Forecasting Asset Returns in Realistic Environments David E. Rapach - - PowerPoint PPT Presentation

Forecasting Asset Returns in Realistic Environments

David E. Rapach

Saint Louis University

CFA Montreal Asset Management Forum October 8, 2015

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Introduction

Forecasting asset returns is fascinating

Better investment performance Better asset pricing models

Forecasting asset returns is also frustrating

Returns inherently contain large unpredictable component

Even best models explain only small part of returns Model sounds too good to be true ⇒ it surely is However, a little goes a long way

Adoption of models can eliminate forecasting ability, unless

Capturing time-varying systematic risk premiums Detecting pockets of inefficiencies & limits to arbitrage

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Forecasting challenges & strategies

Stating the obvious I

We don’t know The Model of asset returns

Actual DGP is highly complex & constantly evolving Substantial model uncertainty & instability

Hedgehog approach inadvisable

Need to incorporate info from many predictors

But also need to avoid overfitting

Effective strategies from recent literature

Forecast combination & diffusion indices

Stating the obvious II

I’m a fox

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Stylized example: equity risk premium

ERP: S&P 500 return minus risk-free return Huge literature on predicting ERP (Rapach & Zhou 2013) Predictive regression forecast: ˆ Rt+1 = ˆ αt + ˆ βtxt

Incorporate info from xt to forecast Rt+1

Prevailing mean benchmark forecast: ¯ Rt+1

Assumes no return predictability (RW with drift) Stringent out-of-sample benchmark (Goyal & Welch 2008)

Out-of-sample R2 (Campbell & Thompson 2008)

Proportional ↓ in MSFE for PR vis-à-vis PM

Sample period: 1926:01–2014:12

Forecast evaluation period: 1960:01–2014:12

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Highly plausible predictors

Dividend yield (Fama & French 1988) T-bill yield (Ang & Bekaert 2007) Term spread (Campbell 1987) Default spread (Fama & French 1989) Inflation (Nelson 1976) Output gap (Cooper & Priestly 2009) Moving-average signal (Neely, Rapach, Tu, & Zhou 2014) Momentum signal (Neely, Rapach, Tu, & Zhou 2014)

David E. Rapach Forecasting Asset Returns

Individual monthly PR forecasts

1960 1970 1980 1990 2000 2010

• 1

1 2 Dividend yield 1960 1970 1980 1990 2000 2010

• 1

1 2 T-bill yield 1960 1970 1980 1990 2000 2010

• 1

1 2 Term spread 1960 1970 1980 1990 2000 2010

• 1

1 2 Default spread

David E. Rapach Forecasting Asset Returns

Individual monthly PR forecasts

1960 1970 1980 1990 2000 2010

• 1

1 2 Inflation 1960 1970 1980 1990 2000 2010

• 1

1 2 Output gap 1960 1970 1980 1990 2000 2010

• 1

1 2 MA signal 1960 1970 1980 1990 2000 2010

• 1

1 2 Momentum signal

David E. Rapach Forecasting Asset Returns

R2

OS stats (%)

Semi- Predictor Monthly Quarterly annual Annual Dividend yield −0.03 −2.27 1.11 −1.87 T-bill yield −0.10 −0.47 −1.86 −2.59 Term spread 0.25 0.45 0.40 2.24 Default spread 0.30 1.11 1.29 3.28 Inflation 0.03 0.63 1.07 1.76 Output gap 0.17 0.45 0.88 1.20 MA signal 0.41 −0.16 −1.05 −1.66 Momentum signal −0.09 −0.46 −1.12 −0.30

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Drawbacks to individual PR forecasts

Individual PR forecasts perform inconsistently/unevenly We can’t identify best predictor a priori Relying on individual PR forecast is too risky

Too ‘hedgehogy’

We need to get foxy

Incorporate info from multiple plausible predictors Forecast diversification (Timmermann 2006)

Bad strategy: include all predictors in one regression

Kitchen sink PR: ˆ Rt+1 = ˆ αt + ˆ β1,tx1,t + · · · + ˆ βK,txK,t R2

OS stats: −0.95%, −6.22%, −5.25%, −9.64%

In-sample overfitting (avoid overfitting like the plague)

David E. Rapach Forecasting Asset Returns

Monthly kitchen sink PR forecast

1960 1970 1980 1990 2000 2010

• 1

1 2

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Good foxy strategies

Incorporate info from all predictors without overfitting Forecast combination (Rapach, Strauss, & Zhou 2010)

Take simple average of individual PR forecasts Avoid overfitting by shrinking forecast to PM

Shrink to ‘outside view’

R2

OS stats: 0.77%, 2.17%, 2.52%, 6.08%

Diffusion index (Ludvigson & Ng 2007)

Extract first few principal components from all predictors PCs serve as predictors for PR forecast Filter noise in individual predictors ⇒ more reliable signal R2

OS stats: 0.60%, 1.62%, 2.66%, 6.97%

David E. Rapach Forecasting Asset Returns

Monthly combination forecast

1960 1970 1980 1990 2000 2010

• 1

1 2

David E. Rapach Forecasting Asset Returns

Monthly diffusion index forecast

1960 1970 1980 1990 2000 2010

• 1

1 2

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation

MV investor allocates monthly across stocks & bills Allocation to risky stocks: wt = (1/γ)(ˆ Rt+1/ˆ σ2

t+1)

Realistic portfolio constraint: −0.5 ≤ wt ≤ 1.5

Certainty equivalent return (CER): ˆ µp − 0.5γˆ σ2

p

ˆ µp (ˆ σ2

p): portfolio mean (variance) over evaluation period

Annualized CER gain vis-à-vis PM for γ = 5

Combination forecast: 1.79% Diffusion index forecast: 2.46%

Return predictability is economically valuable

NB: assuming ‘small’ investor

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Additional elements

Combination weights (Rapach, Strauss, & Zhou 2010)

Place more weight on particular forecasts NB: typically best to hew close to equal weighting

Economic restrictions ⇒ ↓ estimation uncertainty

Sign restrictions (Campbell & Thompson 2008) Valuation ratios (Ferreira & Santa-Clara 2011) Bayesian (Pettenuzzo, Timmermann, & Valkanov 2014) Useful even if not literally true (bias-efficiency tradeoff)

Regime switching (Ang & Timmermann 2012)

Markov switching (Henkel, Martin, & Nardari 2011) Time-varying parameters (Dangl & Halling 2012)

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns

Dynamic asset allocation: two recent studies

MKT components (Kong, Rapach, Strauss, & Zhou 2011)

Allocate across 25 Fama-French size/value portfolios Combination forecasts of component portfolio returns

Based on 39 predictor variables

Combination forecasts valuable inputs for DAA

US stocks/bonds/bills (Almadi, Suri, & Rapach 2014)

Active portfolio management vis-à-vis 60/35/5 benchmark Diffusion index forecasts of stock/bond/bill returns

Extracted from fundamental, macro, and technical variables

Diffusion index forecasts valuable inputs for DAA

Largest gains typically realized during contractions/crises

David E. Rapach Forecasting Asset Returns