1-s2.0-S0378426614001253-main.pdf

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increases in return expectation on buying activity. Portfolio risk levels and changes are more systemat-ically related to return and risk expectations. In line with nancial theory, risk taking increases withreturn expectations and decreases with risk expectations. In response to their expectations, investors alsoadjust the riskiness of assets they trade.

2014 Elsevier B.V. All rights reserved.

at na

investors have been shown to hold underdiversied portfolios

different from pure meanvariance optimization (Lewellen et al.,1977; Grinblatt and Keloharju, 2000). Often these deviations havebeen explained by specic psychological biases, e.g., excessivetrading by overcondence (Odean, 1998; Glaser and Weber, 2007).

tion on beliefs and preferences is needed.xpectations in avestors ate not reprding instit

which imposes some limits on the generality of the resultsever, our focus is on individual investors for which our samrather typical. Participants are well informed about nancial mar-kets as, e.g., their responses in a nancial literacy questionnaireshow. They also have on average many years of investment expe-rience and invest non-trivial amounts of money. In three-monthintervals, survey participants are queried for numerical and quali-tative expectations and their risk tolerance. We then match expec-tations of investors to their actual transactions in their online

Corresponding author. Address: Lehrstuhl fr ABWL und Finanzwirtschaft,Universitt Mannheim, 68131 Mannheim, Germany. Tel.: +49 6211811531; fax:+49 6211811534.

E-mail address: [email protected] (C. Merkle).

Journal of Banking & Finance 46 (2014) 372386

Contents lists availab

Journal of Bank

w.(Goetzmann and Kumar, 2008), to trade frequently (Odean, 1999;Barber and Odean, 2000), to take high idiosyncratic risk (Calvetet al., 2007), and to gamble in the stock market (Kumar, 2009).There is also evidence that they use various investment strategies

To this end, we collect return and risk erepeated panel survey of self-directed private inUK online brokerage provider. These investors artive for the overall investor population incluhttp://dx.doi.org/10.1016/j.jbankn.2014.03.0420378-4266/ 2014 Elsevier B.V. All rights reserved.a largeesenta-utions,. How-ple isindividual investor behavior and what can be observed in theiractual behavior. Portfolio theory assumes that investors formexpectations about return and risk of securities and select portfo-lios according to their expectations and risk preferences(Markowitz, 1952). As a consequence, they should hold broadlydiversied portfolios and trade very little. But instead, private

Empirically, there is only scarce evidence on this question as theinput parameters are hard to obtain. The economic paradigm ofrevealed preferences states that beliefs and preferences can beinferred from observed actions (Samuelson, 1938). But this alreadyimplies that they are perfectly converted into actions. In order toreveal whether and where this transfer might fail, direct informa-D81G02G11

Keywords:ExpectationsBeliefsRiskReturnTrading behaviorPortfolio choice

1. Introduction

There is a large gap between wh nce models predict for

However, this way one learns very little about the actual deci-sion making process people go through when they invest. Howdo investors use their beliefs and preferences in this process?Available online 24 April 2014

JEL-Classication Codes:

expectations, and risk tolerance of these investors in three-month intervals between 2008 and 2010. Wecombine the survey data with investors actual trading data and portfolio holdings. We nd that investorbeliefs have little predictive power for immediate trading behavior. The exception is a positive effect ofDo investors put their money where theiexpectations and investing behavior

Christoph Merkle , Martin WeberChair of Finance and Banking, University of Mannheim, Germany

a r t i c l e i n f o

Article history:Received 21 February 2013Accepted 30 March 2014

a b s t r a c t

To understand how real inpanel survey of self-directe

journal homepage: wwmouth is? Stock market

ors use their beliefs and preferences in investing decisions, we examine anline investors at a UK bank. The survey asks for return expectations, risk

le at ScienceDirect

ing & Finance

elsevier .com/locate / jbf

ankibrokerage accounts. We observe volume, timing, and direction ofall trades within the survey period, and are able to calculate port-folio holdings of participants.

We develop different measures of nancial risk taking based ontrading behavior and portfolio holdings of investors. In a rst step,we consider the direction of stock trading and calculate the ratio ofbuys over total trades, referred to as buysell ratio. This corre-sponds to an increase or decrease in investors total equity posi-tion. We nd that the absolute levels of expectations for marketreturn and risk do not predict buying and selling behavior. Anexplanation could be that previous expectations are alreadyreected in investors portfolios and there is no need for investorsto engage in further transactions. We therefore also test whetherchanges in expectations explain buying and selling behavior corre-sponding to trades reecting changes in portfolios. Indeed, improv-ing return expectations have a positive impact on buysell ratios.Thus, quite intuitively, positive return expectations foster buyingactivity, but there is no effect of changes in risk expectations or riskattitude on buysell ratios.

