Quality Minus Junk. Asness, Cliff S. and Frazzini, Andrea and Pedersen, Lasse Heje, (June 5, 2017)

Quality companies tend to outperform junk companies, even after controlling for commonly used risk models.

0:00 - Introduction 

This paper is called "Quality Minus Junk", and it is written by Asness, Frazzini, and Pedersen.  Prior academic research has shown that companies with higher quality characteristics (e.g., lower leverage, higher profitability, lower volatility, etc.) tend to outperform those with lower quality characteristics (i.e., "junk").  As such, the authors want to explore a new factor (i.e., Quality Minus Junk) in the same way that Fama-French did with their High Minus Low, Small Minus Big, etc. factors. 

0:44 - Table 1. Summary Statistics 

The data under study includes equity securities across 24 developed markets (including the US market) over the 1957 - 2016 time period.

1:13 - Table 2. Persistence of Quality Measures 

The authors suggest that when making decisions, an investor should look to the future of the company in developing his valuations and executing his strategies.  As such, the authors want to understand whether it is possible to predict the future quality of a company.

To do that, the authors explore the persistence of quality in companies (i.e., does a company's quality today continue in the future).  They sort the US and Global stocks according to their quality ranks (including the components of safety, growth, and profitability) today, then see how those stocks rank for quality 1, 3, 5, and 10 years into the future.

They find that companies ranked high (low) in quality today tend to have high (low) quality for all time periods in the future.  As such, investors can possibly rely on the current quality of a company as a gauge for what its future quality might be.

3:24 - Table 3a. Cross Sectional Regressions, The Price of Quality 

Next, the authors want to understand whether investors pay more for higher quality companies.  To do that, they form 6 regressions on Market-to-Book ratios, with various combinations of independent variables to capture the drivers of the Market-to-Book ratios.  In all regressions, they find that a company's quality score significantly explains the Market-to-Book ratio of the companies, on average, even after controlling for several other variables; the quality score explains about 10% of the variation in Market-to-Book ratios on its own.

6:23 - Table 3b. Cross Sectional Regressions, The Price of Quality  

For this table, the authors perform the same study as in Table 3a; only this time, they split the quality score into its components: Profitability, Growth, and Safety.  They find that each of the components have merit on their own; and the overall quality score is not dominated by a single quality component.

7:18 - Table 3c. Cross Sectional Regressions, The Price of Quality  

Since prior studies have found that larger companies typically have higher quality, the authors want to understand how the price of quality is affected by company size.  To do this, the authors form the same regression as in Tables 3a and 3b; however, this time, they split the sample population into deciles of company size.  They find that the Market-to-Book ratios of larger companies (i.e., those in the higher deciles) tend to be more affected by quality scores than those of smaller companies (i.e., the coefficient on the quality factor is larger and more significant on larger companies).

8:17 - Table 4. Quality Sorted Portfolios 

Since in the prior tables we found that quality explains less than 50% of the variation in Market-to-Book ratios, the authors now want to see if there are other variables that explain the Market-to-Book ratios and whether those subsume the quality score's explanatory power.

To do so, they split the sample population into deciles according to their quality score ranks, and they find the alphas on t-bills, the CAPM model (controlling for market return), the 3-factor model (controlling for market return and value and size factors), and the 4-factor model (controlling for market return and value, size, and momentum factors).  A higher alpha on these models would lead us to conclude that there are other variables (i.e., possibly quality factors) that are not explained by the variables controlled for in each of the models.

The authors find that as the quality rank of the companies increases, the alphas and excess returns also increase after controlling for the models' factors.  The higher quality deciles also exhibit higher sharpe ratios, information ratios, and lower betas. 

12:02 - Table 5. Quality Minus Junk - Correlations  

Next, for ease of study and presentation, the authors want to determine how correlated are the components of the quality score (i.e., profitability, safety, and growth) to each other and to the overall quality score.  The authors find they are in fact highly correlated; therefore, the authors decide to scrap the individual components in the study (and only consider the overall quality score) which would ease the complexity of work on the authors and ease the presentation for their readers, without much affecting the conclusions of the study.

14:26 - Table 6. Quality Minus Junk - Returns  

Next, the authors want to explore a new factor: Quality Minus Junk (QMJ).  They build portfolios in the same way that Fama-French did with their factors: they go long the top third and short the bottom third of stocks according to their quality score ranks (also splitting into small and large in order to give fair representation to small companies).  This gives them an understanding of the returns that could be earned by investing in quality companies relative to junk companies.

The authors find a significant alpha to the QMJ portfolios after controlling for t-bills, CAPM, 3-factor, and 4-factor models.  These alphas come about because of the significantly negative relationship between the QMJ factor and the market (i.e., quality companies have lower market betas), size (i.e., quality companies tend to be larger), value (i.e., quality companies tend to be growth companies), and momentum (i.e., quality companies tend to have had a recent increase in price relative to lagging book value) factors.  As such, quality seems to be a major component/contributor to the return of each of these commonly used factors.

Out of all 24 countries under study, only 1 did not show a positive alpha on the 4-factor model (i.e., New Zealand, which represents the smallest market cap in the sample population).  17 of the 24 countries showed a statistically significant alpha.  As such, the efficacy of the quality factor tends to be pervasive across several markets.

17:48 - Figures 1-3. QMJ returns and alphas  

This figure shows Table 6c (discussed above) in graphical form.

This figure shows the cumulative excess returns of the QMJ portfolios over t-bills.  We see a consistently increasing and smooth accumulation.

This figure shows the cumulative alphas of the QMJ portfolios over the 4-factor model.  We see a consistently increasing and smooth accumulation.

19:09 - Table 7. 6-Factor Adjusted Returns  

Next, the authors get into robustness checks.  They perform the same study as table 6; only this time, they control for a 6-factor model (which adds the Conservative Minus Aggressive investment and Robust Minus Weak profitability) to the previous 4-factor model.  They find that the RMW factor subsumes a lot of the quality factor (which makes sense, because a component of the quality factor is profitability); and even so, a significant alpha to the QMJ portfolios is still present.

