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

Size Matters, If You Control Your Junk. Asness, Cliff S. and Frazzini, Andrea and Israel, Ronen and Moskowitz, Tobias J. and Pedersen, Lasse Heje, (January 22, 2015)

Asness, Cliff S. and Frazzini, Andrea and Israel, Ronen and Moskowitz, Tobias J. and Pedersen, Lasse Heje, Size Matters, If You Control Your Junk (January 22, 2015). Fama-Miller Working Paper. Available at SSRN: https://ssrn.com/abstract=2553889 or http://dx.doi.org/10.2139/ssrn.2553889  

Abstract

The size premium has been challenged along many fronts: it has a weak historical record, varies significantly over time, in particular weakening after its discovery in the early 1980s, is concentrated among microcap stocks, predominantly resides in January, is not present for measures of size that do not rely on market prices, is weak internationally, and is subsumed by proxies for illiquidity. We find, however, that these challenges are dismantled when controlling for the quality, or the inverse “junk”, of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk also explains interactions between size and other return characteristics such as value and momentum.

Fact, Fiction, and Value Investing. ASNESS, C., FRAZZINI, A., ISRAEL, R., & MOSKOWITZ, T. (2015)

ASNESS, C., FRAZZINI, A., ISRAEL, R., & MOSKOWITZ, T. (2015). Fact, Fiction, and Value Investing. Journal of Portfolio Management, 42(1), 34–52. https://doi.org/10.3905/jpm.2015.42.1.034

Value investing has been a part of the investment lexicon for the better part of a century, with the diversified systematic value factor (or value effect) studied extensively since at least the 1980s. The authors aim to clarify the many remaining areas of confusion about value investing, focusing on the diversified systematic value strategy, but also exploring how this strategy relates to its more concentrated implementation. They highlight many points about value investing and attempt to prove or disprove each of them, referencing an extensive academic literature and performing simple, yet powerful, tests based on easily accessible, industry-standard public data.

Value and Momentum Everywhere. Asness, Cliff S. and Moskowitz, Tobias J. and Pedersen, Lasse Heje (June 1, 2012)

This is a summary of a paper written by Cliff Asness, Tobias Moskowitz, and Lasse Pedersen called "Value and Momentum Everywhere", published in 2012 in Fama-Miller Working Paper.  A video summary can be found at the link below, or a narrative summary following the video link.

Table 1: Performance of Value and Momentum Portfolios Across Markets and Asset Classes (0:00)

The authors study the period 1972-2011 for US, UK, Europe, and Japan stocks.  They rank the stocks in each of the markets by value and momentum characteristics, and form portfolios for the top third, middle third, and low third of stocks according to those rankings.  They then calculate the mean returns, standard deviation, sharpe ratio, and alpha figures for each of the three portfolios in each of the 4 markets, including value-only, momentum-only, and 50/50 value/momentum.

They find monotonic increases in excess returns from P1 to P3 for the value, momentum, and combined portfolios; and these excess returns have significant t-statistics.  They also find a monotonically increasing and statistically significant sharpe ratio as the value/momentum rankings increase.  The major finding, though, is the results when the value and momentum portfolios are combined.  In that case, there is still a significant excess return; but with the combined portfolio, the standard deviation is much lower resulting in a significantly higher sharpe ratio than if the value or momentum portfolios were invested alone.  This is because the correlation of returns for the value and momentum portfolios are significantly negatively correlated (i.e., a correlation less than -0.60 in most cases).

Next, the authors explored the same value and momentum effects for different asset classes (i.e., country indices, currencies, fixed income, and commodities).  They find the same results as those found in the equities discussed above: significant excess returns, sharpe ratios, and alphas (with the exception of fixed income).  They also found that by combining value and momentum portfolios, the performance metrics were significantly improved over what they were for value and momentum isolated.  The authors also find that when they combine all asset classes in a combined value/momentum portfolio, they achieve a sharpe ratio greater than 1.35, which is higher than any of the asset classes or markets when isolated.  This is due to a significantly reduced standard deviation because of diversification effects, while the excess returns remain elevated.

Next, the authors explore some more value and momentum metrics for fixed income, since the metrics they used before (i.e., the 5 year change in yield) did not perform well.  They added the real bond yield and the term spread as a metric in the analysis.  They find that when using these measures of value, the performance metrics become large and statistically significant; so maybe the value/momentum effect is present in fixed income as well (you just have to use the appropriate measure of value). 

