Risky Value
Atif Ellahie, Michael Katz and Scott Richardson
October 21, 2014
AQR Capital Management, LLC
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Greenwich, CT 06830
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1
Overview
What is ‘value’?
From the perspective of the common equity holder
𝑫𝒊𝒗𝒊𝒅𝒆𝒏𝒅𝒔
𝑷
𝑺𝒂𝒍𝒆𝒔
𝑷
𝑪𝒂𝒔𝒉𝑭𝒍𝒐𝒘
𝑷
𝑬𝒂𝒓𝒏𝒊𝒏𝒈𝒔
𝑷
𝑩𝒐𝒐𝒌
𝑷
𝑿
𝑷
3
X/P
‘X’ is identified via the financial reporting system (S, D, E, C, B etc.)
The accounting system is ‘conservative’:
• ‘Risky’ activities are reflected in financial statements through accruals and
deferrals.
• Examples include expensing of research and development, advertising,
asymmetric asset write-downs etc.
• A consequence of this is that earnings (‘E’) are depressed during periods of
such risky activity.
• ‘E’ is no longer a sufficient statistic for ‘value’.
4
X/P
‘X’ is identified via the financial reporting system
So how does looking at book value (‘B’) help?
• A simple formulation of expected returns (assuming full payout) is:
𝑬
𝒓= +𝒈
𝑷
𝑬
• In the absence of growth, 𝑷 can be sufficient.
• In the presence of growth, and risky deferrals, we need an anchor for ‘g’.
•
𝑩
can be
𝑷
𝟏
𝑬
re-expressed as 𝑹𝑶𝑬 ∗ 𝑷, thus looking at ‘B’ can capture the effect of
accounting distortions on the E/P ratio (which typically lower ROE).
5
X/P
‘X’ is identified via the financial reporting system
A ‘tautology’ to give some structure to how accounting attributes link to firm
value:
𝑬 𝑹𝒕+𝟏
𝑬 𝑬𝒂𝒓𝒏𝒊𝒏𝒈𝒔𝒕+𝟏
𝑷𝒕+𝟏 − 𝑩𝒕+𝟏 − 𝑷𝒕 − 𝑩𝒕
=
+𝑬
𝑷𝒕
𝑷𝒕
Expected returns contain two components:
• Expected forward earnings yield
• Expected subsequent earnings growth
The price deflator incorporates expectations of risk in forward earnings and
subsequent earnings growth.
• Only systematic risk in those attributes matter and we focus on that.
6
Aside
Efficient vs. inefficient ‘prices’ : we are in the ‘efficient’ camp today
Summary of results
Combinations of measures work better
Start with E/P, then look to B/P
To explain cross-sectional variation in country level equity returns:
• E/P works well (R2 of 4.2%)
• B/P also works well (R2 of 8.2%)
• But both together works better (R2 of 9.2%)
• Note that while D/P ‘works’ stand alone, it is subsumed by E/P and B/P.
• When ‘E’ is more persistent, E/P is close to a sufficient statistic for expected
returns. When ‘E’ is less persistent, B/P is needed.
9
Focus on ‘why’ B/P is so successful
Through a ‘risk’ lens
B/P at the country level exhibits the following patterns:
• Positively associated with the first moment of future earnings growth.
• Positively associated with the second moment of future earnings growth (necessary
condition).
–High B/P countries are, on average, facing temporarily depressed ‘E’ and their
recovery in near term earnings growth is uncertain.
–Countries with high B/P also exhibit greater downside sensitivity to
contemporaneous global earnings growth, consistent with B/P reflecting risky
future earnings growth.
• Controlling for future realizations of future earnings growth subsumes B/P
explanatory power.
10
Data
Data
Great cross section, limited time series
• 30 countries (developed and developing markets) for period March 1993
through to June 2011.
–Primary sample is 6,600 country-months.
• Cross-sectional and panel regression analysis of determinants of future
country level stock returns.
–Focus on 12 month ahead excess returns (to local cash rate).
• Investigation of the combined role of E/P and B/P and expectations of risky
subsequent earnings growth.
• ‘Head-ache’ for junior co-author…
–Firm level fundamental, price and analyst data aggregated point-in-time for
over 3 million firm-month observations.
12
Results
Table 3
Panel regressions (inferences same with Fama-Macbeth regressions)
See the Appendix for more information.
14
Table 4
Panel regressions (inclusion of country and time fixed effects)
See the Appendix for more information.
