# Cost of equity and S&P 500 Index revisions.

We examine how the cost of equity changes when firms are added to or removed from the S&P 500 Index during index revisions. Newly added firms experience a significant decline in the cost of equity, while recently removed firms show a significant increase. Liquidity improves for addition firms and declines for removed firms. Addition firms also experience a decline in shadow cost. Changes in cost of equity for included firms are explained by changes in liquidity, shadow cost, and firm size. Finally, included firms with greater investment opportunities benefit more from the reduction in cost of capital.Since inception, Standard and Poor's has changed the composition of its S&P 500 Index as companies move in and out of the index. Numerous studies examine the price effects of these index changes. Earlier studies, such as Harris and Gurel (1986) and Shleifer (1986), document the strong and persistent price increase of newly included firms. Similarly, Jain (1987) and Lynch and Mendenhall (1997) find that excluded stocks experience a temporary decline in price. The extant literature posits five different hypotheses to explain the market reactions to the S&P 500 Index changes as Standard and Poor's maintains that they do not use information about future prospects when selecting firms to be added to or deleted from their index.

The five hypotheses used to explain the price reactions around index changes can be broadly categorized as either undermining or supporting the efficient market hypothesis. The imperfect substitutes hypothesis stands alone against the efficient market theory as the hypothesis suggests a downward-sloping demand curve for S&P 500 stocks. In particular, the hypothesis states that, with no information in the announcements regarding future firm performance or risk, stocks that are included in the index are preferred by investors and cannot be easily substituted. Therefore, in the index revision events, inclusion stocks experience a positive price reaction, while exclusion stocks demonstrate a negative price reaction. This implication contradicts with Scholes' (1972) finding that stocks are perfect substitutes and have flat long run demand curves. In the case of perfect substitutes and perfect elasticity of demand, shocks to supply or demand that do not convey information to the market should not affect prices. Thus, the increased demand by index funds when a firm is added to the S&P 500 Index should not cause a long run effect in price unless information transmission occurs in the announcement of the index inclusion.

The price pressure hypothesis is consistent with Scholes' (1972) flat demand curves, but only holds if price improvements at addition are completely reversed in the short run. Index fund rebalancing might create a temporary imbalance of supply and demand to raise prices. Barring any information conveyed in the inclusion decision, these price changes should be short term. The remaining hypotheses propose that information is conveyed when Standard and Poors makes changes to the index, and this information both supports an increase in price at inclusion and corroborates Scholes' (1972) proposition of long run flat demand curves. Proponents of the liquidity hypothesis claim that documented permanent improvements (declines) in liquidity explain the increase (decrease) in stock prices following an addition (deletion) to the S&P 500 Index. The certification hypothesis encompasses several types of information regarding the firms that are included in (excluded from) the S&P 500 Index. For inclusion stocks, better future cash flows, a lower level of information asymmetry, and closer monitoring of the firms are forms of positive news that may be conveyed to the markets and support a sustained price increase. For deleted stocks, a price decline following the removal is supported by the negative information conveyed in the index revision. Advocates of the investor awareness hypothesis assert that the addition of a stock to the index draws investor attention and these investors do not immediately revoke their attention when stocks are removed. The asymmetric effect of permanent price increases at additions and temporary price decreases at deletions stem from these asymmetric changes in investor awareness. We discuss these hypotheses and related literature in detail in the following section.

In this paper, we examine the cost of equity capital surrounding index additions and deletions to further explain price reactions. In particular, our analysis of cost of equity around index revisions provides evidence for the liquidity and investor awareness hypotheses. Our paper is related to studies by Becker-Blease and Paul (2006) and Chen, Noronha, and Singal (2004). Becker-Blease and Paul (2006) examine the relationship between increased stock liquidity following S&P 500 Index inclusion and expansion of the investment opportunity set. They find a positive correlation between increases in stock liquidity and proxies for investment opportunities including capital expenditures and research and development expense. They argue that if stock liquidity increases, then the cost of equity and, subsequently, the overall cost of capital for the firm decreases. The decrease in cost of capital expands the set of value-creating investment opportunities for the firm. While Becker-Blease and Paul (2006) document the relation between liquidity and investment opportunities, they do not directly examine the cost of capital around index inclusion events. In addition, they do not examine index deletion firms. In addition, our study is related to that of Chen et al. (2004) who find asymmetric price reactions at additions and deletions that support the investor awareness hypothesis. They claim that the excess returns around index changes are due to either changes in expectations of future cash flows or changes in the required rate of return. The required rate of return changes for inclusion due to a reduction in shadow cost, but index deletion firms have no corresponding increase in shadow cost.

Both the liquidity and investor awareness hypotheses suggest a link between stock price reactions and cost of capital. Based on the liquidity hypothesis, stock liquidity changes as a result of index changes thereby explaining the stock price reactions. An increase (decrease) in stock liquidity for inclusion (deletion) stocks can lead to a drop (rise) in the cost of equity. We expect to find a decrease in the cost of equity capital for firms added to the S&P 500 and an increase in the cost of equity capital for firms deleted from the index. Finding symmetric changes in the cost of equity at addition and deletion supports the liquidity hypothesis. Alternatively, the investor awareness hypothesis suggests that investors require a smaller shadow premium (and, as such, a smaller required rate of return) on the stock when the firm is added to the index and do not require a larger shadow premium on the deleted stocks. We expect to find a decrease in the cost of equity for added stocks and an insignificant change in cost of equity for deleted stocks. Thus, asymmetric changes in the cost of capital support the investor awareness hypothesis.

In this study, we estimate the cost of equity using two methods: 1) the market/four-factor model and 2) buy-and-hold returns. From the existing literature, we find support for the use of these two methods to measure the cost of equity. Based on both the market and four-factor models, the cost of equity for firms added to the S&P 500 Index declines significantly after the inclusion events. More importantly, we find that the drop in cost of equity for the inclusion firms is significantly larger than that for their matched firms. For firms deleted from the index, the cost of equity is significantly higher following the removal of the stock from the index. Our second method to estimate changes in the cost of equity uses buy-and-hold returns. Based on this method, our results strongly support the results of the market and four-factor models. We find that the buy-and-hold returns for added firms decrease significantly after the inclusion event. Similarly, the buy-and-hold returns for firms deleted from the index experience a significant jump after the deletion events. These findings are consistent with the liquidity hypothesis rather than the investor awareness hypothesis.

To examine the factors that explain the change in the cost of capital for the index addition and deletion firms, we explore several liquidity measures and shadow cost as suggested by Chen et al. (2004). We examine these measures around the index revision events and link them to the changes in the cost of capital. First, we test the change in the liquidity and shadow cost proxies, and find that liquidity increases for newly added stocks and falls for newly removed ones. For the shadow cost proxy, we report an asymmetric change around additions and deletions. Shadow costs decline significantly upon addition, but remain relatively constant upon deletion. Additionally, using regression analysis, we demonstrate that liquidity and shadow cost changes help to explain the changes in the cost of equity for inclusion firms. For deletion firms, we find no significant explanatory factors for the increase in the cost of equity, except for changes in firm leverage. Our findings imply that the drop in the cost of equity for newly added firms is driven by lower liquidity, a smaller shadow cost, and larger firm size. For deletion firms, the results indicate that only changes in firm leverage help explain the increase in the cost of capital.

In the final component of our analysis, we examine the link between changes in the cost of equity and stock price reactions for index revisions. For inclusion firms, we find significant support for the negative correlation between the cost of equity changes and excess returns. In other words, a drop in the cost of equity leads to positive stock price reaction. We also find a negative and significant association between illiquidity ratio change and excess returns, suggesting that a larger drop in the illiquidity ratio after an index inclusion event is associated with a more favorable stock price reaction. This analysis also finds that firms with larger investment opportunity sets benefit more from declines in the cost of equity as they are able to take advantage of the lower cost of equity. For deletion firms, we find that cost of equity changes have an insignificant impact on stock price reaction. Instead, the stock price reaction is mainly driven by liquidity. In particular, a drop in liquidity proxied by slower turnover and a greater illiquidity ratio is associated with a negative stock price reaction at deletion events.

To recap, our study examines cost of equity changes and determinants thereof for firms added to or removed from the S&P 500 Index. We find support for the liquidity and investor awareness hypotheses in our analysis. First, we demonstrate that there is a symmetric change in the cost of capital around index revisions; that is, the cost of equity decreases after inclusion and increases after deletion from the S&P 500 Index. Inclusion firms experience an improvement in liquidity and a decline in shadow cost, and these changes are correlated with the change in the cost of equity. Conversely, deletion firms have a significant deterioration in liquidity, but insignificant changes in shadow cost. However, the changes in liquidity are not significantly related to the cost of equity changes. Finally, for inclusion firms, excess equity returns are related to the cost of equity change as well as the change in the illiquidity ratio.

