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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Graham/Harvey: Expectations of Risk Premia
Across Time and Different Horizons
• Ten-year risk premium around 3.5% and stable whereas one-year risk premium quite variable
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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
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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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Graham/Harvey: Expectations of Risk Premia
Across Respondents at a Point in Time
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
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< -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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Graham/Harvey: Expectations of Risk Premia
Across Respondents at a Point in Time
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0.05
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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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-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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-20 -15 -10 -5 0 5 10 15
Past quarters' return
Ten
-yea
r pr
emiu
m
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Graham/Harvey: Expectations of Risk Premia
Measuring Volatility
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Graham/Harvey: Expectations of Risk Premia
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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-20 -15 -10 -5 0 5 10 15
Past quarter's return
Ave
rage
vol
atil
ity
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility
• Average one-year volatility not related to past month’s returns
y = -0.0215x + 6.4125
R2 = 0.0158
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-15 -10 -5 0 5 10
Past month's return
Ave
rage
vol
atil
ity
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility
• One-year disagreement volatility not linearly related to past quarter’s returns
y = -0.0342x + 3.9939
R2 = 0.0773
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-20 -15 -10 -5 0 5 10 15
Past quarter's return
Dis
agre
emen
t vo
lati
lity
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility
• Maybe non-linear – but too little data
y = 0.015x2 + 0.0727x + 3.2025
R2 = 0.8158
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-20 -15 -10 -5 0 5 10 15
Past quarter's return
Dis
agre
emen
t vo
lati
lity
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility
• One-year disagreement volatility negatively related to past month’s returns
y = -0.1105x + 3.9944
R2 = 0.3377
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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 Volatility
• Ten-year disagreement weakly negatively related to past returns
y = -0.013x + 2.2725
R2 = 0.1152
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-20 -15 -10 -5 0 5 10 15
Past quarter's return
Dis
agre
emen
t vo
lati
lity
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Volatility
• Ten-year disagreement negatively related to past month’s returns
y = -0.0244x + 2.2925
R2 = 0.1701
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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
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Past quarter's return
Ave
rage
asy
mm
etry
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness
• One-year average skewness weakly positively related to past month’s returns
y = 0.0782x - 2.1149
R2 = 0.1301
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-15 -10 -5 0 5 10
Past month's return
Ave
rage
asy
mm
etry
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness
• One-year disagreement skewness positively related to past quarter’s returns
y = 0.0389x + 0.1577
R2 = 0.3512
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-20 -15 -10 -5 0 5 10 15
Past quarter's return
Dis
agre
emen
t as
ymm
etry
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Graham/Harvey: Expectations of Risk Premia Past Returns Impact Expected Skewness
• One-year disagreement skewness positively related to past month’s returns
y = 0.0618x + 0.0854
R2 = 0.3731
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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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Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk
• One-year average volatility weakly negatively related to expected returns
y = -0.6051x + 6.4669
R2 = 0.1321
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Average volatility
Exp
ecte
d pr
emia
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Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk
• One-year disagreement volatility negatively related to expected returns
y = -0.6927x + 5.4253
R2 = 0.213
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Disagreement volatility
Exp
ecte
d pr
emia
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Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk
• One-year disagreement volatility negatively related to median expected returns
y = -0.8196x + 5.5895
R2 = 0.4862
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Disagreement volatility
Exp
ecte
d pr
emia
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Graham/Harvey: Expectations of Risk Premia Expected Reward and Risk
• Ten-year disagreement volatility positively related to expected returns
y = 0.8732x + 1.8371
R2 = 0.2271
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Disagreement volatility
Exp
ecte
d pr
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Graham/Harvey: Expectations of Risk Premia
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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Graham/Harvey: Expectations of Risk Premia
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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Graham/Harvey: Expectations of Risk Premia
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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Graham/Harvey: Expectations of Risk Premia
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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Graham/Harvey: Expectations of Risk Premia
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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Graham/Harvey: Expectations of Risk Premia
Appendix
0.00
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<3 6 9 12 15 18 20 >20
Proportion
1-year individual volatilitiesSeptember 10, 2001
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Graham/Harvey: Expectations of Risk Premia
Appendix
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-20 -15 -10 -5 0 5 10 15 20 >20
Proportion
1-year individual skewnessSeptember 10, 2001