perceptions of financial volatility: standard deviation is not the be all and end all

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entre forec isionesearchLeedsESA 2007 – Perceptions of Financial Volatility – Duxbury and ESA 2007 – Perceptions of Financial Volatility – Duxbury and

SummersSummers

Perceptions of Financial Volatility:Perceptions of Financial Volatility:Standard deviation is not the be all and end allStandard deviation is not the be all and end all

Darren Duxbury and Barbara SummersDarren Duxbury and Barbara SummersLeeds University Business SchoolLeeds University Business School

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entre forec isionesearchLeeds

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OverviewOverviewOverviewOverview

Financial volatilityFinancial volatility Conventional wisdom – standard deviation, Conventional wisdom – standard deviation, σσ Perceived limitationsPerceived limitations Alternative measuresAlternative measures

Experimental designExperimental design Perception of volatilityPerception of volatility Perception of riskPerception of risk AttractivenessAttractiveness

Analysis of resultsAnalysis of results Univariate/MultivariateUnivariate/Multivariate

Discussion and conclusionsDiscussion and conclusions ImplicationsImplications Future analysis and experimentsFuture analysis and experiments

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Financial Volatility:Financial Volatility:Conventional wisdom - Conventional wisdom - σσ

Financial Volatility:Financial Volatility:Conventional wisdom - Conventional wisdom - σσ

Traditional finance theoryTraditional finance theory Historic volatilityHistoric volatility == dispersion of asset dispersion of asset

returns about their central tendency (i.e. returns about their central tendency (i.e. mean, μ)mean, μ)

Thus conventional measure is standard Thus conventional measure is standard deviation, σ, of asset returnsdeviation, σ, of asset returns

σ = risk in traditional finance theoryσ = risk in traditional finance theory Therefore, finance theory sees volatility as Therefore, finance theory sees volatility as

synonymous with risksynonymous with risk

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Financial Volatility:Financial Volatility:Perceived limitationsPerceived limitations


Many studies question whether risk perception is Many studies question whether risk perception is based on σbased on σ Low (2004)Low (2004)

Suggests finance practitioners regard risk of loss as true riskSuggests finance practitioners regard risk of loss as true risk Duxbury and Summers (2004)Duxbury and Summers (2004)

Experimentally compare P(loss) and variance (σExperimentally compare P(loss) and variance (σ22)) Find higher P(loss) associated with higher risk, but higher Find higher P(loss) associated with higher risk, but higher

variance perceived as variance perceived as lessless risky when P(loss) >=0.5 risky when P(loss) >=0.5 If σ does not adequately capture risk perception, it If σ does not adequately capture risk perception, it

may not capture perception of volatility eithermay not capture perception of volatility either Jones et al (2004)Jones et al (2004)

Question whether σ is an adequate measure of volatilityQuestion whether σ is an adequate measure of volatility Report a simple measure of volatility based on extreme-day Report a simple measure of volatility based on extreme-day

returns that more accurately explains investor behaviour returns that more accurately explains investor behaviour relative to σrelative to σ

σ, risk and volatility may σ, risk and volatility may notnot be synonymous be synonymous

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Price sequences with the same σ may Price sequences with the same σ may not be perceived as equally volatilenot be perceived as equally volatile

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Financial Volatility:Financial Volatility:Alternative measuresAlternative measures

Financial Volatility:Financial Volatility:Alternative measuresAlternative measures

Purpose of this studyPurpose of this study To investigate alternative measures of volatilityTo investigate alternative measures of volatility To compare how well they explain perceived volatility relative To compare how well they explain perceived volatility relative

to to σσ

Alternative measuresAlternative measures Mean absolute price change over the price sequenceMean absolute price change over the price sequence Number of changes in direction over the price sequenceNumber of changes in direction over the price sequence NumberNumber of acceleration changes over the price sequenceof acceleration changes over the price sequence

i.e. change in the rate of changei.e. change in the rate of change NumberNumber of peaks or troughs over the price sequenceof peaks or troughs over the price sequence Range of the price sequenceRange of the price sequence

i.e. min-maxi.e. min-max Number of observations in the extremes of the price sequenceNumber of observations in the extremes of the price sequence

i.e. values within 10% of min/maxi.e. values within 10% of min/max

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Experimental DesignExperimental Design Produced 16 price sequences (graphs)Produced 16 price sequences (graphs)