15
Table 5
B/P sorts countries on the first and second moment of future earnings growth
• B/P sorts on future earnings growth but not future dividend growth.
–Consistent with past research on X/P and future dividend growth.
–But suggests the focus is on the wrong attribute of the financial reporting system.
–Dividends are a measure of value distribution not risky value creation.
• High B/P countries likely experiencing low ‘E’ and hence deferral of risky
earnings growth.
–Unlikely to raise dividends as such times.
See the Appendix for more information.
16
Figure 1
Visual inspection of what is happening to extreme B/P countries
• High B/P countries experience an earnings ‘shock’ and subsequent earnings
growth that is ‘uncertain’.
See the Appendix for more information.
17
Figure 2 and Table 6
Formal tests of what is happening to extreme B/P countries
• High B/P countries experience an earnings ‘shock’ and their subsequent
earnings growth exhibits a strong ‘down-side’ beta.
• Table 6 has formal test of difference in slope: Null rejected in ‘down’ states.
See the Appendix for more information.
18
Table 7
B/P matters ‘more’ when earnings growth is more likely
• Priors are that B/P will matter ‘more’ when there is greater expectation of
earnings growth: (i) smaller countries, (ii) emerging countries, (iii) higher
dispersion in GDP forecasts.
See the Appendix for more information.
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Table 8
Controlling ex post for earnings growth subsumes B/P
See the Appendix for more information.
20
Conclusion
Conclusion
A risk based explanation for B/P anchored in ‘accounting’.
• Understanding how the accounting system ‘works’ suggests natural candidate
𝑿
measures to explain equity returns.
𝑷
𝐸
𝐵
–Both 𝑃 and 𝑃 matter.
• When ‘E’ is more persistent, E/P is close to a sufficient statistic for expected
returns. When ‘E’ is less persistent, B/P is needed.
• Countries with high B/P are facing depressed earnings and an ‘uncertain’
recovery as evident in greater downside sensitivity to contemporaneous
global earnings growth
–Consistent with B/P reflecting risky future earnings growth.
22
What is ‘value’?
From the perspective of the common equity holder
𝑫𝒊𝒗𝒊𝒅𝒆𝒏𝒅𝒔
𝑷
𝑺𝒂𝒍𝒆𝒔
𝑷
𝑪𝒂𝒔𝒉𝑭𝒍𝒐𝒘
𝑷
𝑬𝒂𝒓𝒏𝒊𝒏𝒈𝒔
𝑷
𝑩𝒐𝒐𝒌
𝑷
𝑿
𝑷
23
Appendix
Additional Information on Results
Table 3: Coefficient estimates and test statistics for panel regressions
This table reports coefficient estimates from panel regressions of 12 month value-weighted country excess returns on time t characteristics for 6,600 country-months from March 1993 to
June 2011 along with t-statistics and adjusted R-squared. Where GDP growth and inflation forecasts are included the number of observations is 6,530 country-months. The t-statistics
reported are based on standard errors clustered by country and month. The asterisks *, **, and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively.
Table 4: Coefficient estimates and test statistics for panel regressions (fixed effects)
This table reports coefficient estimates from panel regressions of 12 month value-weighted country excess returns on time t characteristics for 6,530 country-months from March 1993 to
June 2011 along with t-statistics and adjusted R-squared. The t-statistics reported are based on standard errors clustered by country and month. The asterisks *, **, and *** indicate statistical
significance at the 10%, 5% and 1% levels, respectively.
Table 5: Average realized earnings growth and dividend growth two years ahead for country portfolios sorted on B/P
This table reports average growth rates and variability in growth rates for earnings and dividends two years ahead (months 12 to 24) for five portfolios formed each month from March 1993 to
August 2010, by ranking countries on book-to-price, B/P. The series is shortened to enable the calculation of growth rates two years ahead and comprises 6,300 country-months (210 months
for each of the 30 countries). Each month, trailing twelve month earnings and dividends for countries in each portfolio are aggregated to compute portfolio-level earnings and dividends. Growth
rates are calculated as ln(Xt+2/Xt+1) where ln indicates natural logarithm and X is either aggregate earnings or aggregate dividends. The table also reports the average monthly standard deviation
of two year ahead growth rates for each of the five B/P quintiles. The t-statistics for the difference in mean between the high B/P and low B/P portfolios incorporate a Newey-West adjustment
for overlapping monthly observations.
