larryswedroe wrote:The fact that you have an rsquared as high as 40 means that there is valuable information there. It's not like it's 0 or .1
It's really as simple as that
I'm not sure it's really as simple as that. What are the f-test results on this regression analysis? What about a Dickey-Fuller type test? The point being that we don't really know whether we are dealing with a normal distribution of returns, or whether we have non-stationarity (random walk). The R2 of 0.4 may actually be meaningless in terms of predictive power, and we don't realize it.
With that said, your point about the equity risk premium disappearing if the R2 was higher is an interesting one that I hadn't thought of before. Basically, I think you are saying that if the model had a better "fit," more investors would pile into whatever factors the model is currently calling for, which would drive up those equity prices and result in a lower earnings yield. Then again, if that happened, wouldn't the model then fall apart? In other words, it would seem to result in a kind of paradoxical loop where (say) the PE10 indicates that stocks are undervalued, investors immediately pile in, then the PE10 immediately indicates stocks are overvalued, investors immediately sell everything.....and so on.
Simplegift wrote:Their Results: On the chart below, the expected returns for each decade (x-axis) are plotted against the actual real returns (y-axis). The overall fit to the trend line was R^2 = 0.28. However, there are two obvious outliers — the 1910s during World War I (when returns were way below forecast) and the 1990s Tech Bubble (when returns were way above forecast). Without these two unusual outliers, R^2 = 0.62.
Improving the R2 after removing "anomalies" and trying to extract predictive value from it is otherwise known as data mining. To me, it's also an indication that there have been "regime changes" that renders the model as questionable (at best) for forecasting future returns. What can the model tell us about future regime changes? Nothing, of course.
All of this (and more) just reminds me of how difficult (impossible) it really is to predict anything about the future. At best, our statistical models can attempt to explain what has already happened, and the models of our financial markets do a fairly poor job of even doing that.