24 observations each24 observations each All with constant mean = 12All with constant mean = 12

Differ with respect to:Differ with respect to: StDevStDev MeanAbsChgMeanAbsChg NumChgDNumChgD NumAccelChgNumAccelChg NumPeak and NumTroughNumPeak and NumTrough RangeRange Outside10pctOutside10pct

Parameter restrictionsParameter restrictions Unable to manipulate all variables freely independentlyUnable to manipulate all variables freely independently Full factorial design not possibleFull factorial design not possible

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Experimental DesignExperimental DesignGraph

St Dev

MeanAbsChg

NumChgD

NumAccelChg

NumPeak

NumTrough Range

Outside10pct

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

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Experimental DesignExperimental Design Within-subjects design, n=78Within-subjects design, n=78 Graph order randomised and counter-balancedGraph order randomised and counter-balanced

No significant effect, therefore, data aggregatedNo significant effect, therefore, data aggregated Participants asked to rate (from 0-10) the following Participants asked to rate (from 0-10) the following

for each graphfor each graph RiskRisk VolatilityVolatility AttractivenessAttractiveness

Financial incentiveFinancial incentive Cash prize draw; 1 prize per 25 participantsCash prize draw; 1 prize per 25 participants Value of prize determined by;Value of prize determined by;

Attractiveness rating – most attractive graph chosenAttractiveness rating – most attractive graph chosen Random point (1-24) chosen from the graph – corresponds to

price Value of prize = £2 x random point drawn

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Experimental DesignExperimental Design

Example graphExample graph

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Risk rating ___________

0 = no risk at all10 = highest possible risk

Volatility rating ___________

0 = not at all volatile10 = extremely volatile

Attractiveness rating ___________

0 = not at all attractive10 = extremely attractive

GRAPH A

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A pattern emerges, but it seemsA pattern emerges, but it seemsaffected by variation betweenaffected by variation betweenconsecutive values rather thanconsecutive values rather thanspread alonespread alone

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Mean volatility rating = 8.77


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Average mean volatility rating = 5.75


Results – volatilityPatterns of No Significant DifferenceGraphs which are not significantly different from each otherare enclosed in coloured outlines

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Financial Volatility:Financial Volatility:Perceived limitations – same Perceived limitations – same σσFinancial Volatility:Financial Volatility:

Perceived limitations – same Perceived limitations – same σσ

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Mean volatility rating = Mean volatility rating = 2.952.95


Graph 11 (Graph 11 (σσ = 7.66) = 7.66) Graph 2 (Graph 2 (σσ = 7.66) = 7.66)

Significant < 0.01 (Bonferroni adjusted)Significant < 0.01 (Bonferroni adjusted)

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Financial Volatility:Financial Volatility:Perceived limitations – different Perceived limitations – different σσ

Financial Volatility:Financial Volatility:Perceived limitations – different Perceived limitations – different σσ

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Graph 12 (Graph 12 (σσ = 4.89) = 4.89) Graph 2 (Graph 2 (σσ = 7.66) = 7.66)

Insignificant = 1.00 (Bonferroni adjusted)Insignificant = 1.00 (Bonferroni adjusted)

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ResultsVolatilityResultsVolatility

Correlations with volatility Correlations with volatility ratingrating Only NumAccelChg not Only NumAccelChg not

significantsignificant 5/7 significant variables have a 5/7 significant variables have a

higher correlation than StDevhigher correlation than StDev All correlations are positive, All correlations are positive,

other than outside10pct.other than outside10pct. Negative correlation is Negative correlation is

unexpectedunexpected Might imply that situations Might imply that situations

analogous to two outcome analogous to two outcome gambles are not seen as gambles are not seen as volatilevolatile

Indication that risk <> Indication that risk <> volatilityvolatility

Correlations

.206**

.000

1244

.574**

.000

1244

.461**

.000

1244

.010

.729

1244

.510**

.000

1244

.485**

.000

1244

.214**

.000

1244

-.112**

.000

1244

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

StDev

MeanAbsChg

NumChgD

NumAccelChg

NumPeak

NumTrough

range

outside10pct

V volatility

Correlation is significant at the 0.01 level(2-tailed).

