1 expectations of equity risk premia, volatility, and asymmetry: from a corporate finance...

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Expectations of Expectations of Equity Risk Premia, Volatility, and Asymmetry: Equity Risk Premia, Volatility, and Asymmetry:

From a Corporate Finance PerspectiveFrom a Corporate Finance Perspective

John R. GrahamDuke University, Durham, NC USA

http://www.duke.edu/~jgraham

Campbell R. HarveyDuke University, Durham, NC USA

National Bureau of Economic Research, Cambridge, MA USA http://www.duke.edu/~charvey

Western Finance Association MeetingsPark City, Utah

June 2002

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Graham/Harvey: Expectations of Risk Premia

Measuring CFO Market Expectations

• Survey CFOs every quarter• Q2 2000 through Q2 2002 (nine quarters)• ~200 responses per quarter (1,900+ total obs.)

• Why CFOs? – We know they use CAPM from previous surveys– Hence, they have thought hard about risk premium– Should not be biased the way that analyst forecasts

might be

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Across Time and Different Horizons

• Ten-year risk premium around 3.5% and stable whereas one-year risk premium quite variable

0

1

2

3

4

5

6-Jun-00 7-Sep-00 4-Dec-00 12-Mar-01 7-Jun-0110-Sep-01 4-Dec-01 11-Mar-02 4-Jun-02

0

1

2

3

4

5

6-Jun-00 7-Sep-00 4-Dec-00 12-Mar-01 7-Jun-0110-Sep-01 4-Dec-01 11-Mar-02 4-Jun-02

10-year premium 1-year premium

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Across Respondents at a Point in Time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

< -20

-18

-16

-14

-12

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

more

Proportion

10-year premiumSeptember 10, 2001

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Across Respondents at a Point in Time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40Proportion

1-year premiumSeptember 10, 2001

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Graham/Harvey: Expectations of Risk Premia Past Returns and Expected Premia

• One-year risk premium sensitive to past returns

y = 0.1298x + 3.0165

R2 = 0.5377

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1

2

3

4

5

-20 -15 -10 -5 0 5 10 15

Past quarters' return

One

-yea

r pr

emiu

m

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Graham/Harvey: Expectations of Risk Premia Past Returns and Expected Premia

• 10-year risk premium not sensitive

y = -0.0008x + 3.9002

R2 = 0.0001

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1

2

3

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5

-20 -15 -10 -5 0 5 10 15

Past quarters' return

Ten

-yea

r pr

emiu

m

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Measuring Volatility

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Measuring Volatility

• Able to deduce each respondent’s probability distribution

• Market volatility is

average of individual volatilities (average volatility)

+ dispersion of risk premium forecasts (disagreement)

• We consider both components

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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility

• Average one-year volatility not related to past quarter’s returns

y = 0.0214x + 6.5153

R2 = 0.0373

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3

4

5

6

7

8

-20 -15 -10 -5 0 5 10 15

Past quarter's return

Ave

rage

vol

atil

ity

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• Average one-year volatility not related to past month’s returns

y = -0.0215x + 6.4125

R2 = 0.0158

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3

4

5

6

7

8

-15 -10 -5 0 5 10

Past month's return

Ave

rage

vol

atil

ity

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• One-year disagreement volatility not linearly related to past quarter’s returns

y = -0.0342x + 3.9939

R2 = 0.0773

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3

4

5

6

7

8

-20 -15 -10 -5 0 5 10 15


Dis

agre

emen

t vo

lati

lity

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• Maybe non-linear – but too little data

y = 0.015x2 + 0.0727x + 3.2025

R2 = 0.8158

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3

4

5

6

7

8

-20 -15 -10 -5 0 5 10 15


Dis

agre

emen

t vo

lati

lity

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• One-year disagreement volatility negatively related to past month’s returns

y = -0.1105x + 3.9944

R2 = 0.3377

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6

7

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-15 -10 -5 0 5 10

Past month's return

Dis

agre

emen

t vo

lati

lity

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• Ten-year disagreement weakly negatively related to past returns

y = -0.013x + 2.2725

R2 = 0.1152

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1

1

2

2

3

3

-20 -15 -10 -5 0 5 10 15


Dis

agre

emen

t vo

lati

lity

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• Ten-year disagreement negatively related to past month’s returns

y = -0.0244x + 2.2925

R2 = 0.1701

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1

1

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-15 -10 -5 0 5 10

Past month's return

Dis

agre

emen

t vo

lati

lity

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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness

• One-year average skewness weakly positively related to past quarter’s returns

y = 0.0395x - 2.0587

R2 = 0.0792

-5

-4

-3

-2

-1

0

1

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-20 -15 -10 -5 0 5 10 15


Ave

rage

asy

mm

etry

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• One-year average skewness weakly positively related to past month’s returns

y = 0.0782x - 2.1149

R2 = 0.1301

-5

-4

-3

-2

-1

0

1

2

3

-15 -10 -5 0 5 10

Past month's return

Ave

rage

asy

mm

etry

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• One-year disagreement skewness positively related to past quarter’s returns

y = 0.0389x + 0.1577

R2 = 0.3512

-5

-4

-3

-2

-1

0

1

2

3

-20 -15 -10 -5 0 5 10 15


Dis

agre

emen

t as

ymm

etry

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• One-year disagreement skewness positively related to past month’s returns

y = 0.0618x + 0.0854

R2 = 0.3731

-5

-4

-3

-2

-1

0

1

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-15 -10 -5 0 5 10

Past month's return

Dis

agre

emen

t as

ymm

etry

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Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk

• Literature split– Some find negative relation between risk and

expected returns which is consistent with asset pricing models

– Some find a positive relation

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• One-year average volatility weakly negatively related to expected returns

y = -0.6051x + 6.4669

R2 = 0.1321

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1

2

3

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5

1 2 3 4 5 6 7 8

Average volatility

Exp

ecte

d pr

emia

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• One-year disagreement volatility negatively related to expected returns

y = -0.6927x + 5.4253

R2 = 0.213

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1

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1 2 3 4 5 6 7 8

Disagreement volatility

Exp

ecte

d pr

emia

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• One-year disagreement volatility negatively related to median expected returns

y = -0.8196x + 5.5895

R2 = 0.4862

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1 2 3 4 5 6 7 8


Exp

ecte

d pr

emia

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• Ten-year disagreement volatility positively related to expected returns

y = 0.8732x + 1.8371

R2 = 0.2271

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1 2 3 4 5 6 7 8


Exp

ecte

d pr

emia

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Impact of September 11, 2001

Pre-Sept. 11 Post-Sept. 111-year premium

Mean premium 0.05 -0.70Average volatility 6.79 9.76Disagreement volatility 6.61 7.86

10-year premium

Mean premium 3.63 4.82Disagreement volatility 2.36 3.03Observations 127 33

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What have we learned?

• Forecasts impacted by past returns (expectational momentum)

• Some support for the leverage effect with new expectational data

• Individual volatilities seem low

• Positive relation between risk and expected return - only at longer horizons

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Outstanding issues

• One-year forecasts unlikely used as the “hurdle rate” for one-year project evaluation

• Difference between what CFOs think will happen to the market and their internal hurdle rates

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Interviews

• Results of four randomly selected CFO interviews:– All used the CAPM for cost of capital– None viewed the one-year premium as the input in

the cost of equity calculation – even if the project had a short life

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Appendix

• Market volatility

Var[r]= E[Var(r|Z)] + Var(E[r|Z)]

average vol. disagreement vol.

• Individual volatilities (Davidson and Cooper)

Variance = ([r(0.90) - r(0.10)]/2.65)2

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Appendix

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0.45

<3 6 9 12 15 18 20 >20

Proportion

1-year individual volatilitiesSeptember 10, 2001

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Appendix

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-20 -15 -10 -5 0 5 10 15 20 >20

Proportion

1-year individual skewnessSeptember 10, 2001

1 expectations of equity risk premia, volatility, and asymmetry: from a corporate finance...

Documents

past returns slide

expected premia

volatility slide

median expected returns

year volatility

year risk premium sensitive

year average volatility

sensitive slide