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Perceptions of Financial Volatility:
Standard deviation is not the be all and end all
Darren Duxbury and Barbara Summers
Leeds University Business School
C entre for
D e c isio n
Leeds Re se a rc h
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Overview

Financial volatility




Experimental design




Perception of volatility
Perception of risk
Attractiveness
Analysis of results


Conventional wisdom – standard deviation, σ
Perceived limitations
Alternative measures
Univariate/Multivariate
Discussion and conclusions


Implications
Future analysis and experiments
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Financial Volatility:
Conventional wisdom - σ

Traditional finance theory
 Historic
volatility = dispersion of asset returns
about their central tendency (i.e. mean, μ)

σ

Thus conventional measure is standard deviation,
σ, of asset returns
= risk in traditional finance theory
Therefore, finance theory sees volatility as
synonymous with risk
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Financial Volatility:
Perceived limitations

Many studies question whether risk perception is based
on σ

Low (2004)


Duxbury and Summers (2004)



Experimentally compare P(loss) and variance (σ2)
Find higher P(loss) associated with higher risk, but higher variance
perceived as less risky when P(loss) >=0.5
If σ does not adequately capture risk perception, it may
not capture perception of volatility either

Jones et al (2004)



Suggests finance practitioners regard risk of loss as true risk
Question whether σ is an adequate measure of volatility
Report a simple measure of volatility based on extreme-day returns
that more accurately explains investor behaviour relative to σ
σ, risk and volatility may not be synonymous
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Financial Volatility:
Perceived limitations
25
20
20
15
15
value
value
25
10
10
5
5
0
0
0
5
10
15
time period
20
25
30
0
5
10
15
20
25
30
time period
Price sequences with the same σ may not
be perceived as equally volatile
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Financial Volatility:
Alternative measures

Purpose of this study



To investigate alternative measures of volatility
To compare how well they explain perceived volatility relative to σ
Alternative measures



Mean absolute price change over the price sequence
Number of changes in direction over the price sequence
Number of acceleration changes over the price sequence



Number of peaks or troughs over the price sequence
Range of the price sequence


i.e. change in the rate of change
i.e. min-max
Number of observations in the extremes of the price sequence

i.e. values within 10% of min/max
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Experimental Design

Produced 16 price sequences (graphs)



Differ with respect to:








24 observations each
All with constant mean = 12
StDev
MeanAbsChg
NumChgD
NumAccelChg
NumPeak and NumTrough
Range
Outside10pct
Parameter restrictions


Unable to manipulate all variables freely independently
Full factorial design not possible
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Experimental Design
Graph
St
Dev
Mean
AbsChg
Num
ChgD
Num
AccelChg
Num
Peak
Num
Trough
Range
Outside
10pct
1
11.24
22.00
22
0
11
11
22
24
2
7.66
15.00
22
0
11
11
15
24
3
7.95
10.52
22
2
10
10
22
12
4
7.95
11.00
18
15
6
5
22
12
5
7.66
7.83
22
22
6
5
15
24
6
5.42
7.50
11
0
6
5
15
12
7
7.66
4.57
14
14
3
3
15
24
8
7.95
10.52
22
2
10
10
22
12
9
4.09
8.00
22
0
11
11
8
24
10
4.89
5.00
7
0
4
3
15
8
11
7.66
0.65
2
2
0
0
15
24
12
4.89
6.52
14
14
7
7
15
8
13
7.95
0.96
4
4
0
0
22
12
14
4.09
1.04
6
6
1
1
8
24
15
7.95
0.96
4
4
0
0
22
12
16
7.95
11.00
11
0
6
5
22
12
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Experimental Design


Within-subjects design, n=78
Graph order randomised and counter-balanced


Participants asked to rate (from 0-10) the following for
each graph




No significant effect, therefore, data aggregated
Risk
Volatility
Attractiveness
Financial incentive


Cash prize draw; 1 prize per 25 participants
Value of prize determined by;



Attractiveness rating – most attractive graph chosen
Random point (1-24) chosen from the graph – corresponds to price
Value of prize = £2 x random point drawn
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Experimental Design
Example graph
GRAPH A
Risk rating
___________
25
0 = no risk at all
10 = highest possible risk
20
Volatility rating
15
___________
0 = not at all volatile
10 = extremely volatile
value

