The above summary immediately raises two additional issues. First, what is the effect of the October, 1987 crash on the fitted regression equation? We know that unusual observations, such as the crash, may potentially influence the fit a great deal. To this end, the regression was re-run without the observation corresponding to the crash. The motivation for this is that the October 1987 crash represents a combination of highly unusual events (the interaction of several automated trading programs operated by the large stock brokerage houses) that we do not wish to represent using the same model as our other observations. Deleting this observation, the fitted regression is begin{equation*} widehat{LINCOLN} = -0.00181 + 0.956 MARKET, end{equation*} with (R^2=26.4%), (t(b_1)=4.52), (s=0.0702) and (s_y=0.0811). We interpret these statistics in the same fashion as the fitted model including the October 1987 crash. It is interesting to note, however, that the proportion of variability explained has actually decreased when excluding the influential point. This serves to illustrate an important point. High leverage points are often looked upon with dread by data analysts because they are, by definition, unlike other observations in the data set and require special attention. However, when fitting relationships among variables, they also represent an opportunity because they allow the data analyst to observe the relationship between variables over broader ranges than otherwise possible. The downside is that these relationships may be nonlinear or follow an entirely different pattern when compared to the relationships observed in the main portion of the data.
The second question raised by the regression analysis is what can be said about the unusual circumstances that gave rise to the unusual behavior of Lincoln’s returns in October and November of 1990. A useful feature of regression analysis is to identify and raise the question; it does not resolve it. Because the analysis clearly pinpoints two highly unusual points, it suggests to the data analyst to go back and ask some specific questions about the sources of the data. In this case, the answer is straightforward. In October of 1990, the Travelers’ Insurance Company, a competitor, announced that it would take a large write-off in their real estate portfolio. due to an unprecedented number of mortgage defaults. The market reacted quickly to this news, and investors assumed that other large stock life insurers would also soon announce large write-offs. Anticipating this news, investors tried to sell their portfolios of, for example, Lincoln’s stock, thus causing the price to plummet. However, it turned out that investors overreacted to this news and that Lincoln’s portfolio of real estate was indeed sound. Thus, prices quickly returned to their historical levels.