Table 2: Correlation of Value and Momentum Strategies Across Markets and Asset Classes (10:33)

Next, the authors analyze the correlations across the markets as well as the asset classes and value vs momentum strategies.  They find that the correlations between stock value and momentum strategies are significantly negative; this goes for non-stock value and momentum strategies as well (albeit, less significantly negative).  They also find that stock value (momentum) strategies are slightly positively correlated with non-stock value (momentum) strategies.  Finally, they look at the correlations of the markets (i.e., US, UK, Japan, and Europe) within value and momentum strategies, and they find those markets to be significantly positively correlated within both stock and non-stock returns.

Next, the authors explore the correlations of stock strategies to non-stock strategies.  They find in all cases that the stock value (momentum) strategies are positively correlated with non-stock value (momentum) strategies, and that stock value (momentum) strategies are negatively correlated with non-stock momentum (value) strategies.

Figure 1: First Principal Component for Value and Momentum Strategies (13:50)

Next, the authors explore the first principal components for value and momentum strategies.  They find that the first principal components of the momentum strategies are all loaded in the same direction for each of the markets (i.e., US, UK, Europe, and Japan); also, all the first principal components of the value strategies are loaded in the same direction for each of the markets, and in an opposite direction of the momentum strategies (exhibiting a negative correlation between value and momentum strategies in each market).

Next, they perform the same analysis across asset classes (i.e., stocks, countries, currencies, bonds, and commodities), and they find that the first principal components of the momentum strategies are all loaded in the same direction for each asset class; and all the first principal components of the value strategies are loaded in the same direction for each of the asset classes, and in an opposite direction of the momentum strategies (showing the negative correlation between value and momentum strategies in each asset class).

As such, there must be a common global factor structure that produces these results across all asset classes and markets.

Figure 2: Cumulative Returns to Value and Momentum Strategies Across Markets and Asset Classes (15:39)

Next, the authors look at the cumulative returns of value, momentum, and combined strategies across markets and asset classes.  They find that in all markets and asset classes, the combined value/momentum strategy outperforms either the value or momentum strategy on its own.  They also find the value and momentum returns are significantly negatively correlated, causing a significantly higher sharpe ratio in the combined strategy than in the value or momentum strategies alone.

Table 3: Macroeconomic Risk Exposures (16:52)

Next, given the prevalence of the outperformance across markets and asset classes, the authors explore the macroeconomic risk exposures of these strategies to see if there is a common influence on the returns.  They find that returns of US value strategies are positively related to long-run consumption growth, term structure, and default risk and negatively related to the market return; returns of US momentum strategies are negatively related to default risk, and unrelated to other macroeconomic factors; returns of global value stocks are positively related to default risk; returns of global momentum stocks are negatively related to default risk; returns of non-stock assets are negatively related to term risk; and returns of non-stock momentum strategies are negatively related to recessions and GDP growth.

As such, default risk seems to be the common source of returns for the value and momentum strategies across asset classes and markets (i.e., returns of value strategies are positively related to default risk and returns of momentum strategies are negatively related to default risk).

Table 4: Liquidity Risk Exposures (19:46)

Next, the authors explore the relationship of value and momentum strategies to liquidity risk measures (in particular, those of funding liquidity and market liquidity).  For the US market, they find that returns of value strategies tend to be negatively related to liquidity risk and returns of momentum strategies tend to be positively related to liquidity risk.  And in the combined value/momentum strategy, there is no relationship between liquidity risk and the returns of the combined portfolio, suggesting the combined strategy diversifies out the liquidity risk.  They find the same results on a global basis as well.

Figure 3: Time Series of Global Liquidity Shocks (21:05)

As a robustness test of the liquidity risk measures, the authors plotted the shocks over the past 25 years, noting they coincide with well-known market shocks.

Figure 4: Liquidity Risk Beta t-statistics (24:41)

Next, the authors look at the t-statistics of the liquidity risk factors within the regression.  They find that looking at the individual markets and asset classes individually produce insignificant t-statistics; however, when the asset classes and markets are averaged together, the t-statistics become significant.  Had the markets and asset classes not been combined, it might have been found that there is no relationship between liquidity risk and the value and momentum strategies.