20:49 - Table 8. Returns During Different Regimes  

Next, the authors want to understand what happens with QMJ returns in different regimes (e.g., expansions and recessions, bull and bear markets, high and low volatility, etc.).  As would be expected, the QMJ portfolio performs better in bear markets than in bull markets; recessions than in expansions; and low volatility than high volatility.

22:10 - Figure 6. The Price of Quality  

Next, the authors want to understand the price of quality (i.e., how does quality affect a company's market-to-book ratio) and how it has changed over time.  They find that quality is more expensive (i.e., the market-to-book ratio increases more with increases to quality) during periods of market turmoil (such as the dot-com bubble and the housing collapse periods). 

23:51 - Table 9. Quality Sorted Portfolios - Target Prices  

Next, the authors want to understand whether an investor can buy quality at times when it is cheap, and earn excess returns to quality.  To do so, the authors sort the stocks into deciles of the quality scores and determine the price-to-book ratios, price target to book (by analysts), implied expected return, and realized 1-year return for each of the deciles.

They find that analysts typically give a higher price-to-book ratio to higher quality companies (as they should); however, relative to the current price, they are giving a lower and lower expected return to higher quality companies, while the realized 1-year returns increase as quality increases.  This presents the thought process that quality companies are currently underpriced (i.e., their current price-to-book ratio should be higher); if it were, the realized return would be more in line with analyst expectations.  As such, this scenario might give investors an opportunity to capture a return to quality.

26:03 - Equation 11. Price of Quality vs Return to Quality  

Next, the authors want to explore the possibility that lower prices to quality result in higher returns to quality.  They form a regression with the dependent variable being the return to quality and the independent variable being a lagged price of quality (and a variable to control for momentum).  If it is true that a lower price of quality results in a higher return to quality, we would expect a negative relationship between the two variables and therefore a negative coefficient on the lagged price of quality variable.

27:19 - Table 10. High Price of Quality Predicts Low QMJ Returns  

This table presents the results of the above regression.  The authors find there to be negative coefficients on the lagged price of quality variable over periods of 12, 36, and 60 months, even after controlling for t-bills and the 4-factor model.  As such, we can conclude that a lower price of quality today tends to result in a higher future return to quality.

28:46 - Table 11. Asset Pricing Test

Finally, up to this point, the QMJ has been on the left side of the regression (i.e., a dependent variable).  So now, the authors want to see what happens when QMJ is on the right side of the regression (i.e., an independent variable).  The authors find that when QMJ is added to a regression, the size factor is resurrected from insignificance.  The QMJ factor also increases the significant of the value and momentum factors by absorbing some of their explanatory power.

Suggested Citation

Asness, Cliff S. and Frazzini, Andrea and Pedersen, Lasse Heje, Quality Minus Junk (June 5, 2017). Available at SSRN: https://ssrn.com/abstract=2312432 or http://dx.doi.org/10.2139/ssrn.2312432 

Abstract

We define a quality security as one that has characteristics that, all-else-equal, an investor should be willing to pay a higher price for: stocks that are safe, profitable, growing, and well managed. High-quality stocks do have higher prices on average, but not by a very large margin. Perhaps because of this puzzlingly modest impact of quality on price, high-quality stocks have high risk-adjusted returns. Indeed, a quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns in the U.S. and globally across 24 countries. The price of quality varies over time, reaching a low during the internet bubble, and a low price of quality predicts a high future return of QMJ. Analysts’ price targets suggest that the required return of quality stock is low despite the high realized return.
 

Does Dividend Policy Foretell Earnings Growth? Arnott, Robert D. and Asness, Cliff S. (December 2001)

Higher dividend payout ratios tend to predict higher earnings growth going forward.

0:00 - Introduction

This is a paper called "Does Dividend Policy Foretell Earnings Growth?" by Cliff Asness and Robert Arnott.  Back in the 60s, Miller and Modigliani developed the Dividend Puzzle phenomenon, which states that investors should be indifferent as to the level of dividends a company pays (because the dividend or foregone dividend is either put in his own pocket to reinvest or kept in the company's pocket to reinvest on his behalf; he doesn't lose or gain wealth in either scenario).

Although elegant, the authors want to understand whether that thought process has proved to be true throughout history; and whether investors should take into consideration the level of dividends when making investment decisions.  And in fact, one might be swayed to believe that if a company retains more of its earnings for reinvestment, then the company should exhibit higher earnings growth going forward, and vise versa.  So does dividend policy foretell earnings growth?

1:14 - Exhibit 1. S&P 500 Payout Ratio

First, to get an idea of the average amount of dividends that have historically been paid out as a percentage of earnings, the authors have charted the S&P 500's dividend payout ratio (i.e., dividends divided by earnings) from 1950 - 2001.

They find that the historical payout ratio averages around 50% and is volatile, because dividends tend to be sticky, while earnings move up and down over time.  At the date of this paper (i.e., 2001), the payout ratio was at its lowest level in recent history.

2:09 - Exhibit 2a. Payout Ratios and Subsequent ten-year Earnings Growth

Next, the authors want to understand whether historical payout ratios have had any bearing on future earnings growth (and indirectly, whether the Miller Modigliani dividend indifference theory holds).  By creating a scatter plot with the historical payout ratio on the x-axis and the subsequent 10-year earnings growth on the y-axis, they find a positive relationship between the two; for example, the higher the payout ratio (i.e., the less earnings are being retained), the higher the next 10-years' earnings growth.  This is the complete opposite of what might be expected (i.e., one would think if the company retained more earnings, they would likely see more earnings growth in the future; but that's not the case according to this figure).

3:03 - Exhibit 2b. Ten-year Earnings Growth, as function of Payout Ratios

For additional analysis, the authors create regressions over various time periods going back to 1871, with the 10-year earnings growth as the dependent variable and the payout ratio as the independent variable.  They find over all time periods that the coefficient on the payout ratio is positive in all time periods and statistically significant.  As such, this analysis supports the prior figure in confirming that higher payout ratios have resulted in higher earnings growth over the next 10 years.

