for GDP, inflation rates, interest rates, or corporate profitability. Isolating the part of a stock price movement that is attributable to a dividend announcement is not a trivial exercise. The statistical approach that researchers commonly use to measure the impact of a par- ticular information release, such as the announcement of a dividend change, is a marriage of efficient market theory with the index model discussed in Chapter 10. We want to mea- sure the unexpected return that results from an event. This is the difference between the ac- tual stock return and the return that might have been expected given the performance of the market. This expected return can be calculated using the index model. Recall that the index model holds that stock returns are determined by a market factor and a firm-specific factor. The stock return, rt, during a given period t, would be expressed mathematically as   rt a brMt et (12.1)   where rMt is the markets rate of return during the period and et is the part of a securitys re- turn resulting from firm-specific events. The parameter b measures sensitivity to the mar- ket return, and a is the average rate of return the stock would realize in a period with a zero market return.5 Equation 12.1 therefore provides a decomposition of rt into market and firm-specific factors. The firm-specific return may be interpreted as the unexpected return that results from the event. Determination of the firm-specific return in a given period requires that we obtain an es- timate of the term et. Therefore, we rewrite equation 12.1:   et rt - (a brMt) (12.2)       5 We know from Chapter 10, Section 10.3, that the CAPM implies that the intercept a in equation 12.1 should equal rf (1 - ). Nev- ertheless, it is customary to estimate the intercept in this equation empirically rather than imposing the CAPM value. One justifi- cation for this practice is that empirically fitted security market lines seem flatter than predicted by the CAPM (see the next chapter), which would make the intercept implied by the CAPM too small. III. Equilibrium In Capital Markets 12. Market Efficiency The McGraw−Hill Companies, 2001           352 PART III Equilibrium in Capital Markets     Equation 12.2 has a simple interpretation: To determine the firm-specific component of a stocks return, subtract the return that the stock ordinarily would earn for a given