The remainder of the paper is organized as follows. Section I discusses the literature related to index inclusion and deletion events. Section II presents the sample selection process and descriptive statistics of the sample. Section III discusses our methodology and presents our empirical results. In Section IV, we provide our conclusions.

I. Literature Review

From the extensive literature on the price impact of S&P 500 Index changes, we identify five competing hypotheses: 1) imperfect substitutes, 2) liquidity, 3) certification, 4) investor awareness, and 5) price pressure. The imperfect substitutes hypothesis argues against market efficiency as proposed in Scholes (1972), while the remaining four hypotheses support market efficiency. These hypotheses discuss potential sources of information conveyed in index reconstitutions that make observed price patterns consistent with perfect elasticity of demand for stocks. We describe each hypothesis in detail later.

The imperfect substitutes hypothesis claims that stocks are not perfect substitutes for one another and that investors' demand for S&P 500 stocks exceeds that for nonindex stocks. This hypothesis is consistent with a permanent price increase at index additions and a permanent price decline following deletions. Shleifer (1986) and Lynch and Mendenhall (1997) provide support for this hypothesis, while Edmister, Graham, and Pirie (1994) and Hrazdil (2009) conclude that the long run demand curves for stocks are flat. In particular, Shleifer (1986) indicates that abnormal returns are positively related to the amount of index fund purchases of a newly included stock and are not correlated with bond ratings. Based on this evidence, he proposes that demand curves for these stocks are downward sloping and rejects the certification hypothesis. Lynch and Mendenhall (1997) look at a sample of index changes following October 1989 when Standard and Poors began pre-announcing index changes. While a portion of the initial price increase is due to temporary price pressure, they conclude that demand curves for stocks are downward sloping as some of the initial price increase remains. They find an opposite price reaction for stocks deleted from the index.

Alternatively, Edmister et al. (1994) argue that previous research supporting the price pressure and imperfect substitutes hypotheses relies upon biased measures of abnormal returns. They reestimate the abnormal returns using a future estimation period and reject both hypotheses. They reject the price pressure hypothesis because excess returns are not reversed in the short run. They also reject the imperfect substitutes hypothesis as they find no correlation between excess returns and variables measuring increased demand for newly added stocks. Hrazdil (2009) studies the change in the S&P 500 weighting method from a market-based to a free-float based system. If stocks had downward sloping demand curves, abnormal returns should be correlated with the change in the index weight. However, after controlling for other factors, Hrazdil (2009) finds no relationship between abnormal returns and index weight changes.

The liquidity hypothesis is similar to the price pressure hypothesis as it posits that the price increases associated with index inclusions are due to increases in liquidity from more active trading of the index stocks. Amihud and Mendelson's (1986) theoretical model suggests that share price increases as bid-ask spread decreases. In contrast to the price pressure hypothesis, the liquidity benefits can be sustained. This hypothesis suggests a permanent price increase after index additions. Erwin and Miller (1998), Hedge and McDermott (2003), and Becker-Blease and Paul (2006) all find support for this hypothesis.

Erwin and Miller (1998) find that liquidity can explain the documented price increase at inclusion events. They examine the bid-ask spreads of stocks that are added to the index. They find that for stocks without previously traded options, bid-ask spreads decrease, and the increase in price and trading volume for these stocks are sustained. In contrast, stocks with traded options experience a temporary increase in price and no significant decrease in bid-ask spreads after their inclusion. The presence of traded options mitigates the benefit of liquidity improvements, so stocks with no traded options at the time of the inclusion benefit more from their greater liquidity. Hedge and McDermott (2003) report that the cumulative abnormal returns around index additions are negatively related to the change in bid-ask spreads. They also find that decreases in the spread are permanent benefits of increased liquidity, and that a large portion of the drop in spreads is due to the reduction in the direct costs of transactions rather than in the asymmetric information component. Finally, Becker-Blease and Paul (2006) report that firms added to the S&P 500 Index experience an increase in liquidity and growth opportunities, which supports a permanent price increase associated with the addition. They suggest that the link between liquidity and growth opportunities is the cost of capital. In particular, Becker-Blease and Paul (2006) hypothesize that firms have a lower cost of capital due to better liquidity and, as such, are able to take on more projects (measured by capital expenditures and research and development (R&D) expense) after the additions. They did not provide a test regarding whether the cost of capital for added firms falls as a result of greater liquidity. Hodrick and Moulton (2009) provide a model of liquidity for portfolio managers relating liquidity to the abnormal returns around index inclusion.

The certification hypothesis supports a positive and sustained price reaction to index additions as inclusion announcements contain positive information about selected firms. Similarly, deletion firms accrue losses because negative information is conveyed in the announcement. While signaling information about future performance is contrary to the stated practice of Standard and Poor's, work by Dhillon and Johnson (1991), Denis McConnell, and Ovtchinnikov (2003), Kappou, Brooks, and Ward (2008), and Cai (2007) supports this hypothesis. Conversely, Hrazdil and Scott (2009) provide evidence against this hypothesis. In one of the earlier studies of the certification hypothesis, Dhillon and Johnson (1991) examine the returns to bonds and options to distinguish between the price pressure and certification hypotheses. Assuming no positive information, stock options and bonds are not susceptible to price pressure or downward-sloping demand due to index rebalancing. However, Dhillon and Johnson (1991) find that call options and bond prices both increase at the announcement of index inclusion, while put prices fall. These findings support the certification hypothesis.

In recent studies, Denis et al. (2003) and Kappou et al. (2008) find that earnings per share rise in the period following index inclusion events. In addition, Denis et al. (2003) demonstrate that analyst earnings forecasts increase at the same time. Denis et al. (2003) point out that it is unclear as to the source of the increase in earnings per share and analysts forecasts. They suggest that the increased earnings may be due to superior monitoring by the market or the fact that these firms are selected by Standard and Poors for their better earnings potential. Furthermore, Cai (2007) suggests that inclusion events convey positive information about both the industry and the selected company. Hrazdil and Scott (2009) refute the findings of Denis et al. (2003) by reporting that the increases in earnings per share are due to managerial manipulation of the discretionary accruals. They suggest inclusion announcements convey no real information about company performance. While the majority of the studies of the certification hypothesis focus on improved future performance in earnings, the specific type of information conveyed during additions is not clearly identified in these studies. Some studies suggest that newly included firms may experience improvements in information asymmetry, as well as better access to capital markets. While these factors have yet to be studied directly, they may have an impact on the cost of equity. Whereas our study focuses on the liquidity and investor awareness hypotheses, we acknowledge that the certification hypothesis may also play a role in explaining changes in the cost of equity. (1)

Chen et al. (2004) find permanent price increases for addition stocks, but no permanent decline in prices for deletion stocks. Given this finding, they propose an alternate explanation regarding the asymmetric effects of index additions and deletions. The investor awareness hypothesis stems from Merton (1987) model of market segmentation where investors demand a shadow premium because they are only aware of and invest in a subset of stocks. When stocks are added to the index, investors become more aware of them and the shadow premium should decrease. Therefore, the required rate of return for the stock falls. When a stock is removed from the index, investors do not remove it from their sphere of awareness, so a symmetric decrease in stock prices is not expected. In an examination of multiple hypotheses regarding index reconstitution, Elliott, Van Ness, Walker, and Warr (2006) find that changes in investor awareness are the most important determinant of announcement day abnormal returns. Jain and Kim (2006) demonstrate that investor awareness continues to motivate firms to switch from listing on the NASDAQ to the NYSE, even after differences in liquidity dissipated.

The price pressure hypothesis supports a temporary price increase for added stocks to the index due to heavy buying pressure by index funds. Under this hypothesis, the effect of the increased demand of the selected stocks should dissipate in the short run and the positive price effects should be temporary. Similarly, the hypothesis suggests a temporary price drop for stocks that are removed from the index. Harris and Gurel (1986) and Elliott and Warr (2003) find empirical support for this hypothesis. In particular, Harris and Gurel (1986) argue that the price pressure, driven by the rebalancing of index funds, leads to a short-term positive price reaction that is reversed within two weeks of the index change. Since Standard and Poor's states that they do not use forecasts of future performance as a selection criteria for choosing firms for the index, Harris and Gurel's (1986) evidence of increased trading volume and price increases supports the price pressure hypothesis. In addition, they document a positive correlation between the magnitude of the change in trading volume and prices and the size of index funds in the market. Elliott and Warr (2003) examine the differences in price pressure between the added firms on the NYSE and those on the NASDAQ. They find that NASDAQ stocks experience a larger and more sustained price impact. They attribute the difference to the greater ability of auction markets to absorb large increases in demand, but conclude that price pressure drives the positive reaction of stocks added to the S&P 500.

