Empirical Cross-Sectional Asset Pricing

Stefan Nagel. “Empirical Cross-Sectional Asset Pricing” The Annual Review of Financial Economics (2013) 5:167-199.

The author reviews research in several aspects of empirical cross-sectional asset pricing. Other posts here have and will highlight papers which touch on some of them, so I summarize only a couple of general themes.

There are approaches to cross-sectional asset pricing which distinguish explanations for why investors price assets the way they do and approaches which do not. “The economic content of pricing models is … in the restrictions that they impose on the [stochastic discount factor].” Ad hoc factor models and production-based models, while useful in cross-sectional tests, do not rely on investor preferences for their restrictions on the SDF and, so, do not explain the “why”. Rational (consumption-based, long-run risk) as well as sentiment-based tests based on theoretical restrictions on investor preferences give them a higher degree of economic content. Frictions and liquidity risk can cause rational models to fail, but studies in these areas provide evidence for “why” assets are priced the way they are. That is, additional risks exist for which investors rationally require additional return in order to bear the risk.

A significant amount of cross-sectional asset pricing research is centered around finding deviations from accepted models (anomalies). Recent studies have urged caution in this pursuit, however. The possibility for data snooping, where some spurious anomalies are randomly found to be significant, is an ever-present problem. Adjusting critical values and performing out-of-sample testing are ways suggested in the literature to help attenuate the problem. However, the author notes that pseudo out-of-sample testing is not necessarily a solution because data can be mined to find significant result here as well. True out-of-sample testing is necessary to lend validation to results. A true out-of-sample test occurs when data is used that was not available or used for the original study. Some ways this has been done in the literature is the use of data from different markets, post-publication data of the same asset(s) used in the original study, and in some cases even pre-sample data that became available after publication. It has additionally been found that use of r-squared statistics as an indication of how well a model or factor explain the cross-section of asset returns can be misleading when the test assets have a low-dimensional factor structure.

Investor sentiment happens when asset prices are evaluated under a subjective probability distribution. Its effect on asset prices is persistent when this sentiment is correlated across enough investors and there are significant enough risks to dissuade or prevent sophisticated investors from taking opposite positions and driving prices back to their fundamental values. Investor sentiment and rational explanations for return predictability need not be mutually exclusive. Research in this area focuses both on finding and testing empirical proxies for investor sentiment and on investigating the limits to arbitrage preventing sophisticated investors from correcting mispricing. Analyst forecasts, style fund returns, and mutual fund inflows are a few examples of proxies used with some success as proxies for investor sentiment.

Real world investors must learn about the return generating process in real time. Therefore, return predictability obvious to researchers in retrospect may not have been known or obvious to investors. Out-of-sample testing on variables shown to have ability to predict returns is one area of research into investor learning. For example, studies have shown that there is a decay of predictability after the publication of research about return predictors. The implication is that something not known to real-world investors becomes known upon publication and they then move to exploit it to the extent possible. Additional research has been done using pseudo out-of-sample testing where early periods in the data are used as a training sample to predict future returns. The author notes that investor learning does not fall under rational expectations or sentiment.

Empirical cross-sectional asset pricing research has come a long way and there is much yet to be explored. Many avenues of research are fruitful, but the ones with the greatest economic content are those which have something to say about the preferences of investors because they offer insight into understanding not just what is happening but “why” investors are pricing assets the way they are.

Digesting Anomalies: An Investment Approach

Kewi Hou, Chen Sue, Lu Zhang. "Digesting anomalies: an investment approach." The Review of Financial Studies; 28.3 (2015): 650-705. (link)

When it was first introduced, the Fama French three factor model was highly successful at explaining the cross section of expected stock returns. However, since the 90s, this model has not performed as well and many anomalies have been discovered which display abnormal returns within this model. In this paper, the authors present a q-factor model in which expected returns are a factor of market excess returns, the difference in returns of small and big stocks, the difference in returns of low and high investment stocks, and the difference in returns of high and low profitability stocks.

