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

Perceptions of Financial Volatility: Standard deviation is not the be all and end all. Darren Duxbury and Barbara Summers Leeds University Business School. Overview. Financial volatility Conventional wisdom – standard deviation, σ Perceived limitations Alternative measures

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

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  1. Perceptions of Financial Volatility: Standard deviation is not the be all and end all Darren Duxbury and Barbara Summers Leeds University Business School

  2. Overview • Financial volatility • Conventional wisdom – standard deviation, σ • Perceived limitations • Alternative measures • Experimental design • Perception of volatility • Perception of risk • Attractiveness • Analysis of results • Univariate/Multivariate • Discussion and conclusions • Implications • Future analysis and experiments

  3. Financial Volatility:Conventional wisdom - σ • Traditional finance theory • Historic volatility=dispersion of asset returns about their central tendency (i.e. mean, μ) • Thus conventional measure is standard deviation, σ, of asset returns • σ = risk in traditional finance theory • Therefore, finance theory sees volatility as synonymous with risk

  4. Financial Volatility:Perceived limitations • Many studies question whether risk perception is based on σ • Low (2004) • Suggests finance practitioners regard risk of loss as true risk • 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) • 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

  5. Financial Volatility:Perceived limitations Price sequences with the same σ may not be perceived as equally volatile

  6. 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 • Numberof acceleration changes over the price sequence • i.e. change in the rate of change • Numberof peaks or troughs over the price sequence • Range of the price sequence • i.e. min-max • Number of observations in the extremes of the price sequence • i.e. values within 10% of min/max

  7. Experimental Design • Produced 16 price sequences (graphs) • 24 observations each • All with constant mean = 12 • Differ with respect to: • StDev • MeanAbsChg • NumChgD • NumAccelChg • NumPeak and NumTrough • Range • Outside10pct • Parameter restrictions • Unable to manipulate all variables freely independently • Full factorial design not possible

  8. Experimental Design

  9. Experimental Design • Within-subjects design, n=78 • Graph order randomised and counter-balanced • No significant effect, therefore, data aggregated • Participants asked to rate (from 0-10) the following for each graph • 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

  10. GRAPH A Risk rating ___________ 0 = no risk at all 10 = highest possible risk Volatility rating ___________ 0 = not at all volatile 10 = extremely volatile Attractiveness rating ___________ 0 = not at all attractive 10 = extremely attractive Experimental Design • Example graph

  11. Results – volatility Patterns of No Significant Difference Graphs which are not significantly different from each other are enclosed in coloured outlines 1 16 Mean volatility rating = 8.77 12 7 3 5 10 4 2 Average mean volatility rating = 5.75 8 6 9 15 13 A pattern emerges, but it seems affected by variation between consecutive values rather than spread alone 14 Average mean volatility rating = 4.23 Mean volatility rating = 2.95 11

  12. Financial Volatility:Perceived limitations – same σ Graph 11 (σ = 7.66) Graph 2 (σ = 7.66) Mean volatility rating = 7.06 Mean volatility rating = 2.95 Significant < 0.01 (Bonferroni adjusted)

  13. Financial Volatility:Perceived limitations – different σ Graph 12 (σ = 4.89) Graph 2 (σ = 7.66) Mean volatility rating = 7.06 Mean volatility rating = 7.45 Insignificant = 1.00 (Bonferroni adjusted)

  14. ResultsVolatility • Correlations with volatility rating • 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

  15. Volatility • 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)

  16. Volatility • 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

  17. 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

  18. 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

  19. Results – volatility Patterns of No Significant Difference Graphs which are not significantly different from each other are enclosed in coloured outlines 1 16 Mean volatility rating = 8.77 12 7 3 5 10 4 2 Average mean volatility rating = 5.75 8 6 9 15 13 A pattern emerges, but it seems affected by variation between consecutive values rather than spread alone 14 Average mean volatility rating = 4.23 Mean volatility rating = 2.95 11

  20. ResultsHow does Volatility relate to Risk? • Finance theory • Volatility is synonymous with risk • 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

  21. How does Volatility relate to Risk? • Model 1: Starting with a regression predicting risk with volatility and add graph characteristics via stepwise procedure • Adjusted r2 = 37.0% • Significant characteristics are Range, NumTrough and MeanAbsChg • Model 2: Adding information on an individual’s risk tolerance to Model 1 • Variable is significant at 5% level, but reduces adjusted r2 to 36.8% • Model 3: StDev does not enter 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 • 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

  22. ResultsVolatility 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

  23. ResultsAttractiveness 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

  24. Attractiveness and Financial Incentive Finance theory

  25. Attractiveness and Financial Incentive Finance theory Most attractive

  26. ResultsAttractiveness and Financial Incentive • Volatility and risk rating are both negatively correlated with attractiveness rating • Correlation between risk and attractiveness is much stronger • Suggests that there are elements of risk that influence attractiveness but are not related to volatility • Risk alone can explain 5% of variation in attractiveness • 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

  27. Discussion and conclusions • Implications • Traditional finance theory needs a re-think • σ, risk and volatility are not synonymous • Volatility (σ) is the most important variable in option pricing • 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 - ?

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