Finally, another strand of literature studies the changes in equity betas surrounding S&P 500 Index revisions. Vijh (1994) finds, for the period from 1985 to 1989, the betas of newly included stocks to the S&P 500 increase and shows that some of this increase is due to increased trading volume in index stocks. He concludes that the market beta of S&P 500 stocks is overstated following index inclusion. Barberis, Shleifer, and Wurgler (2005) further examine changes to betas of newly added S&P 500 stocks and find increased correlation with other S&P 500 stocks and decreased correlation with non-S&P 500 stocks. A rational view of markets suggests that an increase in market betas would occur with increased co-movement of fundamentals or cash flows of a particular stock. Nevertheless, Barberis et al. (2005) demonstrate that a "sentiment-based" theory of stock movement has support.

II. Sample Selection and Descriptive Statistics

Our sample consists of firms that are added to or deleted from the S&P 500 Index from 1990 to 2007. We begin our sample period in 1990 as Standard and Poors' revised their method of announcing index revisions in October 1989. Prior to this revision, Standard and Poors' announced index changes after trading closed on the day immediately prior to the revision. Following the change in 1989, index changes are pre-announced several days prior to the actual revision of index constituents. According to Benish and Whaley (1996), this change alleviates some buying pressure caused by index funds attempting to purchase shares of the newly added stock on the morning of the change. Using a monthly list of S&P 500 Index constituents from Compustat, we identify the months in which the index constituents change. We then verify, using news articles in Lexis-Nexis, the announcement and effective revision dates for all index changes. This process produces 842 total sample firms with 419 index additions and 419 deletions. Panel A of Table I provides a breakdown of the number of index revisions by year in our sample. We further exclude those sample firms that are associated with the following types of index changes: 1) When a nonindex firm acquires and replaces an existing index firm (11 cases involving 11 added and 11 deleted firms), 2) when an S&P 500 firm acquires another index firm and the acquired firm is removed from the index (five cases involving five deleted firms), 3) when two existing index firms merge and the resulting merged firm remains on the index (9 cases involving 9 added and 18 deleted firms), and 4) when an index firm is replaced by a spun-off subsidiary (17 cases involving 17 added and 17 deleted firms). The final sample contains 382 added firms and 368 deleted firms. Panel B presents the sample screening process described above.

In addition, we create a sample of matched peers for the sample firms by matching on industry and firm size. For each sample firm, we collect a pool of industry peers in the same three-digit standard industrial classification (SIC) code. We then select the peer with a firm size (measured by total assets) that is closest to that of the sample firm. We require that the selected match has valid data in Compustat for the fiscal year prior to the event date, as well as valid stock returns in Center for Research in Security Prices (CRSP) for the period of seven months prior to and after the announcement of the index revision. Finally, we require that the matched firm is not a member of the S&P 500 Index in the five years prior to and after the event. Our annual accounting data is from Compustat, daily and monthly stock returns are retrieved from CRSP, and marginal tax rates are the before-interest expense tax rates from John Graham's website. If these tax rates are missing, the tax rate is computed from Compustat data as the tax expense divided by total pretax income. Remaining missing or negative tax rates are filled in with the median tax rate of the existing inclusion or deletion sample.

Table II reports the descriptive statistics for the sample and matched firms for the inclusion sample in Panels A and B, respectively. For the deletion sample, the same statistics are reported in Panels C and D. On average, sample firms are larger in terms of assets, sales, and market value of equity than the matched pairs, and this holds for both the inclusion and deletion samples. Also, both sets of sample firms have lower leverage than their matched counterparts.

III. Methodology and Empirical Results

According to Becker-Blease and Paul (2006) and Chen et al. (2004), the cost of equity capital should decrease for firms added to the S&P 500 due to increases in liquidity and increases in investor awareness of the firms. The cost of equity capital should increase for deleted firms due to declines in liquidity. In this section, we present the findings of the cost of capital around index revision events and discuss how our results relate to the liquidity and investor awareness hypotheses.

A. Cost of Equity Before and After Index Revisions

To measure the cost of equity, we use two different methods. First, we follow Grullon and Michaely (2004) and estimate the market model to compute changes in the cost of equity. In addition, Hedge and McDermott (2003) suggest that companies are often included in the S&P 500 following a period of positive momentum. Therefore, we estimate Carhart's (1997) four-factor model to account for the possibility of positive momentum in inclusion stocks and negative momentum in deletion stocks. Our estimation window includes three years of monthly returns ending one month prior to the announcement month and three years of monthly returns beginning one month after the announcement month. Using these returns, we compute the coefficients for the market model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

and the four factor model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

where [r.sub.it] is the monthly return on a stock i, r q is the monthly return on the 10-year U.S. Treasury bond, [r.sub.mt] is the monthly return on the NYSE/AMEX/NASDAQ value-weighted index, [SMB.sub.t] is the difference between the monthly return on a portfolio of small and large firms, [HML.sub.t] is the difference between the monthly returns of the portfolios of high book-to-market and low book-to-market stocks, [UMD.sub.t] is the difference between the monthly returns of the portfolios of high and low momentum stocks, and [D.sub.t] is a dummy variable equal to one if t is greater than the announcement date of the inclusion or deletion event. We estimate the model using monthly returns for three years prior to and following the announcement date excluding the announcement month. To calculate the cost of capital based on these models, we compute the average monthly risk premium for the market, small minus big (SMB), high minus low (HML), and unmatched disbursement (UMD) factors over the period from 1926 to 2009 to ensure that our results are not biased by the realized risk premium changes in our sample.

In our second method of measuring the cost of equity, we follow Errunza and Miller (2000) who use buy-and-hold returns for a period prior to and after the American Depository Receipt (ADR) listing of international firms. They use changes in the buy-and-hold returns as a proxy for changes in the cost of equity. We compute buy-and-hold returns for a period of three years prior to and after the announcement date excluding a one-month window around the announcement for both the sample and matched group of firms. The buy-and-hold returns are annualized. Table III reports the estimated cost of equity for all three methods of calculating the cost of equity changes. We winsorize all cost of equity measures at the 99% and 1% levels. For a given sample firm in the inclusion and deletion samples, the unadjusted return is the raw cost of equity measured over the window. The adjusted return is the unadjusted cost of equity of the sample firm minus the unadjusted cost of equity of the matched pair.

The results in Panel A for inclusion firms suggest that the unadjusted cost of capital estimated by all methods is consistently higher in the pre-event period and falls during the postevent period. For the inclusion sample, the unadjusted change in the cost of capital for the market model has a mean of-25.78% (significant at the 1% level) and a median of- 17.00% (significant at the 1% level). More importantly, the mean (median) adjusted change in the cost of equity based on the market model is - 18.86% (- 12.91%), significant at the 1% (1%) level. We find similar results using the four-factor model. In particular, the inclusion firms experience a significant drop in the estimated cost of capital with a mean (median) adjusted change of - 16.65% (- 11.78%), which is significant at the 1% (1%) level. Finally, a similar pattern holds for the buy-and-hold returns. Both the mean and median differences between the pre- and postevent buy-and-hold returns are significantly different at the 1% level. The adjusted buy-and-hold return displays a mean (median) decline of 22.67% (13.84%) (both are significant at the 1% level) indicating that this proxy for the cost of equity of newly included firms decreases more than the matched sample. Based on the buy-and-hold results, the pre-inclusion returns for added firms are significantly higher than those of the matched firms, but following inclusion to the index, no significant difference remains between these returns. Hedge and McDermott (2003) suggest that Standard and Poor's often selects firms after periods of positive momentum which may explain this finding of high returns for added firms. Moreover, high returns in the pre-inclusion period increase firm value and may cause the added firm to surpass the Standard and Poor's minimum size threshold.