**.

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VolatilityVolatility

Model 1: Finance theory viewModel 1: Finance theory view Initial regression of volatility rating with StDev as the only Initial regression of volatility rating with StDev as the only

independent variableindependent variable Coefficient positive and significantCoefficient positive and significant

Higher Higher σσ seen as higher volatility seen as higher volatility But only explains But only explains 4.2%4.2% of variation in ratings (adjusted r of variation in ratings (adjusted r22))

Coefficientsa

4.041 .269 15.023 .000

.274 .037 .206 7.420 .000

(Constant)

StDev

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: V volatilitya.

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Model 2: Look to improve model by adding additional Model 2: Look to improve model by adding additional characteristics characteristics StDev entered as Block 1, then other measures as Block 2 via stepwiseStDev entered as Block 1, then other measures as Block 2 via stepwise MeanAbsChg is the main explanatory variableMeanAbsChg is the main explanatory variable

Entered second after StDev and adjusted rEntered second after StDev and adjusted r22 jumps to jumps to 33.9%33.9% Best model explains Best model explains 39.4%39.4% (adjusted r (adjusted r22) of variation) of variation

NB1: Coefficient on StDev now negative and significantNB1: Coefficient on StDev now negative and significant NB2: Coefficient on NumChgD negative and significantNB2: Coefficient on NumChgD negative and significant NB3: NumAccelChg now significant, but not univariatelyNB3: NumAccelChg now significant, but not univariately

Coefficientsa

6.046 .272 22.199 .000

-.197 .038 -.148 -5.203 .000

.341 .022 .782 15.628 .000

-.032 .015 -.098 -2.193 .028

.063 .010 .176 6.667 .000

-.071 .009 -.191 -8.296 .000

(Constant)

StDev

MeanAbsChg

NumChgD

NumAccelChg

outside10pct

Model1

B Std. Error


Beta


t Sig.


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Multicollinearity concerns Multicollinearity concerns MeanAbsChg and NumChgD correlation >0.78MeanAbsChg and NumChgD correlation >0.78 NumChgD last entered and so omitted from modelNumChgD last entered and so omitted from model StDev and MeanAbsChg unaffected (sign and significance)StDev and MeanAbsChg unaffected (sign and significance)

Model still explains Model still explains 39.2%39.2% of variation of variation Only Only 0.2%0.2% decrease in adjusted r decrease in adjusted r22

StDev still negative coefficient, so look at semi-partialsStDev still negative coefficient, so look at semi-partials MeanABsChg has the largest unique contribution to explaining MeanABsChg has the largest unique contribution to explaining

volatilityvolatility StDev has lowest StDev has lowest unique contribution to explaining volatilityunique contribution to explaining volatility Zero-order, partial and semi-partial correlation coefficients change Zero-order, partial and semi-partial correlation coefficients change

sign on StDevsign on StDev Positive (as univariate), negative and negative, respectivelyPositive (as univariate), negative and negative, respectively Suggests StDev interacts with another variableSuggests StDev interacts with another variable

Coefficientsa

5.795 .247 23.421 .000

-.163 .035 -.122 -4.711 .000 .206 -.133 -.104 .724 1.381

.300 .012 .689 26.033 .000 .574 .595 .576 .699 1.431

.053 .008 .146 6.446 .000 .010 .180 .143 .949 1.054

-.075 .008 -.201 -8.926 .000 -.112 -.246 -.197 .964 1.037

(Constant)

StDev

MeanAbsChg

NumAccelChg

outside10pct

Model1

B Std. Error


Beta


t Sig. Zero-order Partial Part

Correlations

Tolerance VIF

Collinearity Statistics

Dependent Variable: volatilitya.