3:44 - Exhibit 3. Payout Ratios and Subsequent ten-year Earnings Growth

Next, the authors split the payout ratios of the population into quartiles (i.e., 4 groups) to assess the amount of earnings growth (i.e., the average, maximum, and minimum) at different levels of payout ratios.  They find that the average subsequent 10-year earnings growth increases as the quartile of payout ratios increases; and in fact, the quartile with the lowest payout ratio exhibited negative earnings growth.  Further, the worst earnings growth period in the highest payout ratio quartile exhibited higher earnings growth than the average payout ratio at the lowest quartile of payout ratios.  They found a monotonically increasing relationship of payout ratios and subsequent 10-year earnings growth.

5:19 - Potential Explanations for the Positive Relationship of Payout to Growth

The authors have come up with several reasons why this counter-intuitive result might be occurring:

1. Management prefers not to cut dividends: If management prefers not to cut dividends (because it makes the company look bad), they would want to pay out a level of dividends that is sustainable; therefore, the dividend policy might be a reflection of management's confidence in the stability and growth of future earnings.  As such, if management is fairly sure the future earnings growth is attainable, they would be more comfortable paying out more dividends.  And in that case, higher payout ratios might foretell future earnings growth.
2. Marginal attractiveness of reinvestment opportunities: If management has several projects that it can reinvest the earnings in, then it will select the best projects first and each subsequent project will be marginally less profitable.  As such, if management retains a lot of earnings, then it might be forced to reinvest them in less compelling projects.  Therefore, a higher payout ratio might force management to be more selective in the projects it invests in; thereby efficiently managing the company's capital.  And in that case, higher payout ratios might foretell future earnings growth through efficiency and reinvestment selectivity.
3. Empire building: Management might retain too much of its earnings, which gives them the incentive to possibly spend frivolously.  With less earnings retained, management might be more frugal, reduce conflicts of interest, and perhaps curtail empire building.  And in that case, a higher payout ratio might foretell future earnings growth through better management of cash and expenses.
4. Sticky dividends and mean reversion of earnings: Earnings might be temporarily depressed (which produces high payout ratios, because dividends amounts are generally less volatile), then move back up to their long-term mean; thereby giving that appearance that high payout ratios predicted high earnings growth, when in factor it was just the nature of earnings volatility.  
5. Data or experimental design error: The results might be isolated to the period under study, but might not be true across other time periods not studied; the results might be due to another economic variable (as opposed to the payout ratio); or perhaps the recent increase in share repurchases are being done in lieu of dividends, causing misinterpretations of the payout ratios and earnings per share.

The authors have left 1-3 above for other researchers to explore; however, they use robustness tests below to evaluate the likelihood of 4 and 5.

8:24 - Exhibit 2b. Robustness Test Over Time Periods

For the first robustness check, they go back to exhibit 2b and look at the different time periods under study.  The initial time period under study was 1950 - 2001, which showed supporting results for the positive relationship between the payout ratio and subsequent 10-year earnings growth.  So, they next performed the same regression over the 1926 - 2001, 1871 - 2001, and 1871 - 1941 time periods, finding the same results as before (albeit, a bit muted); as such, it does not appear there is an error of isolated time period.

9:54 - Exhibit 4a. Earnings Growth as function of Prior Earnings Growth

The next robustness check is to test the possibility that maybe the positive relationship between payout ratio and subsequent earnings growth is merely the result of mean reversion of earnings and sticky dividends.  The authors created a regression that has 10-year earnings growth as the dependent variable and both payout ratio and lagged 10-year earnings growth as the independent variables.  If high earnings growth (and a high payout ratio) is due to a reversion of earnings upward to the long-term mean, then we would expect a negative coefficient on the lagged 10-year earnings growth variable (because earnings would have had to go down previously, resulting in their go back up to the mean in the subsequent 10 years).

The authors find the coefficient on the lagged 10-year earnings growth variable is not statistically significant; so we might conclude that the prior earnings growth is not related to the future earnings growth; and as a result, the positive relationship of payout ratio and subsequent 10-year earnings growth does not appear to be caused by a mean reversion of earnings and sticky dividends.

11:47 - Exhibit 4b. Earnings Growth as Function of Current dividend by 20-Year Avg

As a second robustness test of the potential for the reversion of earnings to their mean, the authors prepared the same regression; only this time, they replace the lagged earnings variable with a ratio of current earnings to the prior 20-year average of earnings.  As in the prior regression, if the coefficient on the ratio of current earnings to 20-year average is negative, then we might conclude that earnings were temporarily depressed and merely reverted to their mean, thereby causing a positive relationship between earnings growth and payout ratios.  Instead, they find the same result as before: the coefficient on the ratio of earnings to 20-year average is statistically insignificant and therefore determined to not explain the subsequent 10-year earnings growth.  As such, we again find that the positive relationship between payout ratios and subsequent earnings growth is likely not caused by a mean reversion of earnings and sticky dividends.

13:28 - Exhibit 5. Five-Year Growth as function of Payout Ratios

Next, as another robustness test, the authors form a regression to see the relationship between payout ratios and subsequent 5-year earnings growth (whereas, prior exhibits were of 10-year earnings growth); by reducing the 5-year periods, the authors are adding more individual data-points to the analysis at the sacrifice of longer time periods.  They find the same results as before where the payout ratios are significantly positively related to the subsequent five-year earnings growth.

Next, as a robustness check of whether the recent propensity to repurchase shares in lieu of paying dividends, the authors form the same regression; only this time they halt the time period at 1979, because this is around the time that companies started taking part in more stock buybacks.  If these share buybacks are affecting the payout ratios (i.e., companies are repurchasing shares instead of paying dividends), we would expect a less significant relationship between the payout ratio and earnings growth.  But instead, we still find a significant and positive relationship between the payout ratio and earnings growth before 1979; and the 1980 - 2001 period even has a 50% R^2, suggesting that this regression explains a very large portion of the variation in returns, even though more dividends are potentially being "paid out" as stock buybacks.

16:03 - Exhibit 6. Consistency of R2 and T-Stat

Next, the authors want to understand how consistently the a + b*PR regression has explained the variation in 5-year earnings growth over time.  To do so, they do this regression on 30-year rolling periods and plot the R^2.  They find that the R^2 is fairly volatile, ranging from 0.15 to 0.63, but is always at a respectable level.