For deletion firms, the results regarding the change in cost of capital are reported in Panel B of Table III. The results clearly suggest that the deleted firms experience a significant increase in the cost of capital after the deletion event. The unadjusted cost of capital increases are all significant (at the 1% level) in the mean and median for all three methods of estimating the cost of capital. We observe the same qualitative conclusion in the adjusted cost of capital. For example, the unadjusted increase in the cost of capital for deletion firms based on the market model has a mean (median) of 19.49% (14.03%), which is significant at the 1% (1%) level. Based on the four-factor model, the deleted firms experience a significant mean change in the cost of capital of 15.08% (11.90%) after their stocks are removed from the index. Therefore, using the market and four-factor models, we find that the cost of capital for the added (deletion) firm declines (increases) significantly after the index change. For deleted firms, buy-and-hold returns are significantly higher in the postdeletion period. Deleted firms have a buy-and-hold return of 8.52% prior to removal and 10.72% following removal. The mean (median) increase in buy-and-hold returns for newly deleted S&P 500 firms is 14.98% (13.98%), which is significant at the 1% level.

Overall, cost of capital based on the market and four-factor models and the buy-and-hold returns indicate a symmetric pattern in the change in cost of capital for added and deleted firms. In other words, we observe a significant decline in the cost of equity for added firms and a significant increase in the cost of equity for deleted firms. Thus, the evidence supports the liquidity hypothesis as we observe a symmetric reaction in the cost of capital for newly included and removed firms. However, one cannot rule out the investor awareness hypothesis without further examination. If, for example, the decrease in cost of equity following addition is driven by both increases in liquidity and decreases in shadow cost, and the increases in the cost of equity following deletion are driven by declines in liquidity without changes in shadow cost, this finding would support both the liquidity hypothesis and the investor awareness hypothesis. To study what drives the changes in the cost of capital for the sample firms, we next analyze various liquidity measures and shadow costs suggested by Chen et al. (2004).

B. Liquidity and Shadow Cost Changes

Based on the liquidity and investor awareness hypotheses, changes in the cost of equity for addition and deletion firms can stem from one of two main sources: 1) change in liquidity and 2) change in shadow costs. To examine the two sources of changes in the cost of equity, we report the change in three liquidity measures and shadow cost. The three liquidity measures and shadow cost are measured for 36 months preceding the event announcement ending one month prior to the announcement date. Similarly, we measure the liquidity and shadow cost for 36 months following the event beginning one month after the completion date. In particular, the three liquidity measures are: 1) the illiquidity ratio, 2) the trading volume, and 3) turnover. In order to account for market trends in liquidity, we standardize each liquidity measure by the same measure of the overall market. In particular, we include all stocks on the NYSE in the computation of the market liquidity measures. The illiquidity ratio is the average of the absolute value of the daily return divided by the dollar volume traded on that day. The illiquidity ratio is further multiplied by 107 and scaled by the average daily market illiquidity ratio of all stocks on the NYSE. Volume is the average of the daily dollar amount traded. The dollar amount traded is calculated for each day as the number of shares traded multiplied by the closing price. Volume is market adjusted by scaling it by the average of daily total dollar trading volume on the NYSE. The turnover ratio is the average monthly share volume traded divided by the number of shares outstanding. The turnover ratio is market-adjusted by dividing it by the average monthly turnover of all stocks on the NYSE. Alternatively, shadow cost is the product of the residual standard deviation and firm size divided by the product of the S&P 500 Index market capitalization and the number of shareholders. The residual standard deviation is the standard deviation of the difference between the firm's return and the S&P 500 total return. Firm size is measured as the number of shares outstanding multiplied by the closing price on the announcement date. The S&P 500 Index market capitalization is measured in dollars on the announcement date. The number of shareholders is measured before the event date at the closest point prior to the event, and the number of shareholders after the event is measured a minimum of nine months after the announcement date.

Table IV reports the unadjusted and adjusted mean (median) of the three liquidity measures and shadow cost for the inclusion and deletion firms, respectively. The unadjusted mean (median) of a given variable is the sample firm mean (median). The adjusted mean (median) is the mean (median) difference between the sample firms and their matched pairs. We report the results with variables winsorized at the 1% and 99% levels. For inclusion firms, we observe a drop in the illiquidity ratio and an increase in volume. This observation is generally significant for the unadjusted and adjusted means (medians). Results regarding the changes in the market-adjusted turnover ratio are mixed and generally insignificantly different from zero in the mean and median. As developed by Amihud (2002), the illiquidity ratio measures the price impact per dollar of trading activity on a particular date. Larger values indicate deteriorating liquidity. Contrarily, increases in volume signal liquidity improvements. In other words, the results suggest that added firms experience better stock liquidity after the inclusion events using two of our three liquidity measures, which is consistent with the literature. Alternatively, we also find that the shadow cost is significantly lower after the inclusion events suggesting that investors are more aware of the added firms after the index revisions.

For deleted firms, we find that the unadjusted illiquidity ratio is significantly higher and volume drops appreciably after their stocks are excluded from the index suggesting a decrease in liquidity for the deleted stocks. Interestingly, changes in turnover are also insignificant for deletion firms. To ensure that we capture liquidity changes appropriately, we examine changes in all three measures in the univariate analysis, as well as in multivariate regressions discussed in a later section. Moreover, the shadow cost of deleted stocks is not significantly different prior to and after the deletion events. Overall, the findings suggest that liquidity of the deleted stocks decreases after the deletion announcements, and their shadow cost does not change significantly.

The findings of the change in liquidity measures and shadow cost for inclusion and deletion firms lend support for both the liquidity and investor awareness hypotheses. In particular, the increase (decrease) in liquidity for inclusion (deletion) stocks is both economically and statistically significant, suggesting a symmetric change in liquidity in the sample firms. This evidence is consistent with the liquidity hypothesis. In addition, we find that both added and deleted firms experience an increase in stock turnover. More importantly, the shadow cost of the added stocks drops significantly while that of the deleted stocks experiences no significant change. These findings support the investor awareness hypothesis that while inclusion stocks are added to the investors' awareness at the index revisions, deleted stocks are not taken out of the investor's awareness when they are excluded from the index.

C. Factors Explaining Cost of Equity Changes

To examine whether liquidity and/or investor awareness are the main determinants for the change of the cost of capital around index revisions, we perform a multivariate regression analysis. We include the change in the cost of capital as the dependent variable. We measure the cost of capital using the cost of equity estimated by the market model, the four-factor model, and the buy-and-hold returns. For brevity, we present the results using the change in cost of capital based on the market model. The results using the cost of capital based on the four-factor model and buy-and-hold returns are similar to those based on the market model and are available upon request. The independent variables include the change in the illiquidity ratio, volume, turnover, and shadow cost. Since some index funds and exchange-traded funds that mimic the S&P 500 Index only sample a portion of the stocks in the index, we identify the stocks on the S&P 500 Index that encompass the top 50% of market capitalization. We identify these larger firms using a binary variable equal to one if at the date of announcement or inclusion, our sample firm is in the top 50% of the market capitalization of the index. We include this binary variable to mitigate possible issues of collinearity between firm size and trading volume. Cost of equity changes may also be driven by the changes in a firm's capital structure, so we include changes in the book leverage ratio. In particular, we measure the leverage ratio during each fiscal year for three years prior to and following the announcement date as the ratio of the total book value of debt to total assets. Then, we compute the average leverage ratio before and after the event and use the difference in these averages as the change in capital structure. Additionally, we include a variable to capture the change in information asymmetry. Chen et al. (2004) suggest that a lower level of information asymmetry may be a cause of the cost of capital reduction for inclusions. To control for information asymmetry changes that may also impact the cost of capital changes, we measure the cumulative abnormal return on Days -1, 0, and +1 surrounding a quarterly earnings announcement. We measure the average of the absolute value of these returns for the five years prior to and after the event date and compute the change in the average reaction. A decline or increase in the average stock reaction to quarterly earnings announcements is a proxy for a decrease or increase in information asymmetry, respectively. Lobo and Tung (1997) and Dierkens (1991) use this variable to proxy for information asymmetry. We perform the multivariate regressions for the inclusion firms and deletion firms individually and report the results in Table V.

