king of the mountain: finding short-term efficacy in the ......›the 3-d valuation mountain »...

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

»Low (high) PE implies high (low) future returns

Valuation Ratios Mean Revert at Long-Horizon

Source: Prof. Robert Shiller online data.

4

Price/Earnings Ratio (CAPE), United States, 1881.01–2015.09

CA

PE

Source: Research Affiliates, LLC, based on Shiller, Bloomberg, and FactSet. As of June 30 2015. U.S. represented by S&P 500.

High Stock Valuations Produce Lower Returns

5

CAPE vs. Subsequent 10-year Real Returns: January 1990 – June 2015, United States

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.

Same Relationship in EM Equities

6

CAPE vs. Subsequent 10-year Real Returns: January 1990 – June 2015, EM

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.

EM Risk is Priced Again

7

Relative Valuation Ratios vs Relative Subsequent Returns: January 1990 – June 2015

CAPE is Powerful at Forecasting Long-Horizon

Returns, Less So for Short-Horizon Returns

Source: Research Affiliates, based on data from Global Financial Database, Robert Shiller online data, and Morningstar EnCorr.

8

Shiller PE vs. Subsequent 10-Year Real Returns, 1926-2013 R

eal R

etu

rns




9


eal R

etu

rns




10


eal R

etu

rns

CAPE Varies Across ―Growth Cycle‖

*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

The essence of our research: adding one illustrative measure of economic

condition to enhance our understanding of the mean-reversion target for CAPE

» High valuation may be justified under the right conditions

Average CAPE across Business Cycle, 1926–2013

Avera

ge C

APE

Long-Horizon

Average

CAPE and Macro Regimes

12

13

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

*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).

Median P/E at Different Real Yield* Regimes (United States, 1880.12–2013.12)

10.712.2

16.417.1 17.8

19.6

17.2

14.8

10.5

14

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

*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.

Why these results matter? Fed policy intends to depress interest

rates for as long as inflation remains low.

Median P/E at Different Inflation* Regimes (United States, 1880.12–2013.12)

16.017.6

16.2

18.920.3

18.7

15.914.7

9.2

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


15

Median P/E at Different Inflation and Real Yield Regimes (United States, 1880.12–2013.12)

Med

ian

P/E

-

A Nonlinear Model Based on the Valuation Mountain


16

Med

ian

P/E

Mo

dele

d P

/E

-

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

17

*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.

Gaussian Model

Surface Curves

» The ―sweet spot‖ for CAPE in U.S. equity market

› Low inflation (~1.5%)

› Moderate real interest rate (~3%)


18

Gaussian Model—Statistical Fit

»


19

CoefficientAdjusted R2

Model Inflation Real Rate

Non-linear Model 50.7%

Linear Model 1 -2.87 10.1%

Linear Model 2 3.67 9.7%

Linear Model 3 -1.85 2.21 12.3%

Statistical Fit of Various Models Used to Explain P/E (United States, 1880.12–2013.12)

Application:Improving Return Forecasts

20

Horizon

(Months)Coefficient

Newey-West

t-Stat

Non-overlapping

t-StatAdjusted R

2

120 -0.05 -2.29 -0.48 8.9%

60 -0.08 -2.01 -1.63 8.7%

36 -0.11 -2.33 -1.72 9.1%

12 -0.16 -3.26 -2.46 4.9%

6 -0.16 -3.63 -3.20 3.0%

1 -0.18 -3.22 -3.22 0.6%

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


21

Traditional Forecasting Regression using CAPE only Forecasting Regression using both CAPE and Modeled CAPE

𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln 𝑃𝑡

𝐸𝑡−3 + 𝜀𝑡+𝑘 𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln

𝑃𝑡𝐸𝑡−3

− 𝑓 𝑖𝑡 ,𝜋𝑡 + 𝜀𝑡+𝑘

Horizon

(Months)Coefficient

Newey-West

t-Stat

Non-overlapping

t-StatAdjusted R

2

120 -0.07 -6.74 -2.07 33.3%

60 -0.09 -3.74 -3.12 20.3%

36 -0.09 -2.97 -2.18 13.0%

12 -0.10 -3.00 -2.58 4.7%

6 -0.09 -2.75 -2.17 2.0%

1 -0.08 -1.80 -1.79 0.2%

22

Intuition of Observations

» CAPE is a strong predictor for long-horizon (510 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 510 years will differ from today

Global Markets

23

24

Link Between CAPE and Real Interest Rate

Developed Countries (excluding U.S.)