Next, the authors chart the t-statistics of the coefficient on the payout ratio for the 30-year rolling a + b*PR regression.  They find the t-statistic is always at a significant level (except for maybe the 1910ish period), signaling that the payout ratio significantly explains the subsequent 5-year growth throughout the entire time period under study.

17:57 - Exhibit 7. Growth as function of YCS and Payout Ratio

Next, the authors want to understand whether other economic variables might be causing the significance of the positive relationship between payout ratios and subsequent earnings growth (rather than the payout ratios themselves).  To do so, they form regressions with the 5 and 10 year earnings growth as the dependent variable and the yield curve slope (i.e., the ratio of 10-year treasury to 3-month treasury) as the independent variable.  Historically, higher yield curves have predicted higher earnings growth.  The regression on the 10-year earnings growth results in an insignificant coefficient on the yield curve variable; however, the regression on the 5-year earnings growth results in significant and positive between yield curve slope and 5-year earnings growth over all time periods under study.

To determine whether this yield curve slope is supplanting the payout ratios, the authors formed a regression with 5 and 10-year earnings growth as the dependent variable and the payout ratio and the yield curve slope as independent variables.  In both cases, they find that the yield curve slope is statistically insignificant and the payout ratio is positively and significantly related to the subsequent 5 and 10-year earnings growth.  As such, the yield curve slope is a poor predictor of subsequent earnings growth when compared with the explanatory power of the payout ratio.

20:48 - Exhibit 8. Ten Year Growth as function of earnings yield and payout ratio

Finally, as another example of another variable that might be supplanting the payout ratio as a powerful explainer of subsequent earnings growth, the authors form the same regression as above, only this time they've replaced the yield curve slope variable with an earnings yield (i.e., earnings divided by price) variable.  They do find that earnings yield is a significant predictor of earnings growth on its own; however, its explanatory power is crushed when payout ratios are added to the regression.  As such, the payout ratio is much better at predicting earnings growth than is the earnings yield.

As such, in assessing/predicting future earnings growth, it might be more prudent to follow the lead of company management (i.e., by paying attention to their dividend policy) than to investors (i.e., by paying attention to P/E levels).

Abstract

Many market observers point to the very high fraction of earnings retained (or low dividend payout ratio) among companies today as a sign that future earnings growth will be well above historical norms. This view is sometimes interpreted as an extension of the work of Miller and Modigliani. They proved that, given certain assumptions about market efficiency, dividend policy should not matter to the value of a firm. Extending this concept intertemporally, and to the market as a whole, as many do, whenever market-wide dividend payout ratios are low, higher reinvestment of earnings should lead to faster future aggregate growth.

However, in the real world, many complications exist that could confound the expected inverse relationship between current payouts and future earnings growth. For instance, dividends might signals managers' private information about future earnings prospects, with low payout ratios indicating fear that the current earnings may not be sustainable. Alternatively, earnings might be retained for the purpose of "empire-building," which itself can negatively impact future earnings growth.

We test whether dividend policy, as we observe in the payout ratio of the market portfolio, forecasts future aggregate earnings growth. This is, in a sense, one test of whether dividend policy "matters." The historical evidence strongly suggests that expected future earnings growth is fastest when current payout ratios are high and slowest when payout ratios are low. This relationship is not subsumed by other factors such as simple mean reversion in earnings. Our evidence contradicts the views of many who believe that substantial reinvestment of retained earnings will fuel faster future earnings growth. Rather, it is fully consistent with anecdotal tales about managers signaling their earnings expectations through dividends, or engaging in inefficient empire building, at times; either of these phenomena will conform with a positive link between payout ratios and subsequent earnings growth.

Our findings offer a challenge to optimistic market observers who see recent low dividend payouts as a sign of high future earnings growth to come. These observers may prove to be correct, but history provides scant support for their thesis. This challenge is potentially all the more serious, as recent stock prices, relative to earnings, dividends and book values, rely heavily upon this expectation of superior future real earnings growth.

Suggested Citation

Arnott, Robert D. and Asness, Cliff S., Does Dividend Policy Foretell Earnings Growth? (December 2001). Available at SSRN: https://ssrn.com/abstract=295974 or http://dx.doi.org/10.2139/ssrn.295974

Fight the Fed Model: The Relationship between Stock Market Yields, Bond Market Yields, and Future ReturnsAsness, Cliff S., (December 2002)

Using the Fed Model to determine appropriate stock market P/E levels is flawed, primarily due to stocks being "real" assets and bonds being "nominal" assets.

0:00 - Introduction

This is a paper called "Fight the Fed Model" by Cliff Asness of AQR Capital Management, LLC.  In the paper, he discusses the relationship between stock market yields, bond market yields, and future returns in an effort to analyze the validity of the Fed Model.

The Fed Model states that the stock market yield (i.e., Earnings divided by Price, or E/P) should generally be equal to the bond market yield (i.e., the yield on the 10-year treasury, or Y).  When E/P exceeds Y, stocks are considered cheap; when E/P is less than Y, stocks are considered expensive.

 
0:41 - Section 3. Arguments in Favor of the Fed Model

There are generally 3 arguments in favor of the Fed Model:

• The Competing Assets Argument: This rationalizes that an investor could either buy stocks or he could buy bonds, so those securities are competing.  If stocks are cheaper than bonds (i.e., they have a higher yield) or are expected to have a higher risk-adjusted return, investors should buy stocks instead of bonds.
• The Present Value Argument: In present value models, the interest rate is embedded in the denominator; therefore, decreases in interest rates should produce higher stock valuations and ultimately a lower earnings yield (or equivalently a higher P/E ratio).  As such, movements in the P/E ratio should be inversely related to movements in interest rates.
• The Historical Data Argument: Historically (i.e., since 1965), the S&P 500 E/P has moved in line with 10-Year treasury yields, and actually has a 0.81 correlation!  In addition, the S&P 500 P/E ratio has historically been inversely related to the level of inflation (which is a primary component of interest rates).