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Compare StDev and MeanAbsChg and include interaction termCompare StDev and MeanAbsChg and include interaction term StDev now insignificant, but interaction significant and negativeStDev now insignificant, but interaction significant and negative

Model still explains Model still explains 34.3%34.3% of variation of variation

StDev only influences volatility perception via an interaction with StDev only influences volatility perception via an interaction with MeanAbsChg, not as a main explanatory variable MeanAbsChg, not as a main explanatory variable When When MeanAbsChg is low, high StDev is perceived as low volatilityMeanAbsChg is low, high StDev is perceived as low volatility

E.g. graphs 11, 13, 15E.g. graphs 11, 13, 15 When When MeanAbsChg is high, high StDev is perceived as high volatilityMeanAbsChg is high, high StDev is perceived as high volatility

E.g. graphs 1, 2, 3, 4E.g. graphs 1, 2, 3, 4

Coefficientsa

4.138 .393 10.540 .000

-.056 .054 -.042 -1.039 .299 .206 -.029 -.024 .323 3.092

.391 .044 .899 8.875 .000 .574 .244 .204 .052 19.389

-.013 .005 -.317 -2.675 .008 .514 -.076 -.062 .038 26.517

(Constant)

StDev

MeanAbsChg

stdev_i_meanabschg

Model1

B Std. Error


Beta


t Sig. Zero-order Partial Part

Correlations

Tolerance VIF

Collinearity Statistics


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A pattern emerges, but it seemsA pattern emerges, but it seemsaffected by variation betweenaffected by variation betweenconsecutive values rather thanconsecutive values rather thanspread alonespread alone

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Results – volatilityPatterns of No Significant DifferenceGraphs which are not significantly different from each otherare enclosed in coloured outlines

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SummersSummers

ResultsHow does Volatility relate to Risk?

ResultsHow does Volatility relate to Risk?

Finance theory Volatility is synonymous with risk

Correlations

.567**

.000

1243

Pearson Correlation

Sig. (2-tailed)

N

R riskV volatility

Correlation is significant at the 0.01 level(2-tailed).

**.

Volatility and risk significantly correlated, but Volatility and risk significantly correlated, but much less than unitymuch less than unity

Regression with volatility as sole explanatory Regression with volatility as sole explanatory variable gives adjusted rvariable gives adjusted r22 = = 32%32% Thus, although volatility and risk are related they are Thus, although volatility and risk are related they are

not synonymousnot synonymous

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How does Volatility relate to Risk?

How does Volatility relate to Risk?

Model 1: Starting with a regression predicting risk with volatility and Model 1: Starting with a regression predicting risk with volatility and add graph characteristics via stepwise procedureadd graph characteristics via stepwise procedure Adjusted rAdjusted r22 = = 37.0%37.0% Significant characteristics are Range, NumTrough and MeanAbsChgSignificant characteristics are Range, NumTrough and MeanAbsChg

Model 2: Adding information on an individual’s risk tolerance to Model 2: Adding information on an individual’s risk tolerance to Model 1Model 1 Variable is significant at 5% level, but reduces adjusted rVariable is significant at 5% level, but reduces adjusted r22 to to 36.8%36.8%

Model 3: StDev does not enter Model 1Model 3: StDev does not enter Model 1 Forcing StDev to enter pushes out Range and reduces adjusted rForcing StDev to enter pushes out Range and reduces adjusted r22 to to

36.7%36.7% Model 4: Exclude Volatility rating from Model 1 and replace with Model 4: Exclude Volatility rating from Model 1 and replace with

graph characteristicsgraph characteristics NumAccelChg and Outside10pct enter, but reduces adjusted rNumAccelChg and Outside10pct enter, but reduces adjusted r22 to to 20.6%20.6%

Model 5: StDev does not enter Model 4Model 5: StDev does not enter Model 4 Forcing StDev to enter (sig at 10% level) pushes out Range and reduces Forcing StDev to enter (sig at 10% level) pushes out Range and reduces

adjusted radjusted r22 slightly slightly

Coefficientsa

1.562 .234 6.686 .000

.483 .025 .522 18.936 .000

.079 .012 .169 6.415 .000

-.095 .025 -.169 -3.779 .000

.064 .020 .159 3.230 .001

(Constant)

V volatility

range

NumTrough

MeanAbsChg

Model1

B Std. Error


Beta


t Sig.

