# A Regression analysis: logarithm or relative change?

Hi. I am currently studying the market for equity options and the use of these to predict stock return around company earnings announcements. The dependent variable in my regression analyses have been the relative change in stock price or log-return from the day before the announcement to closing price on announcement day. However, would it be reasonable to instead/also run regressions using the logarithm of the closing price itself as the dependent variable. Then the independent variables would still show if they have a tendency to pull the price up or down on the day of the earnings announcement, although there would be no data involved actually showing relative change. Running a few short tests, shows that the log-alternative provides more significant relations and a greater R^2 than when using the relative change as the dependent variable. Am I completely mistaken?

Mons

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#### scottdave

Homework Helper
Gold Member
One thing that may be of concern, suppose you predict a value for the logarithm of the stock price and it is a little bit off from the log of the actual price. So it looks like you have a pretty good model. But a little bit in log scale can be a lot in actual stock values.
Say we are talking log (base 10). If you predict the log is 2.01, but say the log of the actual is 2.00, you think it is only 0.5% off - not bad. But the actual stock prices are $100, while the predicted is$102.33 (2.33% off). As the errors get a little larger, you'll see the price variations increase exponentially.

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#### BWV

You need a stationary series to do decent statistical tests and log prices / returns is the standard method. Regressions on a non-stationary series will show artificially high R^2. In general, you should view any R^2 > around 0.4 with deep suspicion unless is it something trivial, like regressing equity mutual fund returns against a stock index. The beta T-stats are the important variable. For this you are interested in log returns in excess of the market - need to strip out the market return to do this properly

"Regression analysis: logarithm or relative change?"

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