 

2:18 - Section 3. Arguments Against the Fed Model

Next, the author starts with the dividend discount model, and after making several substitutions, comes to the following model of real returns for stocks.  The model generally says that real returns to owning a stock should be equal to half of the earnings yield (assuming a dividend payout ratio of 50%) plus real long-term earnings growth:

In a scenario where the inflation rate changes, the real return to owning the stock should stay the same as well (i.e., because it is net of inflation); therefore, the right side of the equation has to remain the same also.  Since the real growth rate is net of inflation, then the nominal growth rate must have to change to counteract the change in inflation; which makes since, because changes in inflation should change the revenues and expenses earned by the company, and ultimately its profit level, in line with that inflation changed.

Fed Modelers would argue that the E/P in the equation should change with the change in inflation; but our analysis above points to the more likely scenario that the nominal growth rate changes instead.

6:10 - Section 3. Arguments Against the Fed Model (cont')

To verify this empirically, the author forms a regression with the nominal earnings growth as the dependent variable and inflation as the independent variable.  He finds that historical changes in the inflation rate change the nominal earnings growth rate with almost a 1:1 relationship (i.e., the beta on inflation has a 0.94 coefficient).  This means that, on average, 94% of decade-long inflation showed up in nominal earnings growth, explaining 36.5% of earnings' variation.  This is in line with our analysis above, and in stark contrast to the thought process of Fed Modelers.

This leads us to conclude that Fed Modelers are incorrectly trying to compare a real asset (i.e., stocks; because their returns are not affected by inflation) to a nominal asset (i.e., bonds; because their returns ARE affected by inflation).  This can be thought of like the "coupon" of a stock is its earnings (which move with inflation); however, the bond's coupon does not move with inflation.

So now that we understand the arguments for and against the Fed Model, we can revisit each of the Arguments and conclude on their efficacy (or lack thereof):

• The Competing Assets Argument: The argument was that the yields of stocks and bonds should be about the same; and investors should choose the asset class that yields more than the other.  However, as we've seen, the Fed Modelers have left out the understanding that stocks have an earnings growth rate that moves with inflation, while bonds do not.  As such, comparing the two without adjusting for this growth causes an error in thinking.
• The Present Value Argument: The argument is that changes to inflation (and therefore interest rates) should adjust the denominator in the present value of cash flows formula, resulting in a change to the present value.  Which is true; however, the Fed Modelers have failed to take into account that the change in inflation will also change the cash flows in the numerator of the equation, which counteracts the change in the discount rate in the denominator.  As such, a change in inflation should not materially change the present value of cash flows.
• The Historical Data Argument: In Figure 1 and Table 1, we saw that P/E ratios move inversely to interest rates and inflation rates over the 1965 - 2001 period, with a high correlation.  However, if we were to consider this relationship back to 1926, we would see that the relationship falls apart during the 1926 - 1965 period, with a very low correlation.  Therefore, have investors had a mistaking in thinking in more recent times when deciding appropriate P/E ratios? 

15:54 - Table 2. Forecasting 10-Year Real S&P 500 Returns

Next, the author runs a few regressions with the dependent variable being the average 10-year rollings S&P 500 returns, and the independent variables being the E/P, Y, and E/P-Y.  The thought process is that if the Traditional Model holds (i.e., the primary driver of returns is the earnings yield), the E/P should be statistically significant, while the other two variables are insignificant; if the Fed Model holds (i.e., the primary driver of returns is the difference between the earnings yield and 10-year treasury yield), the E/P-Y variable should be significant.

The authors find that over the 1881-2001, 1926-2001, and 1955-2001 time periods, the E/P is significantly positively related to the real S&P 500 returns, while neither the 10-year treasury yield nor the E/P-Y variable are statistically significant.  This would lead us to believe the earnings yield is the primary driver of returns, and the traditional model holds (and the Fed Model fails).

19:11 - Table 3. Forecasting 20-Year Real S&P 500 Returns

Next, the author performs the same regression over the 1881-2001 and 1926-2001 time periods, only this time the dependent variable is average rolling 20-year returns (rather than 10-year returns).  He comes to the same conclusion that the E/P is significantly positively related to the real S&P 500 returns, while neither the 10-year treasury yield nor the E/P-Y variable are statistically significant. Again, this is in favor of the Traditional Model and against the Fed Model.

20:13 - Table 4. Forecasting 1-Year Real S&P 500 Returns

Next, the author performs the same regression over the 1881-2001, 1926-2001, 1955-2001, and 1982-2001 time periods, only this time the dependent variable is average rolling 20-year returns (rather than 10- or 20-year returns).  In this study, the author generally finds that over the more recent periods (i.e., 1965- 2001 and 1982-2001) the E/P nor the Y or E/P-Y do a good job of explaining the real S&P 500 returns over the rolling 1-year periods; in fact, in all cases, the R^2 is less than 10%.  There tend to be significant alphas during the more recent times, which means that something other than the traditional or fed models are explaining the 1-year returns; one would have had to know to be long equities over this period in order to capitalize on this alpha.

22:43 - Section 5. How P/Es and Real Rates Really Move Together

Next, the author creates a regression with the earnings yield (i.e., E/P) being the dependent variable and the 10-year treasury yield (i.e., Y) being the independent variable.  If the Fed Model is appropriate, we should see the earnings yield move with the 10-year treasury yield.  Instead, we get a regression that has a very low R^2 and the coefficient on Y is minuscule.  This would mean that the 10-year treasury yield does not explain a significant portion of the variation in E/P over the time period; as such, there must be other variables that drive the E/P.

Plotting that regression against actual P/E over the years, we would get the following figure, where we see that the equation does a poor job of predicting P/E:

Next, the author adds the ratio of stock volatility to bond volatility as an independent variable.  The thought process is that the E/P of the stock, should be equal to Y plus a risk premium (which might stem from the relative volatility of stocks to bonds).  In adding the relative volatility variable, the R^2 jumps to 58.1% during the 1926-2001 period:

and to 78.9% during the 1955-2001 period:

As such, we see that the E/P figure has moved in an almost 1:1 ratio with the 10-year treasury when we also take into account the volatility of stocks relative to bonds.  The following chart shows how well the new regression fits the actual P/Es over the 1926-2001 period:

The difference in results between the 1926-1965 and the 1965-2001 periods in the earlier figures and tables is due to relative volatility of stocks-to-bonds in recent years being stable, while the pre-1965 volatility ratio was less stable.  This is why the Fed Model seemed to work in the post-1965 period; the volatility ratio piece did not have as much bearing on the results.  As such, investors should consider the relative volatility of stocks to bonds in their assessment of the appropriate P/E ratio (and not just the level of the 10-year treasury yield).

