prosperous based on its amassed trading experience.

the S&P 600 Small Cap Index have been obtained from Yahoo! Finance.

The Conservative Minus Aggressive and Robust Minus Weak factors correspond to the [44] investment and operating profitability factors. [44] use past investment as a proxy for the expected future investment and, based on valuation theory, they suggest that CMA implies a negative relation between the expected investment and the expected internal rate of return. Furthermore, based on the findings of [44], a negative loading is expected for the RMW factor, that is, the excess return of IPO ETFs must be affected by the profitability factor in a negative fashion.

The usage of Eq. (7) aims at capturing the market elements that can affect the performance of IPO ETFs and considering whether these funds can produce any meaningful above market returns, which will be represented by a positive and statistically significant alpha. With respect to the latter, [44] assert that if an asset pricing model fully captures expected returns, the intercept of the model should be indistinguishable from zero in a regression of an asset's excess return on the factor returns of the model.

The model is successively run for six different time periods. The first period concerns the first 21 trading days of each ETF excluding the month in which the ETF began trading on the exchange. We do so as we did when we estimated the long-run performance of ETFs above to allow for the possibility of price support in the first few trading days. This month is also excluded from all the other time intervals over which Eq. (7) is applied.

The second interval assessed concerns the first 63 trading days of each ETF. The third period examined regards the first 6 months of trading, that is, the first 126 trading days of each fund. The next period taken into consideration covers the first 12 months of trading data. In our analysis, the intervals ranging up to 1 year can be considered as a short-term investment horizon. Looking for more long run, we run the model for a period covering the first 18 and the first 24 months of each ETF's trading records. Finally, we run Eq. (7) over the entire history of each ETF so as to define the overall buy-and-hold risk-adjusted performance of ETFs.

#### **3.4 Market trend return analysis**

In the last step, we perform a "market trend" analysis of IPO ETF returns by examining how the return of ETFs responds to the decreasing or increasing swings of the overall stock market as the latter is alternatively represented by the S&P 500 Index and the S&P 600 Small Cap Index.

In our analysis, we first sort the daily returns of benchmark and then compute the number and portion of daily returns of each ETF that are negative or equal to zero and the number and portion of positive ETF daily returns during the descending path and during the ascending path of the stock market. If ETFs follow the market closely, they are expected to decline when the market declines and vice versa. Similarly to the short- and long-term performance analysis in the previous sections, we use three alternative types of returns, which are the absolute, benchmark-adjusted and abnormal return.
