Cumulative Abnormal Returns 0.800000 DAY - 20 T0 +186 0.600000 CUMULATIVE ABNORMAL RETURNS 0.400000 0.200000 0.000000-0.200000-0.400000-0.600000-0.800000 3 5 13 16 7 15 17 23 12-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 DAY RELATIVE TO ANNOUNCEMENT OMX SPLS ODP Office Max Cumulative Abnormal Returns are negative over the sample period. Office Depot Postive CR Staples - Net Negative CR When agreement to sell stores was reached on 3/12, SPLS fell 1.25 to 22.00 When FTC voted to reject the sell off on 4/4, SPLS rose 62.5 cents to 21.875.
Probability Function Look at relationship between probability of merger being cleared and residual of competitor OMX: The transaction was a stock swap. Each share of ODP would be exchanged for 1.14 shares of SPLS. If the merger was going to occur with probability 1, then P ODP = 1.14 P SPLS. If the probability is less than one, the ratio P ODP /1.14P SPLS will be less than one. This ratio cleared by the antitrust authorities. More generally, P ODP = p*1.14 P SPLS ODP ODP = is the price of ODP if the transaction is not completed, and p is the probability that the transaction is completed. Solving for p yields: p = [P ODP - ODP ]/[1.14 P SPLS - ODP ]. The following graph shows the proxy for p, assuming that the post ODP price is 60% of the Post Transaction Staples price (what the relationship was after the merger was denied).
Probability and OMX Cumulative Residual 1.2 0.100000 1 5 7 13 0.000000-0.100000 0.8 23 28-0.200000 0.6 3 12-0.300000 0.4 0.2 17-0.400000-0.500000-0.600000 0-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180-0.700000 DATE RELATIVE TO ANNOUNCEMENT ODP/1.14*SPLS "OMX CAR"
Probability Functions 1.2 1 3 5 7 13 15 16 0.8 23 28 0.6 12 17 Y-Axis 0.4 0.2 0-0.2-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 DATE RELATIVE TO ANNOUNCEMENT PROBABILITY FUNCTIO OMX/1.14*SPLS
Probability and OMX Residual 1.2 0.200000 1 0.150000 0.100000 0.8 0.050000 0.6 0.4 Y-Axis 0.000000-0.050000-0.100000 0.2-0.150000 0-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180-0.200000 DATE RELATIVE TO ANNOUNCEMENT ODP/1.14*SPLS OMX RESIDUAL Under the anticompetitive hypothesis, increases in the probability should generate positive abnormal returns for the competitor OMX. This should result in a positive correlation between the probability function and the residual of OMX (pictured above).
1 Day Residuals Around Primary Events Look closer at specific events:, because low correlation over entire period includes a lot of non events, which would tend to bias the correlation towards zero. Examination of correlation between the abnormal returns of merging firms and competitor. Under the anticompetitive hypothesis, the abnormal returns should move in the same direction. Under the procompetitive hypothesis, there should be a negative correlation between the merging and competitor firms abnormal returns. We observe a negative correlation for the first 4 events, and a positive correlation for the last 4 events. The simple hypotheses were contaminated by the proposed antitrust fix involving the sale of 63 stores.
2 Day Residuals Around Primary Events Here are the two day residuals, which yield similar results. On interesting pattern is to examine the movement of SPLS and ODP for the last 4 events -- they move in the opposite direction, and suggest that SPLS was paying too much after the proposed spinoff. When the agreement to sell stores was reached on 3/12, SPLS fell $1.25 to $22.00. When FTC staff voted to reject the spinoff on 4/4, SPLS rose 62.5 cents to $21.875. Staples rose 1-1/16 to 24-5/16 on announcement of PI decision.
Total Value of the Combination 18000 16000 14000 MILLIONS OF DOLLARS 12000 10000 8000 6000 4000 2000 0-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 DATE RELATIVE TO ANNOUNCEMENT TOTAL VALUE ODP VALUE SPLS
ODP and S&P 500 ODP AND S&P500 DAYS -170 TO -21 0.150000 0.100000 ODP RETURN 0.050000 0.000000 ACTUAL -0.050000-0.100000-0.150000-0.1500000-0.1000000-0.0500000 0.0000000 0.0500000 0.1000000 0.1500000 S&P 500 RETURN
SPLS and S&P 500 SPLS AND S&P500 DAYS -170 TO -21 0.150000 0.100000 SPLS RETURN 0.050000 0.000000 ACTUAL -0.050000-0.100000-0.150000-0.1500000-0.1000000-0.0500000 0.0000000 0.0500000 0.1000000 0.1500000 S&P 500 RETURN
Correlation of Probability & OMX Residual Correlations between the proxies and the OMX residual are small (.04), and regressions yield small and statistically insignificant coefficients. CORR(OMX RESIDUAL,ODP/1.14SPLS) 0.0407677 Regression Output: REGRESSION OF OMX RESIDUAL ON OMX/1.14*SPLS Constant 0.8309783 Std Err of Y Est 0.1100712 R Squared 0.001662 No. of Observations 187 Degrees of Freedom 185 X Coefficient(s) 0.1451976 Std Err of Coef. 0.261635 T-STATISTIC 0.5549625 Regression Output:REGRESSION OF OMX RESIDUAL ON PROBABILITY FUNCTION Constant 0.6123044 Std Err of Y Est 0.2524771 R Squared 0.001662 No. of Observations 187 Degrees of Freedom 185 X Coefficient(s) 0.3330489 Std Err of Coef. 0.6001286 T-STATISTIC 0.5549625
Reverse Regression Reverse Regression Suppose that you have an error in variables problem: Instead of having good price and return data, you only have a proxy for such returns. That is, each variable may be measured with error. z m = r m + u m z i = r i + u i If we run the market model z i = a + bz m + e b = Cov(z i, z m )/Var(z m ) = Cov(r i,r m )/(Var(r m ) + Var(u m )) < Cov(r i,r m )/Var(r m ) = Thus, if the market return is measured with error, then b is downward biased estimate of.
Reverse Regression Now, suppose that the following regression was run. In general, b = R 2 (1/g), so that b < 1/g The slope coefficient equals: Thus, 1/g is an upward biased estimate of, and z m = k + gz i + w 1/g = (Var(r i ) + Var(u i ))/Cov(r i,r m ) b < < 1/g. The extent of the bias is determined by the size variance of the error in measurement Var(u i ). Thus the choice of which variable you call independent or dependent has nothing to do with causality. Instead, the variable measured more precisely should be on the right hand side of the equation.
Reverse Regression
Fwd. & Rev. OMX Cumulative Residuals 0.500000 0.000000 OMX RETURNS -0.500000-1.000000-1.500000-2.000000-20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 DAY RELATIVE TO ANNOUNCEMENT FORWARD REVERSE
Decision Theory and the 1984 Orange Bowl (Mac Version)