The three models in Table V are structured as follows. Model 1 includes the changes in liquidity measures (Illiquidity Ratio Change, Volume Change, Turnover Change) and shadow cost (Shadow Cost Change). In Model 2, we include additional variables to control for firm size (Large Market Cap. Flag), capital structure changes (Leverage Change), and changes in information asymmetry (Earnings Reaction Change). In Model 3, we remove the volume and turnover change to ensure that our findings on the illiquidity ratio are not driven by multicollinearity between our three liquidity proxy variables. For inclusion firms, we observe in Model 1 that the change in the cost of equity is positively related to both the change in the illiquidity ratio and the change in shadow cost. Both of these findings persist in all models. Interestingly, while illiquidity ratio, volume, and turnover are all proxy variables for liquidity changes, only the illiquidity ratio change is significant in predicting the change in the cost of equity for inclusion firms. To ensure that the effect of the illiquidity ratio changes on the changes in the cost of equity exist independent of the other two liquidity proxy variables, we estimate Model 3. This model includes the change in only one liquidity measure, the illiquidity ratio. We find that the positive effect of the illiquidity ratio on the change in cost of capital remains consistent. We also find that the change in shadow cost has a significant and positive impact on cost of capital changes. In other words, a larger drop in shadow cost for inclusion firms leads to a larger drop in the cost of equity. Of the control variables, only large firm size, captured in the large market capitalization dummy variable, is significant in predicting the changes in cost of equity for additions. Larger firms have a larger decline in the cost of equity implying that these larger firms benefit more from inclusion to the S&P 500 Index in terms of declines in the cost of equity. (2)

We implement the same models for deletion firms and the results are reported in Panel B of Table V. Interestingly, we find that liquidity and shadow cost measures, in general, do not have a significant impact on changes in the cost of equity. The only exception to this finding is that in Model 2, we find that the turnover change is positively related to the cost of equity changes for deletion firms. Due to the low R2 of this model and marginal statistical significance of this finding, we cannot conclude that liquidity changes are determinants of cost of equity changes. In terms of control variables, the only variable that is shown to have a significant effect on the increase in cost of equity for deletion firms is changes in leverage. In particular, increases in leverage are associated with declines in the cost of equity. Literature regarding index revision events suggests that deletion firms are a much noisier sample than inclusion firms as deletions are often accompanied by other major corporate events at the same time or shortly thereafter. Major events such as mergers and acquisitions, bankruptcies, deteriorating operational/financial performance, and others can cloud the correlation between potential attributing factors for cost of capital (and stock price reaction to index revisions). Our findings for deletion firms are consistent with the insignificant and mixed results shown in the literature.

D. Relating Cost of Equity Changes to Announcement Returns

We examine the changes in cost of equity around S&P 500 Index revisions to help explain the observed price reaction to the reconstitution announcements. In this section, we examine the determinants of excess returns around the event dates with a focus on the relationship between the change in cost of equity and stock price reaction. In particular, as indicated by the results above, we find that liquidity and investor awareness have a significant impact on the change in cost of equity. Chen et al. (2004) finds that the change in shadow cost is directly related to the excess returns at the announcement of index inclusion. In this analysis, we explore whether liquidity and investor awareness are directly related to announcement returns. Alternatively, these factors may only be related to announcement returns inasmuch as they impact the cost of equity.

The pattern of decreases in the cost of equity for newly added S&P 500 firms and increases in the cost of equity for newly removed firms is observable to investors. If this information is anticipated and incorporated into the announcement period returns, we should observe a correlation between the changes in the firms' cost of equity and returns around index change announcements. Therefore, to analyze whether decreases (increases) in the cost of equity drive the announcement reaction for addition (deletion) firms, we conduct a multivariate regression using the cumulative excess returns as the dependent variable. Following Chen et al. (2004), excess returns are calculated as the difference between a firm's return and the total return of the S&P 500 Index. We measure the cumulative excess returns from the announcement date through 30 days later to capture a long-term response. The independent variables include the change in cost of equity, change in liquidity proxies, and change in shadow cost measures. Since there is a high degree of correlation between the change in cost of equity and the change in shadow cost, we orthoganalize shadow cost and the cost of equity change to avoid potential biases in coefficient estimates. Moreover, we control for the large market capitalization firms, leverage ratio change, and earnings announcement reaction change. Lastly, Becker-Blease and Paul (2006) suggest that changes in liquidity and growth opportunities are positively related at S&P 500 Index reconstitutions due to the impact of liquidity on cost of equity changes. Thus, we include growth opportunities in the regressions and use growth proxies as suggested by the literature. In particular, we use asset growth, capital expenditure growth, and the market-to-book ratio to proxy for firm growth (Goyal, Lehn, and Racic, 2002; Johnson, 2003; Cooper, Gulen, and Schill, 2008; Adam and Goyal, 2008). Asset (capital expenditure) growth is the annual growth in total assets (capital expenditure) in the year preceding the index revision event. Due to a large negative correlation between the cost of equity change and these growth measures, we construct a growth measure flag that is equal to one if the growth measure is higher than our inclusion or deletion sample median.3 Due to the potential problems with the market-to-book ratio (Rajan and Zingales, 1995) and missing observations of capital expenditure, we report the results using the asset growth flag. In addition, we interact the growth measure flag with the cost of capital change. The interaction term is used to examine Becker-Blease and Paul's (2006) argument that the positive price reaction to inclusion events is driven by larger investment opportunity sets (or growth opportunities) due to a lower cost of capital. A negative coefficient estimate suggests that the addition firms are able to take greater advantage of the reduction in the cost of capital and experience larger announcement returns if they have better growth opportunities. The regression results are presented in Table VI, with the results for inclusion events in Panel A and the results for deletion events in Panel B.

In general, a decline in the cost of equity for inclusion firms is expected to be associated with a positive excess return. We perform the regressions based on three models. Model 1 includes the cost of equity change, liquidity proxy variable changes, and the change in shadow cost. Model 2 consists of the aforementioned variables in addition to our control variables. In Model 3, we add the asset growth flag and the interaction between this proxy for growth opportunities and the cost of equity change. In Models 1 and 2, we confirm the negative relationship between the cost of capital change and excess returns by observing a negative and significant coefficient on the change in cost of capital. In other words, a larger drop in the cost of equity is associated with a more favorable price reaction. Interestingly, turnover, volume, and shadow cost changes are generally not directly related to the announcement excess returns. However, the illiquidity ratio change is negatively and significantly related to excess returns in all models. Chen et al. (2004) find that the change in shadow cost is negatively related to excess returns, while our results indicate that the impact of shadow costs is negative, but insignificant. Similarly, Elliott et al. (2006) demonstrate that shadow cost change, not liquidity, is the main determinant of announcement day abnormal returns. As Chen et al. (2004) point out that changes in shadow cost have an impact on the changes in cost of equity, our analysis suggests that the shadow cost change has no significant impact on excess returns once we control for the changes in cost of equity. In fact, changes in shadow costs have an indirect effect on excess returns through their impact on the cost of equity. In Model 3, we add the high asset growth indicator and the interaction between this flag and the cost of equity change. Becker-Blease and Paul (2006) suggest that addition firms benefit from more value-creating investments as a result of the lower cost of capital. Therefore, newly added firms to the S&P 500 benefit most when their cost of equity falls and they face greater opportunities for further growth. We find that firms with above median asset growth have an insignificant impact on excess returns when we consider this variable independently. Interestingly, we find that the coefficient on the interaction term is negative and significant. This indicates that firms with larger investment opportunity sets have larger announcement returns when their cost of capital declines. These firms are able to take better advantage of the reduction in the cost of capital as more of these investment opportunities become positive NPV projects and benefit shareholders. For deletion firms, the results shown in Panel B of Table VI suggest that there is no significant association between the cost of equity changes and excess returns around announcement. However, excess returns for deletion firms can be explained by changes in the illiquidity ratio and turnover. This finding indicates that the stock price reaction for deletion firms is largely driven by the direct effects of liquidity changes after the deletions, rather from cost of equity changes. We also find significant and negative impacts regarding earnings reaction change. In particular, firms with a larger increase in earnings reaction (a larger increase in information asymmetry) are likely to have lower excess returns.

Overall, the multivariate results suggest that cost of capital changes are inversely related to price increases around S&P 500 Index changes for inclusion firms. Additionally, newly included firms with larger investment opportunity sets benefit more from the decline in the cost of equity than those with smaller investment opportunity sets. The results support an important link between the cost of equity change and the price response of inclusion stocks. For deletion firms, we find that liquidity measures have a direct impact on price reaction, whereas cost of capital changes have little, if any, effect on excess returns.

In sum, the results in Section IV suggest many important and interesting implications. We find that liquidity increases for added stocks and decreases for deleted stocks. Conversely, shadow costs decrease for added stocks, but remain constant for deleted stocks. This finding supports both the liquidity and investor awareness hypotheses. In the multivariate regressions of change in the cost of equity, we find that the drop in cost of equity for added stocks is mainly driven by an increase in the illiquidity ratio, a decrease in shadow cost, and large firm size. The increase in cost of equity for deleted stocks cannot be explained by liquidity or shadow cost measures. Finally, changes in the cost of equity and illiquidity ratio are major drivers of the positive stock price reaction for inclusion firms. We also find that firms with more growth opportunities have larger announcement returns when their cost of capital declines. For deletion firms, stock price reaction is directly driven by liquidity measures, rather than from changes in the cost of equity. Taken together, the results from the multivariate analyses further confirm the liquidity and investor awareness hypotheses.