» Remarkable similarity to what we observe in U.S. equity market

*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.


Median P/E at Different Real Yield* Regimes (Developed Countries, 1972.03–2013.12)

14.513.3

17.0

19.2

22.0

19.818.0

16.314.3

25

Link Between CAPE and Inflation


» Weaker mountain-shaped relationship due to fewer episodes of very low inflation in the international sample

*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.


Median P/E at Different Inflation* Regimes (Developed Countries, 1972.03–2013.12)

15.6

20.7 21.9 22.2

20.2

17.8

14.6 14.2

9.6

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


26

Median P/E at Different Inflation and Real Yield Regimes (Developed Countries, 1972.03–2013.12)

Med

ian

P/E

-

Gaussian Model – Surface CurvesDeveloped 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 CurvesDeveloped 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 FitDeveloped Countries (excluding U.S.), 1972.03–2013.12

»


29

Coefficient

Adjusted R2Model Inflation Real Rate

Non-linear Model 29.9%



Linear Model 3 -8.46 -3.31 25.3%

Statistical Fit of Various Models Used to Explain P/E (Developed Countries, 1972.03–2013.12)

Horizon

(Months)Coefficient

Newey-West

t-Stat

Non-overlapping

t-StatAdjusted R

2

120 -0.07 -8.02 -4.14 42.7%

60 -0.17 -8.42 -6.81 40.1%

36 -0.18 -5.04 -3.85 27.4%

12 -0.24 -3.92 -3.00 12.2%

6 -0.24 -4.02 -3.60 6.6%

1 -0.21 -3.06 -3.06 1.1%

Forecasting Returns with CAPE and Modeled CAPEDeveloped Countries, 1972.03–2013.12

» Similar to the U.S sample

» Significant increase in forecasting power at short horizons


30

Traditional Forecasting Regression using CAPE Only Forecasting Regression using both CAPE and Modeled CAPE

𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln 𝑃𝑡

𝐸𝑡−3 + 𝜀𝑡+𝑘 𝑟𝑡+𝑘 = 𝛼 + 𝛽 ln

𝑃𝑡𝐸𝑡−3

− 𝑓 𝑖𝑡 ,𝜋𝑡 + 𝜀𝑡+𝑘

Horizon

(Months)Coefficient

Newey-West

t-Stat

Non-overlapping

t-StatAdjusted R

2

120 -0.05 -20.08 -2.42 47.2%

60 -0.12 -7.20 -4.74 36.2%

36 -0.12 -3.97 -2.72 22.4%

12 -0.14 -2.45 -2.10 7.6%

6 -0.13 -2.51 -2.20 3.6%

1 -0.10 -1.94 -1.94 0.5%

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.

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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%

Current Estimate (2015.09.30)

Source: Research Affiliates, LLC, based on data from Global Financial Data, Bloomberg, and central banks of global developed countries

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

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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


34

Median P/E at Different Inflation and Real Yield Regimes (United States, 1880.12–2013.12)

CAPE Real RateInflation Below -1% -1% to 1% 1% to 3% 3% to 5% Above 5%

Below -1% 11 7 17 17 14

-1% to 1% 11 14 17 18 11

1% to 3% 13 21 19 23 10

3% to 5% 14 16 20 17 11

Above 5% 10 11 9 17

Count Real RateInflation Below -1% -1% to 1% 1% to 3% 3% to 5% Above 5%

-100% to -1% 13 4 49 54 78

-1% to 1% 10 31 106 83 14

1% to 3% 34 95 257 118 22

3% to 5% 16 89 143 35 53

5% to 100% 118 69 80 26 0

-

A 3-D Valuation Mountain



35

Median P/E at Different Inflation and Real Yield Regimes (Developed Countries, 1972.03–2013.12)

CAPE Real RateInflation Below -1% -1% to 1% 1% to 3% 3% to 5% Above 5%

Below -1% 12 23 7 16

-1% to 1% 18 24 25 17

1% to 3% 18 16 24 22 19

3% to 5% 14 17 17 17 15

Above 5% 14 10 11 9 11

Count Real RateInflation Below -1% -1% to 1% 1% to 3% 3% to 5% Above 5%

Below -1% 0 2 29 12 73

-1% to 1% 0 125 545 240 120

1% to 3% 14 365 1523 1061 425

3% to 5% 61 272 541 369 386

Above 5% 136 183 342 327 380

-

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king of the mountain: finding short-term efficacy in the ......›the 3-d valuation mountain »...

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