In this paper, Hou, Xue, and Zhang present an asset pricing model to explain the cross-section of stock returns. The q-factor model describes excess returns in terms of the market return (MKT), a size factor ($r_{ME}$), an investment factor ($r_{I/A}$), and a profitability factor ($r_{ROE}$). They compare their model to the Fama-French (1993) three factor model as well as the Carhart (1997) four factor model. The results show that their q-factor model performs well in relation to these classic models and has better explanatory power over broad collection of anomalies.

The authors develop a two period economic model relateing firm profitability and investment. The model assumes that a firm will continue to invest until the marginal cost of that investment is equal to the expected return in the next period, times the discount rate. Equation (4) relates expected returns with profitability, $E_{0}[\Pi_{i1}]$, and investment, $1+a(I_{i0}/A_{i0})$. All else held constant, it predicts that highly profitable firms should earn higher returns and highly invested firms should earn lower returns.

\[ E_{0}[r_{i1}^S] = \frac{E_{0} [ \Pi_{i1} ] }{ 1 + a (I_{i0} A_{i0} ) } \qquad (4) \]

Using thirty years of data, the authors construct two size, three investment, and three profitability portfolios. Table 1 reports how their factors compare to the CAPM, FF3 and Carhart models. Size has an average monthly return of 0.31%, while Investment has monthly returns of 0.45% and profitability has monthly returns of 0.58%. The alphas of CAPM, FF3 and Carhart are also generally large enough to indicate that these models cannot capture the q-factors. The authors’ size factor has a correlation of 0.95 with SMB, the investment factor has a correlation of 0.69 with HML, and the profitability factor has a correlation of 0.5 with UMD, all of which are significant. Finally, the q-factor model captures a significant amount of HML and UMD with alphas of 0.06% and 0.13% respectively. They suggest their evidence points to HML and UMD representing less accurate variations of their q-factors.

The paper next tests the q-factor model against a broad collection of 80 anomalies. Equation (5) gives the regression used to test the model.

\[ r_{t}^i - r_{t}^f = \alpha_{q}^i + \beta_{\text{MKT}}^i \text{MKT}_{t} + \beta_{\text{ME}}^i r_{\text{ME}, t} + \beta_{\text{I/A}}^i r_{\text{I/A}, t} + \beta_{\text{ROE}}^i r_{\text{ROE}, t} + \epsilon^i \hspace{10}(5) \]

Of the 80 anomalies, only 35 are found to be significant in the cross section. Table 6 presents the factor loadings for the q-factor model with relation to these significant anomalies. It shows that most of the anomalies are combinations of the investment and profitability factors. Specifically, the momentum and profitability anomalies are mostly captured by the profitability factor while value / growth and investment anomalies are mostly captured by the investment factor. 

Earnings and price momentum are analyzed under the q-factor model. Five of the earnings momentum deciles have significant alphas under FF3 while three are significant under Carhart. Only one is significant for the q-factor model. For price momentum, four alphas are significant under FF3, three under Carhart, and zero under the q-factor. Momentum is mostly loaded under the ROE (profitability) factor. This makes intuitive sense since firms with good earnings and increasing prices are more likely to have increased profitability.

The q-factor model developed by Hou, Xue, and Zhang, attempts to explain the cross-section of expected returns using the market factor, combined with size, investment, and profitability. It succeeds in explaining most of a variety of anomalies using the investment and profitability factors, and outperforms the Fama-French 3 factor model and Carhart 4 factor model in almost all the studied anomalies.

Connected Stocks

Miguel Anton and Christopher Polk. "Connected Stocks. The Journal of Finance 69 (2014): 1099-1127.

This paper investigates whether the returns of stocks that are connected through mutual fund owners covary more together. In addition, the paper explores the implications of such comovement arising from common institutional ownership in predicting return variations, from which an implementable trading strategy is devised. A natural experiment for establishing causality is introduced, and how hedge funds may contribute to the occurrence of the documented phenomena (results) is also discussed.