10
Attractiveness rating
5
___________
0 = not at all attractive
10 = extremely attractive
0
0
5
10
15
20
25
30
time period
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
1
25
25
20
20
15
Results – volatility
16
value
value
15
10
10
5
5
0
0
5
10
15
20
25
0
30
0
time period
5
10
15
20
25
30
Patterns of No Significant Difference
time period
Mean volatility
12
rating = 8.77
Graphs which are not significantly different from each other
are enclosed in coloured outlines
25
20
value
15
10
5
0
10
15
20
25
30
time period
20
20
15
15
5
10
5
5
52
25
25
02
20
20
51
15
eulav
10
15
10
01
0
7
10
value
25
value
4
3
25
value
5
value
0
10
5
5
0
0
5
0
0
5
10
15
20
25
30
time period
0
5
10
15
20
25
30
time period
03
52
02
51
01
5
0
0
5
10
15
20
25
30
0
time period
doi r ep e mit
0
5
10
15
20
25
30
time period
25
2
20
25
25
15
value
20
20
10
Average mean
volatility
rating = 5.75
value
15
15
value
5
10
0
0
5
10
15
20
25
10
30
time period
5
5
0
0
5
10
15
20
25
30
time period
25
0
0
5
10
15
20
25
30
time pe riod
8
20
6
value
15
9
10
5
0
0
5
10
15
20
25
15
30
time period
25
25
20
20
25
13
20
15
15
value
value
value
15
10
10
10
5
5
5
0
0
5
10
15
time period
20
25
30
0
0
5
10
15
20
25
30
0
time period
0
5
10
15
20
25
30
time period
14
A pattern emerges, but it seems
affected by variation between
Average mean
volatility
Mean volatility
consecutive values rather than
11
rating = 4.23
rating = 2.95
ESA 2007 – Perceptions of Financial Volatility – Duxbury
and Summers
spread alone
25
20
value
15
10
5
0
0
5
C entre for
D e c isio n
Leeds Re se a rc h
10
15
time period
20
25
30
Financial Volatility:
Perceived limitations – same σ
Graph 11 (σ = 7.66)
Graph 2 (σ = 7.66)
25
20
20
15
15
value
value
25
10
10
5
5
0
0
0
5
10
15
20
25
30
time period
Mean volatility rating = 2.95
0
5
10
15
20
25
30
time period
Mean volatility rating = 7.06
Significant < 0.01 (Bonferroni adjusted)
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Financial Volatility:
Perceived limitations – different σ
Graph 12 (σ = 4.89)
Graph 2 (σ = 7.66)
25
20
20
15
15
value
value
25
10
10
5
5
0
0
0
5
10
15
20
25
30
time period
Mean volatility rating = 7.45
0
5
10
15
20
25
30
time period
Mean volatility rating = 7.06
Insignificant = 1.00 (Bonferroni adjusted)
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Results
Volatility
l

Correlations with volatility
rating
a
ti
o
l
a
t
S
P
t
e
D
6
*
*
S
i
g
0
N
4
M
P
e
e
4
*
*
S
i
g
0
N
4
N
P
u
e
1
*
*
S
i
g
0
N
4
N
P
u
e
0
S
i
g
9
N
4
N
P
u
e
0
*
*
S
i
g
0
N
4

N
P
u
e
5
*
*
S
i
g
0
N
4
r
P
a
e
n
4
*
*

S
i
g
0
N
4
o
P
u
e
t
2
*
*
S
i
g
0
N
4



Only NumAccelChg not
significant
5/7 significant variables have a
higher correlation than StDev
All correlations are positive,
other than outside10pct.
Negative correlation is
unexpected
Might imply that situations
analogous to two outcome
gambles are not seen as volatile
 Indication that risk <> volatility
*
*
.
C
o
(2
-t
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Volatility
i
a
c
d
a
i
i
c
c
B
e
i
E
M
t
g
1
(
1
9
3
0
S
4
7
6
0
0
a
D

Model 1: Finance theory view


Initial regression of volatility rating with StDev as the only
independent variable
Coefficient positive and significant


Higher σ seen as higher volatility
But only explains 4.2% of variation in ratings (adjusted r2)
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Volatility
a
ic
d
a
a
i
i
c
c
S
B
e
M
E
i
t
g
1
(
C
6
2
9
0
S
7
8
8
3
0
M
1
2
2
8
0
N
2
5
8
3
8
N
3
0
6
7
0
o
1
9
1
6
0
a
D

Model 2: Look to improve model by adding additional characteristics


StDev entered as Block 1, then other measures as Block 2 via stepwise
MeanAbsChg is the main explanatory variable

Entered second after StDev and adjusted r2 jumps to 33.9%

Best model explains 39.4% (adjusted r2) of variation

NB1: Coefficient on StDev now negative and significant
NB2: Coefficient on NumChgD negative and significant
NB3: NumAccelChg now significant, but not univariately


ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Volatility
Coefficientsa
Model
1
(Cons tant)
StDev
MeanAbsChg
NumAccelChg
outs ide10pct
Uns tandardized
Coefficients
B
Std. Error
5.795
.247
-.163
.035
.300
.012
.053
.008
-.075
.008
Standardized
Coefficients
Beta
-.122
.689
.146
-.201
t
23.421
-4.711
26.033
6.446
-8.926
Sig.
.000
.000
.000
.000
.000
Correlations
Zero-order
Partial
.206
.574
.010
-.112
-.133
.595
.180
-.246
Part
-.104
.576
.143
-.197
Collinearity Statis tics
Tolerance
VIF
.724
.699
.949
.964
1.381
1.431
1.054
1.037
a. Dependent Variable: volatility

Multicollinearity concerns



MeanAbsChg and NumChgD correlation >0.78
NumChgD last entered and so omitted from model
StDev and MeanAbsChg unaffected (sign and significance)

Model still explains 39.2% of variation
 Only 0.2% decrease in adjusted r2

StDev still negative coefficient, so look at semi-partials



MeanABsChg has the largest unique contribution to explaining volatility
StDev has lowest unique contribution to explaining volatility
Zero-order, partial and semi-partial correlation coefficients change sign on
StDev
 Positive (as univariate), negative and negative, respectively
 Suggests StDev interacts with another variable
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Volatility
Coefficientsa
Model
1
(Cons tant)
StDev
MeanAbsChg
s tdev_i_meanabschg
Uns tandardized
Coefficients
B
Std. Error
4.138
.393
-.056
.054
.391
.044
-.013
.005
Standardized
Coefficients
Beta
-.042
.899
-.317
t
10.540
-1.039
8.875
-2.675
Sig.
.000
.299
.000
.008
Correlations
Zero-order
Partial
.206
.574
.514
-.029
.244
-.076
Part
Collinearity Statis tics
Tolerance
VIF
-.024
.204
-.062
.323
.052
.038
3.092
19.389
26.517
a. Dependent Variable: V volatility

Compare StDev and MeanAbsChg and include interaction term

StDev now insignificant, but interaction significant and negative


Model still explains 34.3% of variation
StDev only influences volatility perception via an interaction with
MeanAbsChg, not as a main explanatory variable
 When MeanAbsChg is low, high StDev is perceived as low volatility


E.g. graphs 11, 13, 15
When MeanAbsChg is high, high StDev is perceived as high volatility

E.g. graphs 1, 2, 3, 4
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
1
25
25
20
20
15
Results – volatility
16
value
value
15
10
10
5
5
0
0
5
10
15
20
25
0
30
0
time period
5
10
15
20
25
30
Patterns of No Significant Difference
time period
Mean volatility
12
rating = 8.77
Graphs which are not significantly different from each other
are enclosed in coloured outlines
25
20
value
15
10
5
0
10
15
20
25
30
time period
20
20
15
15
5
10
5
5
52
25
25
02
20
20
51
15
eulav
10
15
10
01
0
7
10
value
25
value
4
3
25
value
5
value
0
10
5
5
0
0
5
0
0
5
10
15
20
25
30
time period
0
5
10
15
20
25
30
time period
03
52
02
51
01
5
0
0
5
10
15
20
25
30
0
time period
doi r ep e mit
0
5
10
15
20
25
30
time period
25
2
20
25
25
15
value
20
20
10
Average mean
volatility
rating = 5.75
value
15
15
value
5
10
0
0
5
10
15
20
25
10
30
time period
5
5
0
0
5
10
15
20
25
30
time period
25
0
0
5
10
15
20
25
30
time pe riod
8
20
6
value
15
9
10
5
0
0
5
10
15
20
25
15
30
time period
25
25
20
20
25
13
20
15
15
value
value
value
15
10
10
10
5
5
5
0
0
5
10
15
time period
20
25
30
0
0
5
10
15
20
25
30
0
time period
0
5
10
15
20
25
30
time period
14
A pattern emerges, but it seems
affected by variation between
Average mean
volatility
Mean volatility
consecutive values rather than
11
rating = 4.23
rating = 2.95
ESA 2007 – Perceptions of Financial Volatility – Duxbury
and Summers
spread alone
25
20
value
15
10
5
0
0
5
C entre for
D e c isio n
Leeds Re se a rc h
10
15
time period
20
25
30
Results

How does Volatility relate to Risk?
Finance theory
 Volatility
l
is synonymous with risk
a
l
a
R
P
*
S
N
7
0
3
*
C
(


Volatility and risk significantly correlated, but much less
than unity
Regression with volatility as sole explanatory variable
gives adjusted r2 = 32%

Thus, although volatility and risk are related they are not
synonymous
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
How does Volatility relate to Risk?
a
i
c
d
a
a
r
f
f
i
i
c
c
S
B
e
M
E
i
t
g
t
1
(
C
2
4
6
0
V
3
5
2
6
0
r
a
9
2
9
5
0
N
5
5
9
9
0
M
4
0
9
0
1
a
D