Dependent Variable: R riska.

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ResultsVolatility and Risk

ResultsVolatility and Risk

Results show that standard Results show that standard deviation, volatility and risk are deviation, volatility and risk are notnot synonymous as per synonymous as per traditional finance theorytraditional finance theory Although they are correlatedAlthough they are correlated Relationship between volatility and Relationship between volatility and

risk rating is strongestrisk rating is strongest Range appears to replace StDev in Range appears to replace StDev in

models unless StDev is forced inmodels unless StDev is forced in

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ResultsAttractiveness and Financial Incentive


Finance theory based on a risk-return Finance theory based on a risk-return trade-offtrade-off Risk = Risk = σ, expected return = mean valueσ, expected return = mean value Investors should minimise risk for a given Investors should minimise risk for a given

returnreturn All 16 graphs have same mean value All 16 graphs have same mean value

= 12= 12 Finance theory predicts individuals Finance theory predicts individuals

should find graphs with lowest should find graphs with lowest σ to be σ to be the most attractivethe most attractive

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Attractiveness and Financial IncentiveAttractiveness and Financial Incentive

GraphSt

DevMean

AbsChg

MeanAttractivenes

s

MedianAttractivenes

s

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

Finance Finance theorytheory

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Attractiveness and Financial IncentiveAttractiveness and Financial Incentive

GraphSt

DevMean

AbsChg

MeanAttractivenes

s

MedianAttractivenes

s

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

Finance Finance theorytheory

Most Most attractivattractivee

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Volatility and risk rating are both negatively correlated with Volatility and risk rating are both negatively correlated with attractiveness ratingattractiveness rating Correlation between risk and attractiveness is much strongerCorrelation between risk and attractiveness is much stronger Suggests that there are elements of risk that influence Suggests that there are elements of risk that influence

attractiveness but are not related to volatilityattractiveness but are not related to volatility

Risk alone can explain Risk alone can explain 5%5% of variation in attractiveness of variation in attractiveness Adding risk tolerance and an interaction term increases increase Adding risk tolerance and an interaction term increases increase

explanatory power a little to explanatory power a little to 7%7% All 3 variables are significant at 5% level or belowAll 3 variables are significant at 5% level or below

Low explanatory power with respect to attractivenessLow explanatory power with respect to attractiveness Likely due to incentive mechanismLikely due to incentive mechanism Most attractive graph chosen and one of the 24 values chosen Most attractive graph chosen and one of the 24 values chosen

at randomat random Mechanism removes the effect of trendMechanism removes the effect of trend

Necessary due to the transparent patterns in the graphsNecessary due to the transparent patterns in the graphs

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Discussion and conclusionsDiscussion and conclusions ImplicationsImplications

Traditional finance theory needs a re-thinkTraditional finance theory needs a re-think σ, risk and volatility are σ, risk and volatility are notnot synonymous synonymous

Volatility (σ) is the most important variable in option pricingVolatility (σ) is the most important variable in option pricing Black and Scholes,1973Black and Scholes,1973 Is σ the best measure to use?Is σ the best measure to use?

Future analysis and experimentsFuture analysis and experiments Ridge / Bayesian regressionRidge / Bayesian regression

More sophisticated way to remedy mutlicollinearity problemMore sophisticated way to remedy mutlicollinearity problem Random versions of graphs to tranparency of next observationRandom versions of graphs to tranparency of next observation

Same points but in a random orderSame points but in a random order Mean and σ will be unaffected, but other characteristics will varyMean and σ will be unaffected, but other characteristics will vary

May improve multicollinearity problemMay improve multicollinearity problem Investigation of the effect of trend on volatility perceptionInvestigation of the effect of trend on volatility perception

Graphs 13 and 15 are identical except for direction of trendGraphs 13 and 15 are identical except for direction of trend Volatility perception differs significantlyVolatility perception differs significantly

Ceteris paribusCeteris paribus downward trend perceived as more volatile than upward downward trend perceived as more volatile than upward trend trend

New financial incentive mechanism - ?New financial incentive mechanism - ?

perceptions of financial volatility: standard deviation is not the be all and end all

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