The paper has an intellectual link to contagion, which can be defined as excess correlation, or, correlation over and above what one would expect from economic fundamentals. It is also related to the literature on fund flows and institutional-driven price (co)movements, which provides the ground for the assertion that the presence of institutional connectedness may generate cross-stock reversal patterns in returns, especially when the price pressure from fund flows reflects forced selling.

[Data, Sample, and Measurement of Common Ownership]

Common stocks whose market caps are above NYSE median market cap (i.e., big stocks) are retained in the sample. This ensures that the documented patterns are not just due to small or microcap stock effects. Also, common ownership by active managers is not pervasive, especially among the small stocks. The sample period spans from 1980 to 2008.

Common ownership is measured at each quarter-end as the total value of stock held by F common funds of the two stocks, scaled by the total market capitalization of the two stocks. It can be formalized as below;

where f is related to the funds that own shares for the firm pairs (i, j). S denotes the number of shares, and P denotes price at a certain time period.

[Regression Model]

After constructing the common ownership measure as well as other relevant control variables, the following regression model is estimated for predicting cross-sectional variation in comovement;

where the dependent variable represents the within-month realized correlation of each stock pair's daily four-factor residuals in month t+1. Rather than the pooled OLS, Fama-MacBeth regression with Newey-West standard error is used to address any cross-correlation issues in the residuals as well as autocorrelation in the time series.  

[Results]

The table below presents the results from estimating the regression model described above;

Across different specifications, we can see that the coefficients for FCAP are positive and statistically significant, meaning that the degree of connectedness among a pair of stocks via common institutional ownership strongly positively predicts cross-sectional abnormal return correlation as measured by four-factor residual correlations.

[Endogeneity Concern and Natural Experiment]

The results presented above are subject to the endogeneity concern that fund managers may choose to hold similar stocks. To establish causality, the paper exploits a natural experiment based on the mutual fund scandal that occurred in September 2003. Because the implicated families during the scandal experienced significant outflows, it can be argued that the suggested scandal provides an exogenous shock to capital flow, helping to eliminate concerns that the results are driven by the endogenous choices by fund managers. The instrument adopted here is RATIO, which is the total value held by all common 'implicated' funds of the two stocks over the total value held by all common funds. Two-stage least squares regression (2SLS) is estimated. The results are shown below;

Again, across all specifications, the coefficients for the instrumented FCAP are statistically significant, allowing causal interpretation of the results. Also, the fact that most coefficients are insignificant under simple OLS estimation reflects that the endogeneity of common ownership may genuinely be an important issue.

[Cross-Stock-Reversal Strategy]

A profitable trading strategy given the results documented above is to buy (sell) stocks that have gone down (up) if their connected stocks have gone down (up) as well. The underlying intuition is, if we have a highly-connected pair of stocks (i, j), if stock i experiences a negative shock and connected stock j's price also drops, one may conjecture that i's drop is due to price pressure related to fund trading but less to fundamentals, which we expect to revert. In other words, the trading strategy exploits the temporary misvaluation that may arise from mutual fund trading, with the degree of connectedness used as a measure of the extent of that temporary misvaluation.

The figure below presents the cumulative alphas over time for such a trading strategy;

We can clearly see that the long-short portfolio generates positive cumulative alpha. Also, more of the effect comes from the low portfolio than the high portfolio, consistent with the forced selling/price pressure story. 

[Hedge Fund]

Lastly, the paper explores whether the activities by hedge funds either benefit from or exacerbate the documented contagion generated from ownership-based connections.

The table below shows hudge funds' exposure to the strategy exploiting the institutional connectedness (CS strategy);

As the results indicate, hedge funds, especially those that exploit long-short strategy, negatively load on the CS factor and more so when the change in VIX is high. It appears hedge funds do not take full advantage of the opportunities that price pressure from mutual fund flows provide, exacerbating rather than mitigating the comovement patterns documented throughout the paper.

Financial Crises and Risk Premia

Tyler Muir. "Financial Crises and Risk Premia."The Quarterly Journal of Economics" (2017): 765-809.