Model 1: Starting with a regression predicting risk with volatility and add
graph characteristics via stepwise procedure



Model 2: Adding information on an individual’s risk tolerance to Model 1


Forcing StDev to enter pushes out Range and reduces adjusted r2 to 36.7%
Model 4: Exclude Volatility rating from Model 1 and replace with graph
characteristics


Variable is significant at 5% level, but reduces adjusted r2 to 36.8%
Model 3: StDev does not enter Model 1


Adjusted r2 = 37.0%
Significant characteristics are Range, NumTrough and MeanAbsChg
NumAccelChg and Outside10pct enter, but reduces adjusted r2 to 20.6%
Model 5: StDev does not enter Model 4

Forcing StDev to enter (sig at 10% level) pushes out Range and reduces adjusted
r2 slightly
C entre for
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
D e c isio n
Leeds Re se a rc h
Results
Volatility and Risk

Results show that standard deviation,
volatility and risk are not synonymous
as per traditional finance theory
 Although
they are correlated
 Relationship between volatility and risk
rating is strongest
 Range appears to replace StDev in models
unless StDev is forced in
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Results
Attractiveness and Financial Incentive

Finance theory based on a risk-return
trade-off
 Risk
= σ, expected return = mean value
 Investors should minimise risk for a given
return

All 16 graphs have same mean value = 12
 Finance
theory predicts individuals should find
graphs with lowest σ to be the most attractive
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Attractiveness and Financial Incentive
Finance
theory
Graph
St
Dev
Mean
AbsChg
Mean
Attractiveness
Median
Attractiveness
1
11.24
22.00
5.35
5
2
7.66
15.00
5.47
6
3
7.95
10.52
5.62
6
4
7.95
11.00
4.87
5
5
7.66
7.83
5.55
6
6
5.42
7.50
5.36
6
7
7.66
4.57
5.56
5.5
8
7.95
10.52
4.53
5
9
4.09
8.00
6.04
6
10
4.89
5.00
5.47
6
11
7.66
0.65
5.81
6
12
4.89
6.52
5.58
6
13
7.95
0.96
3.97
4
14
4.09
1.04
5.97
6
15
7.95
0.96
6.79
7
16
7.95
11.00
5.18
5
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Attractiveness and Financial Incentive
Finance
theory
Graph
St
Dev
Mean
AbsChg
Mean
Attractiveness
Median
Attractiveness
1
11.24
22.00
5.35
5
2
7.66
15.00
5.47
6
3
7.95
10.52
5.62
6
4
7.95
11.00
4.87
5
5
7.66
7.83
5.55
6
6
5.42
7.50
5.36
6
7
7.66
4.57
5.56
5.5
8
7.95
10.52
4.53
5
9
4.09
8.00
6.04
6
10
4.89
5.00
5.47
6
11
7.66
0.65
5.81
6
12
4.89
6.52
5.58
6
13
7.95
0.96
3.97
4
14
4.09
1.04
5.97
6
15
7.95
0.96
6.79
7
16
7.95
11.00
5.18
5
Most
attractive
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Results
Attractiveness and Financial Incentive

Volatility and risk rating are both negatively correlated with
attractiveness rating



Risk alone can explain 5% of variation in attractiveness



Correlation between risk and attractiveness is much stronger
Suggests that there are elements of risk that influence attractiveness but
are not related to volatility
Adding risk tolerance and an interaction term increases increase
explanatory power a little to 7%
All 3 variables are significant at 5% level or below
Low explanatory power with respect to attractiveness



Likely due to incentive mechanism
Most attractive graph chosen and one of the 24 values chosen at random
Mechanism removes the effect of trend

Necessary due to the transparent patterns in the graphs
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h
Discussion and conclusions

Implications

Traditional finance theory needs a re-think


Volatility (σ) is the most important variable in option pricing



σ, risk and volatility are not synonymous
Black and Scholes,1973
Is σ the best measure to use?
Future analysis and experiments

Ridge / Bayesian regression


More sophisticated way to remedy mutlicollinearity problem
Random versions of graphs to tranparency of next observation


Same points but in a random order
Mean and σ will be unaffected, but other characteristics will vary
 May improve multicollinearity problem

Investigation of the effect of trend on volatility perception


Graphs 13 and 15 are identical except for direction of trend
Volatility perception differs significantly
 Ceteris paribus downward trend perceived as more volatile than upward trend

New financial incentive mechanism - ?
ESA 2007 – Perceptions of Financial Volatility – Duxbury and Summers
C entre for
D e c isio n
Leeds Re se a rc h