28:34 - Section 6. The International Cross-Sectional Evidence

Finally, as a robust test, the author performs an out-of-sample test to verify the results we found above in the US market.  The author forms the same regression of E/P (dependent variable) and Y (independent variable) across 10 developed countries over the 1987-2002 period.  He finds a significant positive relationship between Y and E/P, with an R^2 of 32.2%; as such, countries with higher/lower interest rates tend to have higher/lower earnings yields. 

Next, the author forms another regression of the stock market's real return (dependent variable) and E/P (independent variable); and another regression that add Y as a dependent variable.  In doing so, the author hopes to learn how well do a country's stock earnings yield and interest rates explain the returns to the stock market.  The traditional model would hold if the E/P is positive and significant while the Y is insignificant; and the Fed Model would hold if the E/P is positive and significant and the Y is negative and significant.

The results are that the E/P is significant and positive while the Y is insignificant.  As such, the Traditional Model holds and the Fed Model fails.  In summary, the real returns to the stock market are primarily driven by the the earnings yield at time of purchase, while the level of interest rates are inconsequential.

Abstract

The "Fed Model" has become a very popular yardstick for judging whether the U.S. stock market is fairly valued. The Fed Model compares the stock market's earnings yield (E/P) to the yield on long-term government bonds. In contrast, traditional methods evaluate the stock market purely on its own without regard to the level of interest rates. My goal is to examine the theoretical soundness, and empirical power for forecasting stock returns, of both the "Fed Model" and the "Traditional Model". The logic most often cited in support of the Fed Model is that stocks should yield less and cost more when bond yields are low, as stocks and bonds are competing assets. Unfortunately, this reasoning compares a real number to a nominal number, ignoring the fact that over the long-term companies' nominal earnings should, and generally do, move in tandem with inflation. In other words, while it is a very popular metric, there are serious theoretical flaws in the Fed Model. Empirical results support this conclusion. The crucible for testing a valuation indicator is how well it forecasts long-term returns, and the Fed Model fails this test, while the Traditional Model has strong forecasting power. Long-term expected real stock returns are low when starting P/Es are high and vice versa, regardless of starting nominal interest rates. I also examine the usefulness of the Fed Model for explaining how investors set stock market P/Es. That is, does the market contemporaneously set P/Es higher when interest rates are lower? Note the difference between testing whether the Fed Model makes economic sense, and thus forecasts future long-term returns, versus testing whether it explains how investors set current P/Es. If investors consistently confuse the real and nominal, high P/Es will indeed be contemporaneously explained by low nominal interest rates, but these high P/Es lead to low future returns regardless. I confirm that investors have indeed historically required a higher stock market P/E when nominal interest rates have been lower and vice versa. In addition, I show that this relationship is somewhat more complicated than described by the simple Fed Model, varying systematically with perceptions of long-term stock and bond market risk. This addition of perceived risk to the Fed Model also fully explains the previously puzzling fact that stocks "out yielded" bonds for the first half of the 20th century, but have "under yielded" bonds for the last 40 years. Finally, I note that as of the writing of this paper, the stock market's P/E (based on trend earnings) is still very high versus history. A major underpinning of bullish pundits' defense of this high valuation is the Fed Model I discredit. Sadly, the Fed Model perhaps offers a contemporaneous explanation of why P/Es are high, but no true solace for long-term investors.

Suggested Citation

Asness, Cliff S., Fight the Fed Model: The Relationship between Stock Market Yields, Bond Market Yields, and Future Returns (December 2002). Available at SSRN: https://ssrn.com/abstract=381480 or http://dx.doi.org/10.2139/ssrn.381480  

Deep Value. Asness, Cliff S. and Liew, John M. and Pedersen, Lasse Heje and Thapar, Ashwin K (December 1, 2017)

In this paper, the authors explore the drivers and results of deep value events across several markets and asset classes.

0:00 - Introduction

Other academic studies have explored the returns to value through the construction of zero-cost portfolios (i.e., buying value stocks while shorting growth stocks).  These studies have shown significant excess returns to value that, depending on the study, have noted various risk-based and behavioral-based drivers.

In this paper called "Deep Value", by Cliff Asness and several of his colleagues at AQR Capital Management, the authors explore the returns to deep value portfolios (i.e., zero cost value portfolios occurring at times when the spread between value and growth company values are unusually large).

0:23 - Table 2. Summary Statistics and Value Performance

First, the authors provide some sample statistics and explain their methods for portfolio formation.  In their study, their data includes price/return statistics for stocks in the US, Japan, Europe, and UK markets; and index futures for equities, fixed income and currencies.  In the case of US equities, data goes back to 1926, and the other regions and asset classes generally begin in the 1970s and 1980s, ending in 2015.

For each of the asset classes and regions, the authors sort them by their Price-to-Book ratios (or the equivalent figure, in the case of non-equity asset classes) each month, and they put them into zero cost portfolios going long the top third of B/P ratios and going short the lowest third B/P ratios.  The authors also sort by B/P ratios within intra-asset classes/regions (e.g., within industries; or by pairs for non-equity asset classes).

They find in all regions and asset classes (except UK equities), the zero-cost portfolios earn a positive sharpe ratio.  These sharpe ratios are even more pronounced in intra-asset classes/regions.

 5:28 - Table 3. Value Strategy Returns by Value Spread

Next, the authors organize the zero-cost portfolios into quintiles based on their "value spread" (i.e., the difference between the book-to-price ratios of the long portion of the portfolio vs the short portion of the portfolio).  The thought is that when the value spread is larger (i.e., a "deep value" situation), we might see larger returns to value portfolios than time periods when the spread is narrower.