This paper splits bad economic events into financial crises, recessions, deep recessions, and wars and analyzes data on consumption, dividend yields, stock returns, and credit spreads with an international panel that spans over 140 years across 14 countries. By analyzing this panel data, the paper seeks to answer why do risk premia vary over time, exploring potential underlying economic forces behind the time-varying risk premia.

The occurrence of a financial crisis is based on a major bank run or bank failure, so financial crisis and banking panic are interchangeable in this paper's context. Recession refers to "nonfinancial recessions,"; i.e., recessions that do not coincide with a financial crisis. Deep recessions are defined as nonfinancial recessions for which the initial drop in consumption exceeds 2%. The definition of war is straightforward.

The main proxies for risk premia used in this paper are dividend yields and credit spreads. Previous studies show that dividend yields appear to strongly predict future stock returns and only very weakly forecast future dividend growth. Similarily, fluctuations in credit spreads seem to largely predict excess returns and not default rates (cash flows). These documented stylized facts from previous literature lend support to the use of those two variables as proxies for risk premia, mainly conveying signals related to discount rate news rather than cash flow (related to fundamentals) news.

The main findings of this paper boil down to the figures presented below;

One should note that, as panel B indicates, the decline in consumption and increase in consumption volatility are similar across financial crises and recession or deep recessions, but we can observe a spike in risk premia only for financial crises, not for the other two events. Moreover, war events entail a much higher decline in consumption and an increase in consumption volatility than financial crisis events, but the behavior of risk premia seems not distinctive compared to nonfinancial recessions and deep recessions. In a nutshell, the prices fall for all those types of events, but a considerable degree of the spike in risk premia is only observed during the financial crisis events, making it unique.

The figure below essentially shows the same phenomena discussed above;

As we can clearly observe, the differential behavior of consumption and consumption volatility patterns across each of the different bad macroeconomic events can hardly be reconciled with the evolution of the proxies for risk premia, dividend yields and credit spreads. Here, again, financial crisis events are unique in the sense that only they entail a distinguishably higher level of risk premia compared to the other events relative to the evolutions of consumption behavior and volatilities.mAlso, the figure indicates that financial crises are associated with large price declines that are subsequently reversed, meaning the crisis is largely about a change in discount rates not in fundamentals (cash flows). Overall, the presented results indicate that asset pricing models based on aggregated consumption may have trouble matching the facts provided from the international panel data. In addition, the results imply that financial crises may be particularly important in understanding why risk premia vary.

After presenting the results, the author discusses what type of asset pricing model appears promising to match the data. Obviously, the standard consumption-based models with a representative agent don't seem to fit well. Also, long-run risks model, as well as rare disasters model, seem to have difficulty in explaining the presented facts in the paper. 

Intermediary-based models, in which stochastic discount factor depends on the health of the financial sector, seems promising in the sense that it naturally implies risk premia will be highest in financial crises. In addition, if a behavioral model can successfully exposit why there should be a distinguishably huge drop in investor sentiment that largely or exclusively pertains to financial crises for reasons beyond poor past returns, it may well match the data also. Lastly, the view on heterogeneous agents models is inconclusive in that some models such as models with idiosyncratic income or consumption risk may be linked with the behavior of risk premia during financial crises through the channel of unemployment, which has been uniquely high during the crises relative to the other events.

Does Academic Research Destroy Stock Return Predictability?

McLean, R.D. and Pontiff, J., 2016. Does academic research destroy stock return predictability?. The Journal of Finance, 71(1), pp.5-32.

Research Question and General Results

This paper evaluates the in-sample return, post-sample return and post-publication returns of 97 characteristics shown to predict cross-sectional stock returns in top journals. The authors find that average predictor’s long-short return declines by 26% and 58% out-of-sample and post-publication, respectively. The decay is stronger for predictors with higher in-sample returns and t-statistics. Besides, predictors with less costly arbitrage accelerate a lower post-publication returns and have a higher trading volume after publication. Hence, the aforementioned results indicate that investors learn from academic publications to take advantage of mispricing of stock returns.