IV. Conclusion

We examine the cost of capital for newly included and excluded firms to the S&P 500 Index and find support for the liquidity and investor awareness hypotheses. We extend prior work by Becker-Blease and Paul (2006) whose study implies that changes in the cost of equity improve the set of value-creating investment opportunities for inclusion firms. We also draw upon the work of Chen et al. (2004) who document asymmetric changes in shadow costs following index revisions. Using three proxy measures of the cost of equity, we find support for the liquidity hypothesis as the cost of equity increases upon index inclusion and decreases when firms are removed from the index. Further analysis of liquidity measures and shadow cost imply support for both the liquidity and investor awareness hypotheses. In particular, we find that liquidity increases (decreases) for added (deleted) stocks. Alternatively, shadow cost increases for added stocks but remains constant for deleted stocks. Using a multivariate regression framework, we find that the change in the cost of equity for addition firms can be explained by an increase in liquidity, a decline in shadow cost, and large firm size. Contrarily, for deleted firms, leverage is the only significant determinant of the change in cost of equity. Neither changes in liquidity or shadow cost impact the cost of equity for excluded firms. In examining the determinants of the announcement reaction for index inclusion events, we demonstrate that firms whose cost of equity decreases have larger excess returns. Moreover, firms with a larger investment opportunity set may be more poised to take advantage of the reduction in the cost of equity experienced by newly included S&P 500 firms.

We acknowledge the helpful comments and suggestions of Bill Christie (Editor), an anonymous referee, Steven Ott, and Jennifer Troyer. We also thank the seminar participants at the 2009 Midwest Finance Association Meeting for input.

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(1) We thank an anonymous referee for pointing this out.

(2) Our findings in Table V are also robust to taking the log of all variables (excluding the Large Market Cap flag) to capture percentage changes rather than the level of changes.

(3) Correlation between asset growth and the cost of equity change is -0.4037 and is significant at the 1% level.

Lindsay Baran and Tao-Hsien Dolly King *

* Lindsay C. Baran is an Assistant Professor at Kent State University in Kent, OH. Tao-Hsien Dolly King is the Rush S. Diekson Professor of Finance at the University of North Carolina at Charlotte in Charlotte, NC.