Indeed for all stock regions (except the UK) and asset classes, we do see increasing return as the value spread increases, monotonic increases for US equities. These are much more pronounced in the intra class portfolios.  The non-equity asset classes exhibit the same results, albeit muted.  When combining all stocks together, all non-equity asset-classes together, and all asset classes/regions together, we see monotonic increases in returns as the value spread increases.  In addition, we see significant t-statistics for the top-ranked value spread portfolios, making these results robust.

10:57 - Table 4. Value Strategy Returns Regressed on Value Spreads

Next, the authors regress the returns of the zero-cost value portfolios (i.e., the dependent variable) against the value spread (i.e., the independent variable).  They find the beta in the regression to be positive in all asset classes and regions, with significant t-statistics, giving evidence to the thought that returns to value are positively related to the value spread.

13:13 - Figure 1. The Returns to Value Investing

Next, the authors rank the stocks and non-equity asset classes by their book-to-price ratios and categorize them into quintiles based on those ranks.  They find that as the level of book-to-price ratios decrease from high (i.e., value companies) to low (i.e., growth companies), the returns of those buckets decrease monotonically, which is in line with other studies who find that value companies tend to outperform growth companies on average.

Next, the authors perform an event study that shows cumulative returns of the zero-cost portfolio in the 24 months leading up to portfolio formation and up to 24 months after portfolio formation.  They find that for all levels of value spread, the zero-cost portfolio has a negative return leading up to portfolio formation, then has positive returns up to 24 months after portfolio formation.  This means that before portfolio formation, the value (i.e., long) side of the portfolio underperforms the growth (i.e., short) side; and after portfolio formation, the value (i.e., long) side outperforms the growth (i.e., short) side.  These returns are more pronounced in deep value periods than in periods of a narrow value spread.

They performed the same analysis with non-equity asset classes (i.e., equity index, fixed income, and currency futures) as well, and find the same results.

17:36 - Figure 2. Risk Dynamics of Value Investing

Next, the authors perform the same analysis as with Figure 1, only this time they look at the market betas (rather than returns) for each B/P bucket.  They find that the market betas are near 1 for each bucket, and they slightly decrease as the buckets move from value to growth.

They also perform an event study showing the market beta of the zero cost portfolio for 2 years before to 2 years after portfolio formation.  They find that the betas (i.e., the beta of the long value side, minus the beta of the short growth side) are all below zero, signaling the zero-cost portfolio is a good hedge against market risk.  We also see that periods of deep value result in even more significantly negative betas for the zero-cost portfolio, relative to the narrow value spread periods.

Next, the authors performed the same analysis, only this time they sort the quintiles by the value betas.  As would be expected, the value portfolios load positively on the value factor and the growth portfolios load negatively on the value factor.  Also, the zero-cost portfolio (i.e., going long value stocks and short growth stocks) tends to load more on the value factor during deep value periods than during narrow value periods.  The zero-cost portfolio's loading on the value factor tends to decrease after portfolio formation as it becomes less "cheap".

The authors also perform the same analysis for non-equity asset classes and find the same results. 

21:51 - Figure 3. Earnings Fundamentals of Value

Next, the authors perform the same analysis as in figures 1 and 2, but this time they present the return-on-equity for the different value vs growth buckets.  Consistent with other research, they find the growth stocks tend to have larger returns-on-equity than do value stocks.  They also perform an event study that shows the return-on-equity for the zero-cost value portfolio 24 months before and after formation.  They find the returns-on-equity (i.e., the ROE for the long value, minus ROE for the short growth) decrease beginning 24 months before portfolio formation and continuing 24 months after portfolio formation, consistent with the idea that the ROE for growth companies exceed those of value companies.  This decrease is also more pronounced during periods of deep value than for periods of narrow value spreads.

Next, the authors perform the same analysis, only this time they present analyst earnings revisions by bucket.  They find that earnings revisions are negative for all buckets (as is consistent with the thought that analysts typically reduce earnings expectations rather than raise them); however, value companies tend to have the largest negative earnings revisions compared to growth companies.  This is also evident in the event study which shows the earnings revisions of value minus the earnings revisions of growth stocks to decrease over time; this trend does seem to reverse a year after formation, however.  Deep value events tend to exacerbate these results compared to narrow value spread events.

24:25 - Figure 4. News Sentiment of Value 

Next, the same analysis as figures 1, 2, and 3 is performed, only this time the authors look at news sentiment across the different value/growth buckets and over the -2/+2 year event horizon.  They find that growth companies tend to have more positive news sentiment than do value companies.  During the 2 years leading up to the zero-cost value portfolio formation, the sentiment for growth stocks exceeds that of value stocks; however, in the 2 years after formation, the sentiment for value stocks exceeds that of growth stocks.  Deeper value time periods show more extreme differences in sentiment between value and growth than do more narrow value spread periods.

26:02 - Figure 5. Demand Pressure

Next, the authors perform the same analysis as figures 1-4, only this time they look at demand pressure for value vs growth stocks (i.e., dollar buys, less dollar sells for stocks).  They find that growth stocks tend to be more in demand than value companies.  As a result of this, the cumulative difference between demand for the value side and the growth side of the demand pressure decreases over the 4 year event horizon; this difference tends to be more pronounced for deep value periods as opposed to narrow value spread time periods.

27:19 - Table 5. What Do Investors (Over-)React To

Next, the authors explore the drivers of the demand pressure and returns to zero-cost value portfolios, by regressing each of these against past returns and past return on equity.

They find the demand pressure is positively related to the past returns and past ROE; however, the ROE factor is subsumed by the past returns when combined in a regression.  This signals that past returns and past ROE or correlated, and confirms prior studies that suggest investors over-extrapolate past returns when making investment decisions.

They also find the 1-month returns are positively related to 1-year past returns and negatively related to 5-year past returns, confirming prior studies that suggest investors over-react to past short-term returns, which results in initial momentum and a reversal later on.  The authors also find that when controlling for past returns, the past ROE is positively related to the 1-month returns; this might suggest that investors under-react to fundamental information, consistent with other studies.