Research Methodology

The paper identifies 97 characteristics shown to predict cross-sectional returns in top economics, accounting, and finance journals. Then, authors construct a long-short portfolio based on each predictor in each month and compute equal-weighted returns across all portfolios. Meanwhile, authors identify specific in-sample dates, out-of-sample dates and publication dates anomaly and create corresponding dummy variables foor them. For instance, Post_sample_dummy equals to one if month t is after the end of original sample but before publication.

The general estimation is the following,

 The purpose of this approach is to evaluate how average predictor’s return is different from in-sample, post-sample and post-publication periods.

Empirical Results

Post-sample and post-publication returns decline relative to in-sample returns by 26% and 58%. This suggests that academic researchers cautiously choose their in-sample date and their results are susceptible to statistical biases. However, investors also learn information about mispricing variables from academic publications because average predictor’s returns decrease more in post-publication periods. The main result remains almost unchanged after controlling for time trends and persistence.

The authors also find stronger results for predictors with high in-sample means and t-statistics and less costly arbitrage. Simultaneously, investors trade more in post-sample and post-public time. These consequences reveal the existence of statistical biases and bolster the notion that investor obtain useful information about mispricing variables from academic publication and apply it to their trading activity.

Analysts and Anomalies

Joseph Engelberg, R. David McLean, Jeffrey Pontiff. “Analysts and anomalies.” Journal of Accounting & Economics, Forthcoming, (2019).  (link)

Since the 1960s, researchers have found various cross-sectional characteristics that predict returns in the market.  These anomalies provide additional information to the market which could serve as a valuable supplement to other forms of analysis.  Engelberg, McLean, and Pontiff examine whether analyst price targets and recommendations account for the information these anomalies provide.  Using a collection of 125 anomalies documented in the literature, the authors find that, while anomalies tend to predict returns, analysts tend to forecast the opposite of the anomalies.

For each stock, the twelve month price target is estimated with the median target of each analyst covering the stock.  The mean recommendation is also calculated where a value of 1 represents a strong sell and 5 a strong buy.  The data has a mean return forecast of 36% with a 56% standard deviation while the mean recommendation is 3.77 with a standard deviation of 0.67.  The analyst data spans about twenty years, up through 2017.

Each month, long and short portfolios are formed for each of the anomalies.  The index Net is then created for each stock which represents the number of long portfolios minus the number of short portfolios which the stock appears in.  Following Jegadeesh et al. (2004), about 30 of the anomalies are also sorted based on whether they are related to Momentum or Contrarian strategies.

Table 2 presents the main results of monthly portfolios sorted on Net, momentum, and contrarian anomalies.  The returns of the Net portfolios are monotonically increasing with 18.1% annually for the long portfolio and 9.3% for the short.  The analyst return forecast, however, predicts the exact opposite of this.  Forecasted returns are 46.4% for the short portfolio but 32.2% for the long portfolio.  Both these spreads are statistically significant and the difference between them, return forecast error, is also significant.  The spread in analyst recommendation in column Rec. is consistent with the analyst forecasts but not statistically or economically significant.

Table 2

Table 2 also presents results for anomalies sorted on momentum and contrarian characteristics.  As with Net, the forecast returns contradict the realized return and the difference is statistically significant.  Unlike Net, both momentum and contrarian anomalies present significant spreads in analyst recommendations, but in different directions.  For contrarian anomalies the recommendation spread is consistent with forecasted returns and contradicts the anomaly portfolios.  However, for momentum anomalies the analyst recommendations are in agreement with the anomalies.  It is noticeable that analyst recommendations for the momentum anomalies are positively correlated with realized returns while the return forecasts are negatively correlated with realized returns.

The authors further subdivide the set of analysts and stocks into categories such as stocks with recent analyst coverage increase, “All-Star Analysts” and analysts not associated with investment banking business.  For all subsamples, forecast returns are negatively and significantly correlated with realized returns.