Table I. Number of Events by Year The sample consists of all firms added to or deleted from the S&P 500 Index during the period of 1990 to 2007. Panel A includes all additions and deletions. Panel B describes the screening process to remove certain events to arrive at the final sample. Events are removed if an outside firm acquires an S&P 500 firm and replaces it on the index, if an S&P firm acquires another S&P firm and the acquired firm is removed from the index, if two S&P 500 firms merged and the merged firm remains on the index, and if an S&P 500 firm spins off a subsidiary and the subsidiary replaces the parent firm. Panel A. Number of Additions and Deletions by Year Additions/Deletions 1990 11 1991 11 1992 7 1993 12 1994 16 1995 31 1996 23 1997 28 1998 42 1999 41 2000 56 2001 28 2002 22 2003 9 2004 19 2005 19 2006 31 2007 13 Total 419 Panel B. Sample Screening Process Reason for Removal Additions Deletions A nonindex firm 11 11 acquired and replaced an index firm. An S&P 500 firm 0 5 acquires another index firm and the acquired firm is removed from index. Two index firms 9 18 merge and the remaining merged firm remains in index. Spun-off subsidiary 17 17 replaces index firm. Final sample total 382 368 Table II. Descriptive Statistics of Sample and Matched Pair Firms The sample consists of all firms added or deleted from the S&P 500 during the period of 1990 to 2007. We exclude added firms and deleted firms where the added firm acquires the deleted firm, where two index firms merge and the merged firm remains, and where an added firm is a subsidiary spun-off from a deleted firm. We match each sample firm with a matching pair firm in the same three-digit SIC code and the matched pair is the closest possible match by asset size. Matched firms cannot be constituents of the S&P 500 for a period of 10 years surrounding the event. Assets, sales,long-term debt, and short-term debt are the book value of these measures from the fiscal year end immediately prior to the index change. Market value of equity is the value of the target's outstanding equity at the end of the fiscal year prior to the announcement. Assets, sales, and market value of equity are reported in millions of 2007 dollars and are adjusted using the Consumer Price Index. Leverage is the ratio of the book value of total debt (long-term debt plus debt in current liabilities) to the market value of assets, where the market value of assets is estimated as the book value of assets minus the book value of equity plus the market value of equity. All values are expressed in millions of 2007 dollars. Mean Median N Min Max Panel A. Inclusion Firms Total assets 16,302.08 4,309.34 379 259.66 360,924.72 Total sales 5,113.03 2,564.17 379 136.84 58,930.82 M.V of equity 8,979.95 6,512.49 332 598.16 129,033.75 Long-term debt 1,844.11 539.65 369 1,844.11 35,854.57 Short-term debt 2,678.27 33.41 372 0.00 175,345.89 Leverage 0.13 0.08 328 0.00 0.82 Panel B. Inclusion Matched Pair Firms Total assets 11,782.68 2,751.70 379 21.08 347,785.60 Total sales 2,911.65 1,708.02 377 9.10 31,644.41 M.V of equity 2,972.62 1,958.87 363 0.00 45,324.76 Long-term debt 1,527.68 640.73 378 1,527.68 38,517.59 Short-term debt 1,780.63 39.15 377 0.00 235,024.51 Leverage 0.24 0.19 358 0.00 0.94 Panel C. Deletion Firms Total assets 21,148.25 4,909.08 365 115.38 395,540.71 Total sales 7,661.41 3,732.01 367 53.73 120,860.82 M.V of equity 9,994.89 3,890.84 318 24.11 120,511.31 Long-term debt 3,683.06 1,045.78 341 3,683.06 64,035.80 Short-term debt 2,999.78 148.55 341 0.00 223,993.49 Leverage 0.20 0.17 317 0.00 0.93 Panel D. Deletion Matched Pair Firms Total assets 12,656.01 2,804.80 362 37.74 330,988.96 Total sales 4,271.04 2,058.24 360 27.78 43,356.36 M.V of equity 4,356.35 1,435.67 344 0.01 113,819.15 Long-term debt 1,973.56 645.33 361 1,973.56 34,724.00 Short-term debt 773.64 42.51 358 0.00 41,248.95 Leverage 0.24 0.22 337 0.00 0.98 Std. Dev. Panel A. Inclusion Firms Total assets 39,786.75 Total sales 7,502.00 M.V of equity 10,664.16 Long-term debt 3,796.67 Short-term debt 14,464.10 Leverage 0.16 Panel B. Inclusion Matched Pair Firms Total assets 30,997.19 Total sales 3,996.55 M.V of equity 3,700.29 Long-term debt 3,244.52 Short-term debt 12,973.26 Leverage 0.21 Panel C. Deletion Firms Total assets 46,973.00 Total sales 12,128.07 M.V of equity 17,391.82 Long-term debt 7,215.22 Short-term debt 15,215.45 Leverage 0.16 Panel D. Deletion Matched Pair Firms Total assets 33,226.73 Total sales 6,864.77 M.V of equity 10,945.04 Long-term debt 4,030.63 Short-term debt 3,363.60 Leverage 0.19 Table III. Changes in Cost of Capital The sample consists of all firms added or deleted from the S&P 500 during the period of 1990-2007. We exclude added firms and deleted firms where the added firm acquires the deleted firm, where two index firms merge and the merged firm remains, and where an added firm is a subsidiary spun-off from a deleted firm. We match each sample firm with a matching pair firm in the same three-digit SIC code and the matched pair is the closest possible match by asset size. Matched firms cannot be constituents of the S&P 500 for a period of 10 years surrounding the event. The table reports the mean and median values of the cost of capital measured by the market model [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], and the four-factor model [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], where [r.sub.it], is the monthly return on a stock i, [r.sub.ft], is the monthly return on the 10-year U.S. Treasury bond, [r.sub.mt], is the monthly return on the NYSE-AMEX-Nasdaq value-weighted index, SMB, is the difference between the monthly return on a portfolios of small and large firms, HML, is the difference between the monthly returns of the portfolios of high book-to-market and low book-to-market stocks, UMD, is the difference between the monthly returns of the portfolios of high and low momentum stocks, D, is a dummy variable equal to 1 if t is greater than the announcement date of the inclusion or deletion event. We estimate the model using monthly returns for three years prior to and following the announcement date excluding the announcement month. The cost of capital for the market and four- factor models are calculated using the mean monthly market, SMB, HML, and UMD risk premia over the period from 1926 to 2009. Buy-and-hold returns are calculated for three years before and after the event date. Buy-and-hold returns are annualized. If the sample firm is missing 25% or less of the total monthly returns, we compute the buy- and-hold return for the shorter window based on valid returns. The adjusted cost of capital for all methods is equal to the unadjusted cost of capital for the sample firms minus the estimated cost of capital for the matched firms. All cost of capital measures are winsorized at the 1% and 99% levels. We measure statistical significance using a Mest for means and the Wilcoxon ranked sign test for the medians for before and after the event and the Wilcoxon- Mann-Whitney test for difference in medians. Panel A. Inclusion Firms N Before Change After Market Model Unadjusted mean 331 0.4496 *** -0.2578 *** 0.1918 *** Adjusted mean 314 0.2171 *** -0.1886 *** 0.0285 Unadjusted median 331 0.3123 *** -0.1700*** 0.1663 *** Adjusted median 314 0.1443 *** -0.1291 *** 0.0118 Four factor model Unadjusted mean 331 0.4586 *** -0.2759 *** 0.1826 *** Adjusted mean 314 0.1977 *** -0.1665 *** 0.0311 Unadjusted median 331 0.3243 *** -0.1652 *** 0.1416 *** Adjusted median 314 0.1223 *** -0.1178 *** 0.0029 Buy-and-Hold returns Unadjusted mean 315 0.4100 *** -0.3722 *** 0.0422 *** Adjusted mean 285 0.2340 *** -0.2267 *** -0.0040 Unadjusted median 315 0.3089 *** -0.2389 *** 0.0511 *** Adjusted median 285 0.1542 *** -0.1384 *** -0.0023 Market Model Unadjusted mean 116 0.0398 0.1949 *** 0.2347 *** Adjusted mean 111 -0.0469 0.0708 0.0239 Unadjusted median 116 -0.0094 0.1403 *** 0.1750 *** Adjusted median 111 -0.0555 ** 0.0336 -0.0009 Four factor model Unadjusted mean 116 0.0713 ** 0.1508 *** 0.2221 *** Adjusted mean 111 -0.0660 * 0.0827 0.0168 Unadjusted median 116 0.0271 0.1190 *** 0.1636 *** Adjusted median 111 -0.0595 *** 0.0187 -0.0121 Buy-and-Hold returns Unadjusted mean 339 0.0852 *** 0.1498 *** 0.1072 *** Adjusted mean 297 0.0101 0.0388 0.0222 Unadjusted median 339 0.0785 *** 0.1398 *** 0.0946 *** Adjusted median 297 0.0049 0.0609 0.0144 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table IV. Liquidity and Shadow Cost Measures The sample consists of all firms added or deleted from the S&P 500 during the period of 1990-2007. We exclude added firms and deleted firms where the added firm acquires the deleted firm, where two index firms merge and the merged firm remains, and where an added firm is a subsidiary spun-off from a deleted firm. We match each sample firm with a matching pair firm in the same three-digit SIC code and the matched pair is the closest possible match by asset size. Matched firms cannot be constituents of the S&P 500 for a period of 10 years surrounding the event. The unadjusted mean (median) for each variable is the sample firm average (median) value, and the adjusted mean (median) for each variable is the mean (median) difference between the sample and matched firms. The three liquidity measures and shadow cost are measured for three years before and after the inclusion or deletion event beginning one month prior to or after the announcement month. We standardize each liquidity measure by the same measure of the overall market which includes all stocks on the NYSE. The illiquidity ratio is the average of the absolute value of the daily return divided by the dollar volume traded on that day. The illiquidity ratio is further multiplied by 10' and scaled by the average daily market illiquidity ratio of all stocks on the NYSE. Volume is the average of the daily dollar amount traded. The dollar amount traded is calculated for each day as the number of shares traded multiplied by the closing price. Volume is market adjusted by scaling it by the average of daily total dollar trading volume on the NYSE. The turnover ratio is the average monthly share volume traded divided by the number of shares outstanding. The turnover ratio is market-adjusted by dividing it by the average monthly turnover of all stocks on the NYSE. Finally, the shadow cost is the ratio of the product of the residual standard deviation and firm size divided by the product of the S&P 500 index market capitalization and the number of shareholders. The residual standard deviation is the standard deviation of the difference between the firm's return and the S&P 500 total return. Firm size is measured as the number of shares outstanding multiplied by the closing price on the announcement date. The S&P 500 index market capitalization is measured in dollars on the announcement date. The number of shareholders is measured before the event date at the closest point prior to the event, and the number of shareholders after the event is measured at least nine months after the announcement date. We measure statistical significance using a t- test for means and the Wilcoxon ranked sign test for the medians for before and after the event and the Wilcoxon-Mann-Whitney test for difference in medians. Panel A. Inclusion Firms N Before Change After Illiquidity Ratio Unadjusted mean 345 0.0065 *** -0.0022 *** 0.0044 *** Adjusted mean 341 -0.1487 ** -0.0939 ** -0.2548 *** Unadjusted median 345 0.0047 *** -0.0012 *** 0.0031 *** Adjusted median 341 -0.0102 -0.0012 -0.0111 *** Volume Unadjusted mean 345 