The Dog That Did Not Bark: A Defense of Return Predictability

The Dog That Did Not Bark: A Defense of Return Predictability

By: John H. Cochrane

          In this paper, Cochrane makes the determination that either returns or dividend growth are forecastable.  Using this line of reasoning, he states that the absence of predictability of one variable implies the presence of predictability in the other variable.  Cochrane works to prove the absence or presence of dividend growth and returns here to see what can actually be predicted and how much.  Table 1 is given at the beginning, showing some regressions that would forecast returns and dividend growth.

          In the table, real return, real return minus real return on 3-month T-bills, and dividend growth are forecasted using the dividend-price ratio.  Real return and real return minus real return on 3-month T-bills have a positive and significant coefficient.  Conversely, dividend growth has a very small coefficient and is not statistically significant.  It would be easy to simply say that this means returns can be forecasted by the dividend-price ratio, but Cochrane says the coefficient on the return regressions is biased upward and the t-statistic is biased toward rejection.  This means we cannot trust the result of the returns forecasting regressions in the table.  Does this mean return forecastability is dead? No.

          Looking at table one, clearly dividend growth is not forecastable using the dividend-price ratio.  Cochrane says that “If both returns and dividend growth are unforecastable, then present value logic implies that the price/dividend ratio is constant, which it obviously is not.” Using this theory, it means that either returns or dividend growth must be forecastable.  Based on this logic, it leads to the simple conclusion that if dividend growth is clearly not forecastable, returns must be forecastable despite the regressions’ bias mentioned above.  Cochrane then uses different measures to prove if dividend growth is forecastable including vector auto-regressions and analyzing long-horizon regression coefficients.  He uses a joint distribution with a joint hypothesis/null that if returns are forecastable then dividend growth is not and vice versa.

Vector Auto-Regressions

          After going through these processes, Cochrane says there is not a shred of evidence proving that high market price-dividend ratios are associated with higher subsequent dividend growth.  Using this result and the line of reasoning discussed above, this means that real returns are forecastable.  Cochrane notes that excess return forecastability is not a comforting result.  Life would be easier if you could trace price movements back to visible news about dividends or cashflows.  The evidence so far seems to be that most aggregate price/dividend variation can be explained only by rather nebulous variation in Sharpe-ratios.  Cochrane says “the only good news is that observed return forecastability does seem to be just enough to account for the volatility of price dividend ratios. If both return and dividend-growth coefficients were small, we would be forced to conclude that prices follow a “bubble” process, moving only on news (or, frankly, opinion) of their own future values.

          In conclusion, setting up simple regressions for returns and dividend growth using the dividend/price ratio to determine their forecastability is inconclusive.  Using present value logic, we know that one of the two measures must be forecastable.  This means Cochrane only has to test one hypothesis and it will prove the other.  He chooses to prove whether dividend growth is forecastable and finds that it is not by using measures such as basic linear regression, VARs, and long-horizon regression estimates.  This leads to a final conclusion that returns are forecastable.  A conclusion that isn’t as definitively proven by going through the same process for returns as is done for dividend growth.