King of the Mountain:
Finding Short-Term Efficacy in the
Shiller P/E Ratio
Rob Arnott
Chairman
Oct 19, 2015
King of the Mountain
» CAPE in forecasting subsequent returns
› Powerful at forecasting long-horizon returns
› Less so for short-horizon returns
» CAPE and macro regimes
› Link with real interest rate and inflation
› The 3-D valuation mountain
» Application
› Potential of forecasting short-term returns
2
CAPE in forecasting subsequent
returns
3
Valuation Ratios Mean Revert at Long-Horizon
»Low (high) PE implies high (low) future returns
CAPE
Price/Earnings Ratio (CAPE), United States, 1881.01–2015.09
Source: Prof. Robert Shiller online data.
4
High Stock Valuations Produce Lower Returns
CAPE vs. Subsequent 10-year Real Returns: January 1990 – June 2015, United States
Source: Research Affiliates, LLC, based on Shiller, Bloomberg, and FactSet. As of June 30 2015. U.S. represented by S&P 500.
5
Same Relationship in EM Equities
CAPE vs. Subsequent 10-year Real Returns: January 1990 – June 2015, EM
Source: Research Affiliates, LLC, based on Bloomberg and FactSet. As of June 30 2015. U.S. represented by S&P 500. EM represented by MSCI EM Index.
6
EM Risk is Priced Again
Relative Valuation Ratios vs Relative Subsequent Returns: January 1990 – June 2015
Source: Research Affiliates, LLC, based on Shiller, Bloomberg, and FactSet. As of June 30 2015. U.S. represented by S&P 500. EM represented by MSCI EM Index.
7
CAPE is Powerful at Forecasting Long-Horizon
Returns, Less So for Short-Horizon Returns
Real Returns
Shiller PE vs. Subsequent 10-Year Real Returns, 1926-2013
Source: Research Affiliates, based on data from Global Financial Database, Robert Shiller online data, and Morningstar EnCorr.
8
CAPE is Powerful at Forecasting Long-Horizon
Returns, Less So for Short-Horizon Returns
Real Returns
Shiller PE vs. Subsequent 5-Year Real Returns, 1926-2013
Source: Research Affiliates, based on data from Global Financial Database, Robert Shiller online data, and Morningstar EnCorr.
9
CAPE is Powerful at Forecasting Long-Horizon
Returns, Less So for Short-Horizon Returns
Real Returns
Shiller PE vs. Subsequent 1-Year Real Returns, 1926-2013
Source: Research Affiliates, based on data from Global Financial Database, Robert Shiller online data, and Morningstar EnCorr.
10
CAPE Varies Across ―Growth Cycle‖
» High valuation may be justified under the right conditions
Average CAPE
Average CAPE across Business Cycle, 1926–2013
Long-Horizon
Average
The essence of our research: adding one illustrative measure of economic
condition to enhance our understanding of the mean-reversion target for CAPE
*Growth / Slowdown: When economy is growing faster / slower than trend.
Source: Prof. Robert Shiller online data, Morningstar EnCorr, and St. Louis FRED. From Jan-1926 through Sep-2013.
11
CAPE and Macro Regimes
12
Link Between CAPE and Real Interest Rates
» Median CAPE plummets when…
› Real interest rate is negative  reflecting a desire to aggressively
stimulate the economy, or
› Real interest rate unusually high  reflecting a desire to rein in an
overheated economy
Median P/E at Different Real Yield* Regimes (United States, 1880.12–2013.12)
19.6
16.4
17.1
17.8
17.2
12.2
10.7
14.8
10.5
*Real yield is defined as 10-year government bond yield less the 3-year inflation.
Source: Research Affiliates, based on data from Global Financial Database. See also Leibowitz and Bova (2007).
13
Link Between CAPE and Inflation
» Median CAPE also plummets when…
› Inflation is unusually high  increased money supply without growth
› Inflation is zero or negative  decreased price leads to lower production
Median P/E at Different Inflation* Regimes (United States, 1880.12–2013.12)
18.9
17.6
16.0
16.2
20.3
18.7
15.9
14.7
9.2
Why these results matter? Fed policy intends to depress interest
rates for as long as inflation remains low.