They also regress forecast error on the anomaly variables.  The results show that a stock with Net of 10 (10 more long than short anomalies) has a 20% lower forecast error compared to a stock with Net -10.  This confirms that return predictions for anomaly shorts are extremely high.

Finally, the authors find that analysts’ revisions to return forecasts tend to more correctly, although not fully, reflect the information from anomalies.  For a firm with Net 10, the return forecast increases by 0.56% the next month compared to an average 0.09% monthly increase. A regression finds that analysts continue to update their forecasts to incorporate anomaly information up to eighteen months out.

This paper finds that, while anomalies accurately predict returns, analyst return forecasts run contrary to the anomaly predictions.  Analysts predict extremely high returns for anomaly shorts while predicting lower returns for anomaly longs; a difference which is statistically significant.  The literature documents that anomalies may be caused by investors’ biased expectations. The results of this paper indicate that analysts are susceptible to these same biases and overlook publicly available anomaly information.

A Comprehensive Look at The Empirical Performance of Equity Premium Prediction

Goyal, Amit and Ivo Welch. “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction” The Review of Financial Studies Vol. 21 No. 4 (2008) 1455-1508.

Many variables, in research prior to the present article, had been suggested and tested as predictors of the equity premium. Here, the authors do a study of the in-sample and out-of-sample performance of these variables. The overall results suggest that many of these variables, even prominent ones, now perform very poorly in-sample, out-of-sample, or both. Indeed, in their conclusion, the authors suggest only one variable for which they feel judgement should be reserved and that there are some which should be investigated more in longer term predictions. These results come even as the authors wave their hands at the question of how someone might have known what would have worked in real-time.

One-year predictions:

 

The first panel of Table 1 is analysis of variables which were not significant in-sample. The authors point out that even if these variables were significant out-of-sample, they wouldn’t be that interesting, but they include them because of their place in prior literature. None of the variable are significant out-of-sample for testing period beginning 20 years after the beginning of the data (the first 20 years being used as the initial in-sample period for the out-of-sample predictions), none are significant at with forecasting beginning in 1965, and only two (dividend-yield and earning-price ratio) are significant in in-sample tests using data from 1927-2005.

Among variables in the second panel (those which were significant in-sample), only one (percent equity issuing) has significant out-of-sample performance. This is the one mentioned earlier for which the authors feel judgement should be reserved. It does not have significant out-of-sample performance when forecasts begin in 1965.

In the remainder of the table, one variable has significant out-of-sample performance, though it seems to be a result of construction. The present authors design the test for cayp in similar fashion to the original authors. The representative agent here has knowledge of the full sample cay coefficient, but not the prediction coefficient and thus has to continually update. With this in mind, Goyal and Welch construct caya for true out-of-sample testing where the agent does not have advance knowledge of the cay coefficient. As we see, this entirely nullifies the apparent out-of-sample success of the variable.

Five-year predictions:

The authors disclose that the results of the five-year predictions are preliminary and possibly naïve prompting their suggestion that a few variables deserve further investigation in this realm. Dividend-price ratio and investment-capital ratio are significant in-sample for the full sample and in out-of-sample testing. However, neither is significant in-sample for the 20-year period used to begin the out-of-sample testing.

Similar to the one-year prediction result, cayp is strongly significant. What is different is that caya, the true out-of-sample test variable, is now also significant. Term spread was not significant in-sample for the full sample of available data but was with data beginning in 1927 as well as out-of-sample for forecasts beginning in 1965. Though, it too, failed to be significant for the in-sample portion of the data used to begin the forecast period.

One-month predictions:

The one-month prediction performance looks more promising based on in-sample testing. However, the authors note that only a few of them merit further investigation. In doing so, the variables seem to be inconsistent or heavily rely on only a short period for their overall success.

In summary, many of the variables used in the literature as predictors of the equity premium may be inconsistent and/or spurious. The authors state, “We view OOS performance not as a substitute but as a necessary complement to IS performance.”

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.