Figure 5: Explaining Value and Momentum in One Market with Value and Momentum in Other Markets (25:40)

Next, the authors form regressions for each of the high, low, medium portfolios across each market and each asset class.  Then using those regressions, they calculate an expected return and compare that to the actual return for each portfolio.  They find that a regression with just the market, value, and momentum factors (the AMP 3-factor model) on a global basis do a reasonable job of predicting actual returns, with an R^2 of 0.55 and a very small alpha.

Figure 6: Asset Pricing Tests of the Cross Section of Expected Returns (28:31)

Next, the authors perform this same regression using other common asset pricing models, such as the CAPM and the Fama-French 4-factor and 6-factor models.  They find their AMP 3-factor model (at an R^2 of 0.71) does a better job at predicting the actual returns to the portfolios than do the other common pricing models.  They also perform this for US assets only, using the global factor loadings; they find that the Fama-French 4-factor and 6-factor models do a better job at predicting the portfolio returns than does the AMP 3-factor model, but this is because the AMP model is using global data to form the regression, while the Fama-French models are using US data to form the regressions.  It makes sense that US data does better at predicting US returns; however, the authors want to emphasize how well the global data in the AMP model predicts returns of US assets, further exhibiting the interconnectedness of the markets and factors.

Table 5: Cross-Sectional Asset Pricing Tests of Global Value and Momentum Strategies (31:58)

Next, the authors want to see how various economic indicators explain the returns of each of the 48 portfolios in this study.  They find that liquidity risk is significantly positively related to the returns of the portfolios when regressed along, and term risk and default risk are also significantly related; however, when those risk measures are combined in a regression, the liquidity risk subsumes the term and default risk; and further, when value and momentum factors are included in the regression, the liquidity risk is subsumed by those factors.  As such, the value and momentum premiums may be capturing liquidity risk.

Next, the authors explore funding and market liquidity separately, and they find that the funding liquidity is the factor that has the most influence on the returns (and not necessarily market liquidity); in both cases, however, the value and momentum factors subsume the liquidity risk measure.

Table 6: Time Series Asset Pricing Tests of Global Value and Momentum Strategies (34:42)

Next, the authors explore the regressions of several asset pricing models (i.e., the CAPM, Fama-French models, macroeconomic models, and APM 3-factor model).  They find the APM 3-factor model best explains the cross-section of returns (i.e., it has the highest R^2, the lowest alpha, and the lowest F-stat).  This means that a regression with the global zero-cost value, zero-cost momentum, and market factor do a good job of explaining the returns to these portfolios.

Next, they use the Fama-French 25 value / 25 momentum portfolios for forming the regression. As we saw in a previous table, the Fama-French 6-factor model does a better job of explaining the US returns because it uses US data in forming the regression; but the AMP 3-factor model (global market, value and momentum) still does a good job of explaining the returns.

Next, the authors explore how well the models can explain hedge fund returns (given the increased use by hedge funds in using factor-based portfolios).  They find the AMP 3-factor model does the best at explaining the hedge-fund returns. 

Table 7: Dynamics of Value and Momentum Returns (40:07)

Finally, given the success of these value and momentum strategies, the authors look at the performance of the strategies over different time periods ('72-'91 and '92-'10).  They find that the returns and sharpe ratios of the value and momentum strategies have decreased in the more recent period than the former period; however, the returns of the combined momentum/value strategy has remained constant across both periods.  The correlations within the value and momentum strategies have significantly increased from the prior period to the more recent period; however, the correlations between value and momentum strategies have become more negative.

Abstract

We study the returns to value and momentum strategies jointly across eight diverse markets and asset classes. Finding consistent value and momentum premia in every asset class, we further find strong common factor structure among their returns. Value and momentum are more positively correlated across asset classes than passive exposures to the asset classes themselves. However, value and momentum are negatively correlated both within and across asset classes. Our results indicate the presence of common global risks that we characterize with a three factor model. Global funding liquidity risk is a partial source of these patterns, which are identifiable only when examining value and momentum simultaneously across markets. Our findings present a challenge to existing behavioral, institutional, and rational asset pricing theories that largely focus on U.S. equities.

Suggested Citation: 

Asness, Cliff S. and Moskowitz, Tobias J. and Pedersen, Lasse Heje, Value and Momentum Everywhere (June 1, 2012). Chicago Booth Research Paper No. 12-53; Fama-Miller Working Paper. Available at SSRN: https://ssrn.com/abstract=2174501 or http://dx.doi.org/10.2139/ssrn.2174501