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The variable on which firms will be classified is defined, using the investment strategy as a guideA. Event Study An event study is designed to examine market reactions to, and excess returns around specific information events. The information events can be market-wide, such as macro-economic announcements, or firm-specific, such as earnings or dividend announcements. The steps in an event study are as follows (1) The event to be studied is clearly identified, and the date on which the event was announced pinpointed. The presumption in event studies is that the timing of the event is known with a fair degree of certainty. Since financial markets react to the information about an event, rather than the event itself, most event studies are centered around the announcement date4 for the event. Announcement Date (2) Once the event dates are known, returns are collected around these dates for each of the firms in the sample. In doing so, two decisions have to be made. First, the analyst has to decide whether to collect weekly, daily or shorter-interval returns around the event. This will, in part, be decided by how precisely the event date is known (the more precise, the more likely it is that shorter return intervals can be used) and by how quickly information is reflected in prices (the faster the adjustment, the shorter the return interval to use). Second, the analyst has to determine how many periods of returns before and after the announcement date will be considered as part of the event window. That decision also will be determined by the precision of the event date, since more imprecise dates will require longer windows. (3) The returns, by period, around the announcement date, are adjusted for market performance and risk to arrive at excess returns for each firm in the sample. For instance, if the capital asset pricing model is used to control for risk Excess Return on period t = Return on day t - (Riskfree rate + Beta * Return on market on day t) (5) The question of whether the excess returns around the announcement are different from zero is answered by estimating the t statistic for each n, by dividing the average excess return by the standard error T statistic for excess return on day t = Average Excess Return / Standard Error If the t statistics are statistically significant5, the event affects returns; the sign of the excess return determines whether the effect is positive or negative. Illustration 8.1: Example of an event study - Effects of Option Listing on Stock prices Academics and practitioners have long argued about the consequences of option listing for stock price volatility. On the one hand, there are those who argue that options attract speculators and hence increase stock price volatility. On the other hand, there are others who argue that options increase the available choices for investors and increase the flow of information to financial markets, and thus lead to lower stock price volatility and higher stock prices. One way to test these alternative hypotheses is to do an event study, examining the effects of listing options on the underlying stocks prices. Conrad(1989) did such a study, following these steps The date on which the announcement that options would be listed on the Chicago Board of Options on a particular stock was collected. Step 2:The prices of the underlying stock(j) were collected for each of the ten days prior to the option listing announcement date, the day of the announcement, and each of the ten days after. Step 3:The returns on the stock (Rjt) were computed for each of these trading days. The beta for the stock (?j) was estimated using the returns from a time period outside the event window (using 100 trading days from before the event and 100 trading days after the event). The excess returns are cumulated for each trading day. Step 7:The average and standard error of excess returns across all stocks with option listings were computed for each of the 21 trading days. The t statistics are computed using the averages and standard errors for each trading day. Table 6.1 summarizes the average excess returns and t statistics around option listing announcement dates Table 6.1: Excess Returns around Option Listing Announcement Dates Trading Day Average Excess Cumulative T Statistic Based upon these excess returns, there is no evidence of an announcement effect on the announcement day alone, but there is mild6 evidence of a positive effect over the entire announcement period. B. Portfolio Study In some investment strategies, firms with specific characteristics are viewed as more likely to be undervalued, and therefore have excess returns, than firms without these characteristics. In these cases, the strategies can be tested by creating portfolios of firms possessing these characteristics at the beginning of a time period, and examining returns over the time period. To ensure that these results are not colored by the idiosyncracies of one time period, this analysis is repeated for a number of periods. The steps in doing a portfolio study are as follows (1) The variable on which firms will be classified is defined, using the investment strategy as a guide. This variable has to be observable, though it does not have to be numerical. Examples would include market value of equity, bond ratings, stock price, price earnings ratios and price book value ratios. (2) The data on the variable is collected for every firm in the defined universe7 at the start of the testing period, and firms are classified into portfolios based upon the magnitude of the variable. Thus, if the price earnings ratio is the screening variable, firms are classified on the basis of PE ratios into portfolios from lowest PE to highest PE classes. The number of classes will depend upon the size of the universe, since there have to be sufficient firms in each portfolio to get some measure of diversification. (3) The returns are collected for each firm in each portfolio for the testing period, and the returns for each portfolio are computed, generally assuming that the stocks are equally weighted. (4) The beta (if using a single factor model) or betas (if using a multifactor model) of each portfolio are estimated, either by taking the average of the betas of the individual stocks in the portfolio or by regressing the portfolios returns against market returns over a prior time period (for instance, the year before the testing period). (5) The excess returns earned by each portfolio are computed, in conjunction with the standard error of the excess returns. (6) There are a number of statistical tests available to check whether the average excess returns are, in fact, different across the portfolios. Some of these tests are parametric8 (they make certain distributional assumptions about excess returns) and some are nonparametric9. (7) As a final test, the extreme portfolios can be matched against each other to see whether there are statistically significant differences across these portfolios. 7 Though there are practicial limits on how big the universe can be, care should be taken to make sure that no biases enter at this stage of the process. An obvious one would be to pick only stocks that have done well over the time period for the universe. 8 One parametric test is an F test, which tests for equality of means across groups. This test can be conducted assuming either that the groups have the same variance, or that they have different variances. 9 An example of a non-parametric test is a rank sum test, which ranks returns across the entire sample an then sums the ranks within each group to check whether the rankings are random or systematic. Practitioners have claimed that low price-earnings ratio stocks are generally bargains and do much better than the market or stocks with high price earnings ratios. This hypothesis can be tested using a portfolio approach Step 1: Using data on price-earnings ratios from the end of 1987, firms on the New York Stock Exchange were classified into five groups, the first group consisting of stocks with the lowest PE ratios and the fifth group consisting of stocks with the highest PE ratios. Firms with negative price-earnings ratios were ignored. Step 2: The returns on each portfolio were computed using data from 1988 to 1992. Stocks which went bankrupt or were delisted were assigned a return of -100%. Step 3: The betas for each stock in each portfolio were computed using monthly returns from 1983 to 1987, and the average beta for each portfolio was estimated. The portfolios were assumed to be equally weighted. Step 4: The returns on the market index was computed from 1988 to 1992. Step 5: The excess returns on each portfolio were computed using data from 1988 to 1992. Table 6.2 summarizes the excess returns each year from 1988 to 1992 for each portfolio. Step 6: While the ranking of the returns across the portfolio classes seems to confirm our hypothesis that low PE stocks earn a higher return, we have to consider whether the differences across portfolios is statistically significant. There are several tests available, but these are a few: * An F test can be used to accept or reject the hypothesis that the average returns are the same across all portfolios. A high F score would lead us to conclude that the differences are too large to be random. * A chi-squared test is a non-parametric test that can be used to test the hypothesis that the means are the same across the five portfolio classes. * We could isolate just the lowest PE and highest PE stocks and estimate a t statistic that the averages are different across these two portfolios. |
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