30:27 - Figure 6. The Limits of Value Arbitrage

Next, the authors explore a few costs or hindrances to value arbitrageurs, which might be contributing to the persistence of value returns.

First, they find that bid-ask spreads for value companies tend to be much larger than those for growth companies.  These bid-ask spreads for implementing the zero-cost value portfolio are more pronounced during deep value periods as opposed to narrow value spread periods.

Next, they find that short fees (i.e., the cost of shorting the growth side in the zero-cost portfolio) are expensive for both value and growth companies, but not so much for the interior buckets.  Looking at the growth side only (because that's the side that is being shorted in the zero-cost portfolio), they find the short fees are much higher during periods of deep value as opposed to periods of narrow value spreads.

Finally, the authors find that value stocks tend to be more volatile than growth stocks.  In addition, the volatility of the zero-cost portfolio is much higher during deep value periods compared to narrow value spread periods.

These higher bid-ask spreads, higher short fees, and higher volatility all present larger costs and risks to a value arbitrageur, therefore contributing to the persistence of excess value returns.

33:27 - Figure 7. Value Arbitrage Activity

Next, the authors explore whether investors (i.e., by shorting growth companies), the value companies themselves (i.e., through share buy-backs) or acquirers (i.e., by acquiring value companies) might be the value arbitrageurs.

First, they look at short-interest for the different buckets of value vs growth stocks.  They find no meaningful difference between the short interest of growth companies than value companies. There is also not a meaningful change in short interest for growth companies over the 4 year event horizon; although, there is a dip around the portfolio formation time period possibly signaling investors' capital problems as growth stock prices are increasing as their short positions falter.  There is much larger short interest for growth companies during deep value events as opposed to those of narrow value spread periods.

Next, the authors explore the difference in stock buy-backs for value vs growth companies, in an effort to determine whether the companies themselves are arbitraging their stock values that they perceive as cheap.  They find that growth companies tend to issue more shares relative to value companies, although value companies still tend to issue more shares than they buy back.  When exploring the buy-backs of the value companies minus the buy-backs of the growth companies, they find that after portfolio formation date, the value companies are buying back more shares than are the growth companies.  This result is more pronounced for deep value periods compared to narrow value spread periods.

Finally, the authors explore whether acquirers are buying value companies when they get cheap.  They find that value companies are acquired more often than are growth companies.  They also find that the difference between the acquisition of value companies vs the acquisition of growth companies increases for the next two years after formation date; and this result is more pronounced for deep value periods compared to narrow spread periods.

All of this suggests that investors, the companies themselves, and acquirers are doing their part to arbitrage away the mispricing of value vs growth stocks; and these opportunities are taken advantage of more often when the value spreads get extremely deep.

37:21 - Table 6. The Alpha of Deep Value Out-of-Sample

Next, the authors explore out-of-sample tests for all 4 equity markets and all 3 asset classes to see what would the returns and characteristics of those returns have been under various trading strategies.  First, they developed a trading strategy of buying into the zero-cost value portfolio (i.e., go long value companies and short growth companies) when the value spread (i.e., the spread between the B/P ratio of the value companies and the B/P ratio of the growth companies) exceeds its 80th percentile of data to that point; and exiting the zero-cost value portfolio when the value spread goes back below its median.

For each of the individual markets or asset classes, they find that the returns load significantly positively on the global value factor and significantly negatively on the momentum factor, with no significant loading on alpha (i.e., timing the value factor doesn't necessarily result in better performance than a passive value strategy).  However, when all markets and asset classes are combined, they find a significant alpha figure.

The authors also perform this analysis for the intra-portfolios as well and find similar results, albeit with even more significant alphas. 

39:51 - Table 7. The Alpha of Deep Value Out-of-Sample: Robustness

Next, the authors explore different trading strategies similar to the one in Table 6.  They implement a "deep value" strategy (i.e., in at 80th percentile, out at median), "deeper value" strategy (i.e., in at 2 standard deviations, out at 1 standard deviation), "threshold" strategy (i.e., in at 80th percentile, out at 80th percentile), and "linear" strategy (i.e., allocation in proportion to the value spread level).  They find that the "deeper value" strategy performs slightly better (i.e., it has a higher alpha) than the "deep value" strategy, and significantly better than the others; however, the results are similar across all strategies, where there are significant positive loadings to the value factor and alpha and a significant negative loading to the momentum factor.  The intra-portfolios have similar results.

42:00 - Figure 8. Deep Value Strategy Cumulative Returns and Opportunity Set

Next the authors quantify and chart the cumulative returns to the "deep value" strategy as well as the opportunity set (i.e., the number of times the portfolios are in a "deep value" situation).  They find deep value events clustered around significant world/US events, such as the 2001 and 2008 recessions, Iraq War in the early 90s, and Volker experiments.  They also find significant and positive returns during the deep value event periods and across the entire sample period.

42:59 - Table 8. Deep Value Returns Vs The Number of Deep Value Opportunities

Finally, the authors developed a regression of returns, volatility, and sharpe ratios of the deep value portfolios against the size of the opportunity set.  They find that the larger the opportunity set of deep value event periods, the higher the return, volatility, and sharpe ratios of the deep value strategy.

Abstract

We define “deep value” as episodes where the valuation spread between cheap and expensive securities is wide relative to its history. Examining deep value across global individual equities, equity index futures, currencies, and global bonds provides new evidence on competing theories for the value premium.

Following these episodes, the value strategy has:

(1) high average returns;
(2) low market betas, but high betas to a global value factor;
(3) deteriorating fundamentals;
(4) negative news sentiment;
(5) selling pressure;
(6) increased limits to arbitrage; and
(7) increased arbitrage activity.

Lastly, we find that deep value episodes tend to cluster and a deep value trading strategy generates excess returns not explained by traditional risk factors.


Suggested Citation:
Asness, Cliff S. and Liew, John M. and Pedersen, Lasse Heje and Thapar, Ashwin K, Deep Value (December 1, 2017). Available at SSRN: https://ssrn.com/abstract=3076181 or http://dx.doi.org/10.2139/ssrn.3076181