*Inflation is defined as 1-year trailing inflation, calculated using 12-month changes in the Consumer Price Index (CPI).
Source: Research Affiliates, based on data from Global Financial Database.
14
The Macroeconomic Sweet Spot for A Soaring CAPE
» Common belief: rock-bottom levels of inflation and real interest
rates
» 3-D valuation mountain: moderate levels of inflation and real
interest rates
Median P/E
Median P/E at Different Inflation and Real Yield Regimes (United States, 1880.12–2013.12)
-
Source: Research Affiliates, based on data from Global Financial Database.
15
Median P/E
Modeled P/E
A Nonlinear Model Based on the Valuation Mountain
-
Source: Research Affiliates, based on data from Global Financial Database.
16
Use Gaussian Model to Fit a Continuous Function
» Polynomials are simple, but are not bounded
» Gaussian function is a better alternative
» Seven parameters are found by minimizing the weighted* sum of
squared errors on a 10 x 10 grid
*Weights are proportional to square root of numbers of observations within each region of the grid and inversely proportional to the standard deviation of those observations.
17
Gaussian Model
Surface Curves
» The ―sweet spot‖ for CAPE in U.S. equity market
› Low inflation (~1.5%)
› Moderate real interest rate (~3%)
Source: Research Affiliates, based on data from Global Financial Database.
18
Gaussian Model—Statistical Fit
»
Statistical Fit of Various Models Used to Explain P/E (United States, 1880.12–2013.12)
Coefficient
Model
Inflation
Real Rate
Non-linear Model
Linear Model 1
50.7%
-2.87
Linear Model 2
Linear Model 3
Adjusted R2
-1.85
10.1%
3.67
9.7%
2.21
12.3%
Source: Research Affiliates, based on data from Global Financial Database.
19
Application:
Improving Return Forecasts
20
Forecasting Returns with CAPE and Modeled CAPE
United States, 1880.12–2013.12
» CAPE is more powerful in forecasting long-horizon returns
» Adjusted CAPE enhances short-term return forecast
Traditional Forecasting Regression using CAPE only
𝑟𝑡+𝑘
Forecasting Regression using both CAPE and Modeled CAPE
𝑃𝑡
= 𝛼 + 𝛽 ln
+ 𝜀𝑡+𝑘
𝐸𝑡−3
𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln
𝑃𝑡
− 𝑓 𝑖𝑡 , 𝜋𝑡
𝐸𝑡−3
+ 𝜀𝑡+𝑘
Horizon
(Months)
Coefficient
Newey-West
t-Stat
Non-overlapping
t-Stat
Adjusted R2
Horizon
(Months)
Coefficient
Newey-West
t-Stat
Non-overlapping
t-Stat
Adjusted R2
120
60
36
12
6
1
-0.07
-0.09
-0.09
-0.10
-0.09
-0.08
-6.74
-3.74
-2.97
-3.00
-2.75
-1.80
-2.07
-3.12
-2.18
-2.58
-2.17
-1.79
33.3%
20.3%
13.0%
4.7%
2.0%
0.2%
120
60
36
12
6
1
-0.05
-0.08
-0.11
-0.16
-0.16
-0.18
-2.29
-2.01
-2.33
-3.26
-3.63
-3.22
-0.48
-1.63
-1.72
-2.46
-3.20
-3.22
8.9%
8.7%
9.1%
4.9%
3.0%
0.6%
Source: Research Affiliates, based on data from Global Financial Database.
21
Intuition of Observations
» CAPE is a strong predictor for long-horizon (510 years) returns
› Long-term valuations mean-revert, with high statistical significance
» CAPE is a weak predictor for short-horizon (up to 3 years) returns
› Current macroeconomic environment affects normal CAPE
› Provides better estimate of fair market valuation
› Leads to better ability to forecast returns at short-horizon
› Improves results shorter than 3 years in U.S.
› Current CAPE does not matter, except relative to model CAPE
» Transitioning from short to long horizon
› Usefulness of ―current‖ macroeconomic variables fades
› The macroeconomic environment in 510 years will differ from today
22
Global Markets
23
Link Between CAPE and Real Interest Rate
Developed Countries (excluding U.S.)
