1 Expectations of Equity Risk Premia, Volatility, and Asymmetry: From a Corporate Finance Perspective John R. Graham Duke University, Durham, NC USA jgraham.

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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

0

1

2

3

4

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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5

6

7

8

-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

0

1

1

2

2

3

3

-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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3

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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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3

-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

4

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

0

1

2

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4

5

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

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5

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

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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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Proportion

1-year individual skewnessSeptember 10, 2001

1 Expectations of Equity Risk Premia, Volatility, and Asymmetry: From a Corporate Finance Perspective John R. Graham Duke University, Durham, NC USA jgraham.

Documents

past returns slide

expected premia

volatility slide

median expected returns

year volatility

year risk premium sensitive

year average volatility

sensitive slide