1.4333 *** 0.7261 *** 2.0668 *** Adjusted mean 341 0.9314 *** 0.7354 *** 1.5845 *** Unadjusted median 345 0.7242 *** 0.2499 *** 0.9475 *** Adjusted median 341 0.4622 *** 0.2198 *** 0.6732 *** Turnover Unadjusted mean 345 2.3957 *** -0.2169 *** 2.1139 *** Adjusted mean 341 0.6176 -0.0697 0.5014 *** Unadjusted median 345 1.5296 0.0223 1.4288 *** Adjusted median 341 0.3044 -0.0240 0.2970 *** Shadow Cost Unadjusted mean 332 1.4882 *** -0.4893 *** 0.9989 *** Adjusted mean 303 0.9110 *** -0.5015 *** 0.4095 *** Unadjusted median 332 0.4151 *** -0.0091 *** 0.3169 *** Adjusted median 303 0.2006 *** -0.0186 *** 0.0737 *** Panel B. Deletion Firms Illiquidity Ratio Unadjusted mean 143 0.0219 *** 0.1563 *** 0.1855 *** Adjusted mean 141 -0.3707 * -0.5093 * -0.9871 Unadjusted median 143 0.0055 *** 0.0146 *** 0.0308 *** Adjusted median 141 -0.0121 0.0077 -0.0083 Volume Unadjusted mean 143 1.1529 ** -0.2252 ** 0.5018 *** Adjusted mean 141 0.6978 -0.1207 0.2656 *** Unadjusted median 143 0.5665 *** -0.0638 *** 0.1378 *** Adjusted median 141 0.2843 ** -0.0369 ** 0.0396 *** Turnover Unadjusted mean 143 1.6519 0.0279 1.6779 *** Adjusted mean 141 0.3134 0.1151 0.1176 Unadjusted median 143 1.3184 -0.0287 1.3898 *** Adjusted median 141 0.2706 0.0328 0.1270 Shadow Cost Unadjusted mean 112 0.0918 -0.0089 0.0829 *** Adjusted mean 102 -0.4811 -0.2009 -0.6820 ** Unadjusted median 112 0.0283 ** 0.0030 ** 0.0394 *** Adjusted median 102 -0.0273 -0.0017 -0.0212 *** *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table V. Multivariate Analysis of Cost of Equity Changes The sample consists of all firms added or deleted from the S&P 500 during the period of 1990-2007. We exclude added firms and deleted firms where the added firm acquires the deleted firm, where two index firms merge and the merged firm remains, and where an added firm is a subsidiary spun-off from a deleted firm. The dependent variable in each regression is the change in the cost of capital estimated from the market model. The three liquidity measures and shadow cost are measured for three years before and after the inclusion or deletion event beginning one month prior to or after the announcement month. The change in these measures is the difference between the measure before and after the announcement date. We standardize each liquidity measure by the same measure of the overall market which includes all stocks on the NYSE. The illiquidity ratio is the average of the absolute value of the daily return divided by the dollar volume traded on that day. The illiquidity ratio is further multiplied by [10.sup.7] and scaled by the average daily market illiquidity ratio of all stocks on the NYSE. Volume is the average of the daily dollar amount traded. The dollar amount traded is calculated for each day as the number of shares traded multiplied by the closing price. Volume is market adjusted by scaling it by the average of daily total dollar trading volume on the NYSE. The turnover ratio is the average monthly share volume traded divided by the number of shares outstanding. The turnover ratio is market-adjusted by dividing it by the average monthly turnover of all stocks on the NYSE. Finally, the shadow cost is the ratio of the product of the residual standard deviation and firm size divided by the product of the S&P 500 index market capitalization and the number of shareholders. The residual standard deviation is the standard deviation of the difference between the firm's return and the S&P 500 total return. Firm size is measured as the number of shares outstanding multiplied by the closing price on the announcement date. The S&P 500 index market capitalization is measured in dollars on the announcement date. The number of shareholders is measured before the event date at the closest point prior to the event, and the number of shareholders after the event is measured at least nine months after the announcement date. Large market capitalization flag is equal to 1 if the newly added or removed firm is in the top 50% of the total market capitalization of the S&P 500 on the announcement date. The leverage ratio is defined as the ratio of the book value of total debt (long-term debt plus debt in current liabilities) to the total assets. We measure the average leverage ratio in the three years prior to the announcement date and the three years following the announcement date. The abnormal reaction to quarterly earnings announcements is measured for every quarter for days [-1, +1]. We find the average of the abnormal reaction for the 20 quarters preceding and following the announcement date, respectively. The change in the quarterly earnings announcement is the difference in the average abnormal reaction following the event and preceding the event. Parameter estimates are presented with t- statistics later. Model 1 Model 2 Model 3 Panel A. Inclusion Firms intercept -0.1678 *** -0.1662 *** -0.1654 *** -5.76 -5.43 -5.67 Illiquidity ratio change 8.7764 ** 8.5744 ** 8.9111 ** 2.18 2.07 2.29 Volume change -0.0058 -0.0008 -0.55 -0.08 Turnover change 0.0010 -0.0050 0.05 -0.23 Shadow cost change 0.1211 *** 0.1136 *** 0.1129 *** 6.73 5.91 6.02 Large market cap. flag -0.4819 *** -0.4738 *** -2.86 -2.96 Leverage change -0.0248 -0.0265 -0.11 -0.12 Earnings reaction change -0.0036 -0.0043 -0.28 -0.35 N 322 307 307 Adjusted [R.sup.2] 0.1595 0.1649 0.1703 Panel B. Deletion Firms Intercept 0.2456 *** 0.2338 *** 0.2338 5.24 4.71 4.79 Illiquidity ratio change -0.0618 -0.0878 -0.0858 -0.69 -1.02 -0.99 Volume change 0.0520 0.0297 1.19 0.68 Turnover change 0.0683 0.0680 * 1.65 1.70 Shadow cost change 0.0719 -0.1085 0.1127 0.22 -0.34 0.39 Large market cap. flag -0.4672 -0.4158 -1.07 -0.97 Leverage change -0.9054 ** -0.9848 -2.63 -2.93 Earnings reaction change 0.0195 0.0155 1.47 1.18 N 106 101 101 Adjusted [R.sup.2] 0.0280 0.0836 0.0669 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table VI. Multivariate Analysis of Excess Returns The sample consists of all firms added or deleted from the S&P 500 during the period of 1990-2007. We exclude added firms and deleted firms where the added firm acquires the deleted firm, where two index firms merge and the merged firm remains, and where an added firm is a subsidiary spun-off from a deleted firm. The dependent variable in each regression is the excess abnormal return from the index change announcement date through the implementation date. The cost of capital change is estimated from the market model. The three liquidity measures and shadow cost are measured for two years before and after the inclusion or deletion event beginning one month prior to or after the announcement month. The change in these measures is the difference between the measure before and after the announcement date. We standardize each liquidity measure by the same measure of the overall market which includes all stocks on the NYSE. The illiquidity ratio is the average of the absolute value of the daily return divided by the dollar volume traded on that day. The illiquidity ratio is further multiplied by 10' and scaled by the average daily market illiquidity ratio of all stocks on the NYSE. Volume is the average of the daily dollar amount traded. The dollar amount traded is calculated for each day as the number of shares traded multiplied by the closing price. Volume is market adjusted by scaling it by the average of daily total dollar trading volume on the NYSE. The turnover ratio is the average monthly share volume traded divided by the number of shares outstanding. The turnover ratio is market- adjusted by dividing it by the average monthly turnover of all stocks on the NYSE. Finally, the shadow cost is the ratio of the product of the residual standard deviation and firm size divided by the product of the S&P 500 index market capitalization and the number of shareholders. The residual standard deviation is the standard deviation of the difference between the firm's return and the S&P 500 total return. Firm size is measured as the number of shares outstanding multiplied by the closing price on the announcement date. The S&P 500 index market capitalization is measured in dollars on the announcement date. The number of shareholders is measured before the event date at the closest point prior to the event, and the number of shareholders after the event is measured at least nine months after the announcement date. We orthogonalize the shadow cost and cost of capital change due to multicollinearity and include the residual of the shadow cost. Large market capitalization flag is equal to 1 if the newly added or removed firm is in the top 50% of the total market capitalization of the S&P 500 on the announcement date. The leverage ratio is defined as the ratio of the book value of total debt (long- term debt plus debt in current liabilities) to the total assets. We measure the average leverage ratio in the three years prior to the announcement date and the three years following the announcement date. The abnormal reaction to quarterly earnings announcements is measured for every quarter for days [-1, +1]. We find the average of the abnormal reaction for the 20 quarters preceding and following the announcement date, respectively. The change in the quarterly earnings announcement is the difference in the average abnormal reaction following the event and preceding the event. The asset growth flag is equal to 1 if the included (excluded) firm has asset growth above the median in the inclusion (deletion) sample. We measure asset growth as the percent change in total assets from the fiscal year prior to the event to the fiscal year of the event. We include an interaction of the cost of capital change and the asset growth flag. Parameter estimates are presented with t-statistics later. Model 1 Model 2 Model 3 Panel A. Inclusion Firms Intercept 0.0348 *** 0.0340 *** 0.0401 *** 4.55 4.26 3.94 Cost of capital change -0.0244 * -0.0243 * 0.0454 -1.86 -1.78 1.63 illiquidity ratio change -2.6735 *** -2.9960 *** -2.9667 *** -2.65 -2.89 -2.88 Volume change 0.0033 0.0036 0.0043 1.23 1.32 1.55 Turnover change -0.0103 ** -0.0078 -0.0079 -2.03 -1.42 -1.45 Panel A. Inclusion Firms Shadow cost change -0.0077 -0.0074 -0.0050 -1.60 -1.48 -0.98 Large market cap. flag 0.0320 0.0143 0.75 0.34 Leverage change 0.0608 0.0738 1.13 1.37 Earnings reaction change -0.0038 -0.0032 -1.19 -1.00 Asset growth flag -0.0122 -0.80 Asset growth flag * -0.0914 *** cost of capital change -2.83 N 322 307 306 Adjusted [R.sub.2] 0.0580 0.0681 0.0870 Panel B. Deletion Firms Intercept -0.0168 -0.0033 0.0173 -0.69 -0.13 0.44 Cost of capital change 0.0066 0.0403 0.0371 0.15 0.81 0.57 Illiquidity ratio change -0.0961 ** -0.0758 * -0.0817 * -2.37 -1.86 -1.96 Volume change 0.0235 0.0260 0.0307 1.18 1.26 1.38 Turnover change 0.0319 * 0.0223 0.0234 1.67 1.17 1.21 Shadow cost change -0.1107 -0.0267 -0.0525 -0.75 -0.18 -0.33 Large market cap. flag -0.0229 -0.0206 -0.11 -0.10 Leverage change 0.1803 0.1821 1.07 1.07 Earnings reaction change -0.0176 *** -0.0177 *** -2.80 -2.78 Asset growth flag -0.0327 -0.67 Asset growth flag * -0.0129 cost of capital change -0.13 N 106 101 101 Adjusted [R.sup.2 0.0549 0.1063 0.0935 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level.

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Title Annotation: | Standard & Poor's Corp. |
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Author: | Baran, Lindsay; King, Tao-Hsien Dolly |

Publication: | Financial Management |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jun 22, 2012 |

Words: | 14599 |

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