» Remarkable similarity to what we observe in U.S. equity market
Median P/E at Different Real Yield* Regimes (Developed Countries, 1972.03–2013.12)
22.0
19.2
19.8
18.0
17.0
14.5
13.3
16.3
14.3
*Real yield is defined as 10-year government bond yield less the 3-year inflation. Pooled data across 22 countries: Australia, Austria, Belgium, Canada, Denmark,
Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland and the
U.K.
Source: Research Affiliates, based on data from Global Financial Database.
24
Link Between CAPE and Inflation
Developed Countries (excluding U.S.)
» Weaker mountain-shaped relationship due to fewer episodes of very
low inflation in the international sample
Median P/E at Different Inflation* Regimes (Developed Countries, 1972.03–2013.12)
20.7
21.9
22.2
20.2
15.6
17.8
14.6
14.2
9.6
*Inflation is defined as 1-year trailing inflation, calculated using 12-month changes in the Consumer Price Index (CPI). Pooled data across 22 countries: Australia,
Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore,
Spain, Sweden, Switzerland and the U.K.
Source: Research Affiliates, based on data from Global Financial Database.
25
Observe Similar Valuation Mountain in Developed
Countries (excluding U.S.)
» Common belief: rock-bottom levels of inflation and real interest
rates
» 3-D valuation mountain: moderate levels of inflation and real
interest rates
Median P/E
Median P/E at Different Inflation and Real Yield Regimes (Developed Countries, 1972.03–2013.12)
-
Source: Research Affiliates, based on data from Global Financial Database.
26
Gaussian Model – Surface Curves
Developed Countries (excluding U.S.), 1972.03–2013.12
» Near-identical location of the ―Sweet Spot‖
Developed ex-US PE Curve
US PE Curve (from earlier)
Source: Research Affiliates, LLC, based on data from Global Financial Database
27
Gaussian Model – Surface Curves
Developed Countries (excluding U.S.), 1972.03–2013.12
» Near-identical location of the ―Sweet Spot‖
Developed ex-US PE Curve
US PE Curve (from earlier)
Source: Research Affiliates, LLC, based on data from Global Financial Database
28
Gaussian Model – Statistical Fit
Developed Countries (excluding U.S.), 1972.03–2013.12
»
Statistical Fit of Various Models Used to Explain P/E (Developed Countries, 1972.03–2013.12)
Coefficient
Model
Inflation
Real Rate
Non-linear Model
Linear Model 1
29.9%
-8.13
Linear Model 2
Linear Model 3
Adjusted R2
-8.46
23.0%
-1.95
0.8%
-3.31
25.3%
Source: Research Affiliates, based on data from Global Financial Database.
29
Forecasting Returns with CAPE and Modeled CAPE
Developed Countries, 1972.03–2013.12
» Similar to the U.S sample
» Significant increase in forecasting power at short horizons
Traditional Forecasting Regression using CAPE Only
𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln
Horizon
(Months)
Coefficient
120
60
36
12
6
1
-0.05
-0.12
-0.12
-0.14
-0.13
-0.10
Forecasting Regression using both CAPE and Modeled CAPE
𝑃𝑡
+ 𝜀𝑡+𝑘
𝐸𝑡−3
𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln
Newey-West Non-overlapping
Adjusted R2
t-Stat
t-Stat
-20.08
-7.20
-3.97
-2.45
-2.51
-1.94
-2.42
-4.74
-2.72
-2.10
-2.20
-1.94
47.2%
36.2%
22.4%
7.6%
3.6%
0.5%
Horizon
(Months)
Coefficient
120
60
36
12
6
1
-0.07
-0.17
-0.18
-0.24
-0.24
-0.21
𝑃𝑡
− 𝑓 𝑖𝑡 , 𝜋𝑡
𝐸𝑡−3
+ 𝜀𝑡+𝑘
Newey-West Non-overlapping
Adjusted R2
t-Stat
t-Stat
-8.02
-8.42
-5.04
-3.92
-4.02
-3.06
-4.14
-6.81
-3.85
-3.00
-3.60
-3.06
42.7%
40.1%
27.4%
12.2%
6.6%
1.1%
Source: Research Affiliates, based on data from Global Financial Database.
