Western Finance Association Meetings
Park City, Utah
June 2002
Expectations of
Equity Risk Premia, Volatility, and Asymmetry:
From a Corporate Finance Perspective
John R. Graham
Duke University, Durham, NC USA
http://www.duke.edu/~jgraham
Campbell R. Harvey
Duke University, Durham, NC USA
National Bureau of Economic Research, Cambridge, MA USA
http://www.duke.edu/~charvey
1
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
2
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
5
5
4
4
3
3
2
2
1
1
0
0
6-Jun-00
10-Sep-01
7-Sep-00
4-Dec-01
4-Dec-00
11-Mar-02
12-Mar-01
4-Jun-02
10-year premium
7-Jun-01
6-Jun-00
10-Sep-01
7-Sep-00
4-Dec-01
4-Dec-00
11-Mar-02
12-Mar-01
4-Jun-02
7-Jun-01
1-year premium
3
Graham/Harvey: Expectations of Risk Premia
Across Respondents at a Point in Time
Proportion
0.40
10-year premium
September 10, 2001
0.35
0.30
0.25
0.20
0.15
0.10
0.05
20
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-1
0
-1
2
-1
6
-1
4
-1
8
m
or
e
<
-2
0
0.00
4
Graham/Harvey: Expectations of Risk Premia
Across Respondents at a Point in Time
Proportion
0.40
1-year premium
September 10, 2001
0.35
0.30
0.25
0.20
0.15
0.10
0.05
18
16
14
12
10
8
6
4
2
0
-2
-4
-6
-8
-1
0
-1
2
-1
6
-1
4
-1
8
20
m
or
e
<
-2
0
0.00
5
Graham/Harvey: Expectations of Risk Premia
Past Returns and Expected Premia
• One-year risk premium sensitive to past returns
5
One-year premium
y = 0.1298x + 3.0165
R2 = 0.5377
4
3
2
1
0
-20
-15
-10
-5
0
5
10
15
Past quarters' return
6
Graham/Harvey: Expectations of Risk Premia
Past Returns and Expected Premia
• 10-year risk premium not sensitive
Ten-year premium
5
4
3
2
y = -0.0008x + 3.9002
R2 = 0.0001
1
0
-20
-15
-10
-5
0
5
10
15
Past quarters' return
7
Graham/Harvey: Expectations of Risk Premia
Measuring Volatility
8
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
9
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
• Average one-year volatility not related to past
quarter’s returns
8
Average volatility
7
6
5
y = 0.0214x + 6.5153
R2 = 0.0373
4
3
2
-20
-15
-10
-5
0
5
10
15
Past quarter's return
10
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
• Average one-year volatility not related to past
month’s returns
8
Average volatility
7
6
5
y = -0.0215x + 6.4125
R2 = 0.0158
4
3
2
-15
-10
-5
0
5
10
Past month's return
11
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
Disagreement volatility
• One-year disagreement volatility not linearly
related to past quarter’s returns
8
y = -0.0342x + 3.9939
R2 = 0.0773
7
6
5
4
3
2
-20
-15
-10
-5
0
5
10
15
Past quarter's return
12
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
• Maybe non-linear – but too little data
Disagreement volatility
2
8
+ 0.0727x + 3.2025
y = 0.015x
2
= 0.8158
R
7
6
5
4
3
2
-20
-15
-10
-5
0
5
10
15
Past quarter's return
13
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
• One-year disagreement volatility negatively
related to past month’s returns
8
Disagreement volatility
y = -0.1105x + 3.9944
7
R2 = 0.3377
6
5
4
3
2
-15
-10
-5
0
5
10
Past month's return
14
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
Disagreement volatility
• Ten-year disagreement weakly negatively related
to past returns
3
3
2
2
y = -0.013x + 2.2725
R2 = 0.1152
1
1
0
-20
-15
-10
-5
0
5
10
15
Past quarter's return
15
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Volatility
Disagreement volatility
• Ten-year disagreement negatively related to past
month’s returns
3
3
2
2
y = -0.0244x + 2.2925
R2 = 0.1701
1
1
0
-15
-10
-5
0
5
10
Past month's return
16
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Skewness
Average asymmetry
• One-year average skewness weakly positively
related to past quarter’s returns
3
y = 0.0395x - 2.0587
R2 = 0.0792
2
1
0
-20
-15
-10
-5
-1
0
5
10
15
-2
-3
-4
-5
Past quarter's return
17
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Skewness
Average asymmetry
• One-year average skewness weakly positively
related to past month’s returns
3
y = 0.0782x - 2.1149
R2 = 0.1301
2
1
0
-15
-10
-5
-1
0
5
10
-2
-3
-4
-5
Past month's return
18
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Skewness
Disagreement asymmetry
• One-year disagreement skewness positively
related to past quarter’s returns
3
2
1
0
-20
-15
-10
-5
-1
0
5
10
15
-2
y = 0.0389x + 0.1577
R2 = 0.3512
-3
-4
-5
Past quarter's return
19
Graham/Harvey: Expectations of Risk Premia
Past Returns Impact Expected Skewness
Disagreement asymmetry
• One-year disagreement skewness positively
related to past month’s returns
3
2
1
0
-15
-10
-5
-1
0
5
10
-2
y = 0.0618x + 0.0854
R2 = 0.3731
-3
-4
-5
Past month's return
20
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
21
Graham/Harvey: Expectations of Risk Premia
Expected Reward and Risk
Expected premia
• One-year average volatility weakly negatively
related5 to expected returns
4
3
y = -0.6051x + 6.4669
R2 = 0.1321
2
1
0
1
2
3
4
5
6
7
8
Average volatility
22
Graham/Harvey: Expectations of Risk Premia
Expected Reward and Risk
• One-year disagreement volatility negatively
related to expected returns
Expected premia
5
y = -0.6927x + 5.4253
R2 = 0.213
4
3
2
1
0
1
2
3
4
5
6
7
8
Disagreement volatility
23
Graham/Harvey: Expectations of Risk Premia
Expected Reward and Risk
• One-year disagreement volatility negatively
related to median expected returns
Expected premia
5
4
y = -0.8196x + 5.5895
R2 = 0.4862
3
2
1
0
1
2
3
4
5
6
7
8
Disagreement volatility
24
Graham/Harvey: Expectations of Risk Premia
Expected Reward and Risk
• Ten-year disagreement volatility positively
related to expected returns
Expected premia
5
4
y = 0.8732x + 1.8371
R2 = 0.2271
3
2
1
0
1
2
3
4
5
6
7
8
Disagreement volatility
25
Graham/Harvey: Expectations of Risk Premia
Impact of September 11, 2001
Pre-Sept. 11 Post-Sept. 11
1-year premium
Mean premium
Average volatility
Disagreement volatility
0.05
6.79
6.61
-0.70
9.76
7.86
10-year premium
Mean premium
Disagreement volatility
Observations
3.63
2.36
127
4.82
3.03
33
26
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
27
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
28
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
29
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
30
Graham/Harvey: Expectations of Risk Premia
Appendix
Proportion
0.45
1-year individual volatilities
September 10, 2001
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
<3
6
9
12
15
18
20
>20
31
Graham/Harvey: Expectations of Risk Premia
Appendix
Proportion
0.45
1-year individual skewness
September 10, 2001
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
-20
-15
-10
-5
0
5
10
15
20
>20
32