Figure 1: Realized earnings, earnings growth, realized dividends and return on equity for B/P portfolios
This figure shows the evolution of earnings (Panel A), earnings growth (Panel B), dividends (Panel C) and return on equity (Panel D) for portfolios formed by sorting countries each month from
March 1993 to August 2010 into the highest and lowest quintiles of book-to-price, B/P. Each month, trailing twelve month earnings and dividends for countries in each portfolio are aggregated
to compute portfolio-level earnings and dividends. Y0 references the portfolio formation month, and the plots span the period from three years before (Y-3) to three years after (Y+3) portfolio
formation. Panel A plots portfolio earnings in natural logarithms, Panels B plots average realized earnings growth, Panel C plots portfolio dividends in natural logarithms, and Panel D plots
portfolio return on equity. Earnings growth is calculated as ln(Earningst+2/Earningst+1) where ln indicates natural logarithm. Return on equity is calculated as Earningst/Book Equityt-1. The dashed
lines indicate 95% confidence intervals
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Appendix
Additional Information on Results
Figure 2: Relation between realized earnings growth and global earnings growth for high and low B/P countries
This figure shows three scatter plots of average realized earnings growth two years ahead (on vertical axis) and contemporaneous global earnings growth (on horizontal axis) for the high and low
B/P quintiles from Table 5. Each month, quintiles were formed by ranking countries on book-to-price, B/P and only the high and low B/P quintiles were used for the plots. Global earnings growth
is calculated using the sum of country-level earnings for the 30 countries over the 210 months from March 1993 to August 2010 (the series is shortened from 220 months to enable the
calculation of growth rates two years ahead. Growth rates are calculated as ln(Earningst+2/ln(Earningst+1) where ln indicates natural logarithm. Global earnings growth realizations are partitioned
into downside states (1.0 standard deviation below the mean) and upside states (1.0 standard deviation above the mean). Panel A uses only downside global earnings growth observations, Panel
B uses all 210 monthly observations for global earnings growth, and Panel C uses only upside global earnings growth observations. Also see Table 6 which reports the slope coefficients and
statistical significance of the difference in slopes between the high and low B/P portfolios for different global earnings growth states.
Table 6: Relation between realized earnings growth and global earnings growth for high and low B/P countries
This table reports the slope coefficients from regressions of average realized earnings growth two years ahead on contemporaneous global earnings growth for the high and low B/P portfolios
from Table 5. Global earnings growth is calculated using the sum of country-level earnings for the 30 countries over the 210 months from March 1993 to August 2010. Growth rates are
calculated as ln(Earningst+2/ln(Earningst+1) where ln indicates natural logarithm. Global earnings growth is partitioned into negative and positive global earnings growth realizations, as well as
those that are over ±1.0 and ±0.5 standard deviation away from the mean global earnings growth. Each column reports the slope coefficient of the high and low B/P portfolios for the different
partitions of global earnings growth realizations. For each partition, the t-statistic for the slope coefficient, as well as the t-statistic for the difference in slope coefficients between the high and
low B/P portfolios is also reported. The asterisks *, **, and *** indicate statistical significance at the 10%, 5% and 1% levels, respectively. The number of months available for estimating each
slope coefficient is also reported. Also see Figure 1 which shows scatter plots of average realized earnings growth for high and low B/P portfolios against global earnings growth. For the scatter
plots, only the partitions from column I, IV, and VII are used.
Table 7: Panel estimations for cross-sectional country partitions
This table reports coefficient estimates from panel regressions of 12 month excess returns on time t characteristics for the time period March 1993 to June 2011 along with t-statistics and Rsquared. For the samples used in models I and II, three portfolios were formed each month by ranking countries on size. The smallest and largest size portfolio results are reported in model I and
model II respectively. Model III classifies 21 of the 30 countries as Developed Markets including Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Great Britain, Hong
Kong, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, and USA. Model IV classifies 9 countries as Emerging Markets including China, India,
Indonesia, Israel, Malaysia, South Africa, South Korea, Taiwan and Thailand. For Models V and VI, four monthly portfolios were formed by ranking countries on GDP growth forecast variability.
The models also include time fixed effects. The t-statistics reported are based on standard errors clustered by country and month. The F-statistics reported are for significance of the difference
between B/P – E/P across the various partitions. The last row of the table also reports dispersion in forward earnings growth for each partition.
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