30
Current Implications
» If current real rates were natural, not a consequence of QE
» … and, if the resulting real bond yields were natural
› The natural valuation levels would be lower than today, by a wide margin.
Current Estimate (2015.09.30)
Market
Shiller PE Inflation Real YieldModel PE Delta
US (Large)
24.1
0.20%
1.84%
16.7
-31%
Australia
14.4
1.50%
1.11%
16.0
11%
Canada
17.3
1.27%
0.16%
14.7
-15%
France
14.8
0.05%
0.94%
15.8
7%
Germany
16.1
0.19%
0.40%
15.1
-6%
Hong Kong
15.5
2.40%
-0.87%
13.2
-15%
Italy
10.6
0.19%
1.54%
16.5
55%
Japan
24.1
0.29%
0.06%
14.6
-39%
Spain
11.1
-0.42%
2.31%
16.9
52%
Sweden
18.9
-0.17%
0.89%
15.8
-17%
Switzerland
21.8
-1.40%
1.26%
16.2
-26%
United Kingdom
11.0
0.08%
1.68%
16.6
51%
Source: Research Affiliates, LLC, based on data from Global Financial Data, Bloomberg, and central banks of global developed countries
31
Valuation Matters…Even for the Intermediate Term
» Understanding CAPE in a more comprehensive way
› A 3-D valuation mountain better describe fair value of CAPE
» Finding the ―Sweet Spot‖ for Equity Market Valuations
› Stock prices can be high under the right condition
› Moderate inflation and real interest rate are ideal
› Today’s conditions are not in that sweet spot, but QE is arguably a special
kind of easy money, perhaps fueling asset bubbles .
» Application of the 3-D mountain valuation model
› Valuations matter –not just in the long term, but in the short term
› Incorporating macroeconomics conditions significantly increases short-term
return forecasting power
32
Appendix
33
A 3-D Valuation Mountain
CAPE vs. Real Interest Rate and Inflation
» What are the ideal macroeconomic conditions for a soaring CAPE?
› Common belief: rock-bottom levels of inflation and real interest rates
› 3-D valuation mountain: moderate levels of inflation and real interest
rates
Median P/E at Different Inflation and Real Yield Regimes (United States, 1880.12–2013.12)
CAPE
Real Rate
Inflation
Bel ow -1%
Bel ow -1%
-1% to 1%
1% to 3%
3% to 5%
Above 5%
Count
11
11
13
14
10
-1% to 1%
7
14
21
16
11
1% to 3%
17
17
19
20
9
3% to 5%
17
18
23
17
17
Above 5%
14
11
10
11
Real Rate
Inflation
-100% to -1%
-1% to 1%
1% to 3%
3% to 5%
5% to 100%
Bel ow -1%
-1% to 1%
1% to 3%
3% to 5%
Above 5%
13
10
34
16
118
4
31
95
89
69
49
106
257
143
80
54
83
118
35
26
78
14
22
53
0
-
Source: Research Affiliates, based on data from Global Financial Database.
34
A 3-D Valuation Mountain
Developed Countries (excluding U.S.)
Median P/E at Different Inflation and Real Yield Regimes (Developed Countries, 1972.03–2013.12)
CAPE
Real Rate
Inflation
Bel ow -1%
12
18
16
17
10
Bel ow -1%
-1% to 1%
1% to 3%
3% to 5%
Above 5%
Count
-1% to 1%
18
14
14
1% to 3%
23
24
24
17
11
3% to 5%
7
25
22
17
9
Above 5%
16
17
19
15
11
Real Rate
Inflation
Bel ow -1%
-1% to 1%
1% to 3%
3% to 5%
Above 5%
Bel ow -1%
-1% to 1%
1% to 3%
3% to 5%
Above 5%
0
0
14
61
136
2
125
365
272
183
29
545
1523
541
342
12
240
1061
369
327
73
120
425
386
380
-
Source: Research Affiliates, based on data from Global Financial Database.
35
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