On the Present Value Model in a Cross Section of Stocks

We construct a cross-section of stock prices and their corresponding present values of future cash flows. A regression of present value on the initial stock price should have a slope coefficient equal to 1.0. For short horizons, this is a cross-section version of checking the random walk model and the present value model holds up well. In contrast, using three different samples that go as far back as 1926, the present value model is rejected decisively at moderate and long horizons. We can rule out the possibility that the failure of the present value relationship is due to a misunderstanding of the dividend process. The remaining possibilities are either that agents do not discount very far into the future in a manner consistent with the present value model, or that models of discount rates are too limited to allow the present value model to be a good fit to the data for most firms. We find that the present value works much better, albeit still imperfectly, for larger firms. We also find that stocks that appear on the exchanges for fewer years than longer-lasting stocks deviate even more from the present value model. Our results can be interpreted as a cross-section version of the variance-bounds test, with the result that prices are very much more variable than they ought to be.