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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 7 10 value 25 value 4 3 25 15 value 5 value 0 10 01 10 5 5 0 0 5 0 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 5 time period 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 f ic ic S B e M E ig t t 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 Zero-order .206 .574 .010 -.112 Correlations Partial -.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 7 10 value 25 value 4 3 25 15 value 5 value 0 10 01 10 5 5 0 0 5 0 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 5 time period 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