While immediate trading behavior and direction of trade is ameans to alter ones risky position, we also directly investigateportfolio risk. We calculate portfolio volatility and beta for inves-tors in our panel as standard risk measures. This is complementedby additional measures such as relative volatility and averagecomponent volatility (Dorn and Huberman, 2005). We considerboth, levels of portfolio risk at the point in time of survey roundsand changes in portfolio risk between survey rounds. Levels ofrisk taking of investors can be well explained by their beliefs,preferences and demographics. All portfolio risk measures arepositively related to return expectations and risk tolerance, andnegatively related to risk expectations, age, and wealth of inves-tors. These results are consistent with nancial theory and previ-ous literature.

An advantage of our dataset is that it allows studying thedynamics of this relationship between expectations and risk tak-ing, i.e., whether investors react to changes in expectations bychanging their portfolio composition and thus alter risk exposure.For the volatility measures this is the case, as we nd a positivechange in volatility when return expectations improve and a neg-ative change if investors expect increasing stock market risk. Therelationship is weakest for short-term volatility and portfolio beta,indicating that investors manage their portfolios rather based onlong-term volatility as a proxy for risk taking. Our results arerobust to several alternative specications including the use oflagged values to address endogeneity concerns. Risk toleranceremains insignicant in most of our regressions (both levels andchanges), which sheds some light on the debate, whether investorscan translate their level of risk aversion into an adequate portfoliochoice (Ehm et al., 2014).

Finally, we combine the perspectives of trades and portfolio riskand analyze the volatility of transactions by investors. This allowsus to gain a deeper understanding of how investors regulate theirportfolio risk. The analysis reveals that more optimistic investorsshift part of their investments to more volatile securities. In addi-tion to expanding their total equity position by purchases in excessof sales, they also buy riskier assets. This is consistent with thending that portfolio volatility not just passively moves with mar-ket volatility, but also relative portfolio volatility increases for opti-mistic investors.

We continue with a theoretical motivation and an overview ofrelated literature in Section 2, followed by a description of the dataset, which contains two main sources, the survey and the tradingdata. In Section 4 we present results about the relationship

C. Merkle, M. Weber / Journal of Bbetween investor expectations and trading behavior, which wethen discuss in Section 5. A nal section concludes.2. Theory and literature

People acting on their beliefs and preferences are such a basicassumption in economic theory that it has seldom been contested.Exemplarily, portfolio theory as the canonical nance model positsthat investors form expectations about return and risk of securitiesand then choose an optimal portfolio according to their risk prefer-ences (Markowitz, 1952). We will now in a more formal but simpleway derive directional predictions for the inuence of returnexpectations, risk expectations, and risk tolerance on nancial risktaking behavior.

We assume an investor to have power utility dened overwealth W of the form UW W1h 1=1 h. Power utilityhas the desirable property of declining absolute risk aversion andconstant relative risk aversion, which is most consistent with realworld observations. The investor in a simple two-period economyfaces the budget constraint W1 W01 r0;1, implying that theonly source of wealth at time t = 1 is wealth in t = 0 plus the returnearned on wealth. The corresponding maximization problem thusis:

maxE0W01 r0;11h=1 h: 1Under the additional assumption that future wealth W1 is lognor-mally distributed, expression (1) simplies to (for a detailed deriva-tion cp. Campbell and Viceira, 2002):

max ln E01 r0;1 12 hr20; 2

where r20 is the conditional variance of the log return,r20 Var0ln W1W0 Var0ln1 r0;1. In expression (2) the ingredientsof the maximization problem are visible: the investor trades offexpected return against expected risk (variance of returns). Theparameter h of the utility function describes the investors relativerisk aversion.

With only two assets, a risky asset s and a riskless asset f, returnon wealth is r0;1 rf ;0;1 ws;0rs;0;1 rf ;0;1, where ws;0 representsthe weight an investor puts on the risky asset. However, whiler0;1 is a linear combination of the two asset returns, the log returnon wealth cannot be expressed as a linear combination of the logreturns. Instead, Campbell and Viceira (2002) suggest a Taylorapproximation to rewrite (2) in the form

max ws;0E0rs;0;1 rf ;0;1 12ws;01ws;0r20

121 hw2s;0r20; 3

which can be solved by

ws;0 E0rs;0;1 rf ;0;1 r20=2

hr20: 4

The equation implies that the share of risky investment shouldincrease with expected returns for the risky asset, and decreasewith risk expectations and risk aversion. This result can be general-ized to a multi-asset or multi-period framework and is fairly robustto the relaxation of several of the chosen assumptions. A simplemeanvariance optimization comes to the same conclusions, asdoesfrom a slightly different anglerisk-value theory (Sarin andWeber, 1993). We take the results of this model as a predictionfor the role of expectations and risk preferences in investingbehavior.

Empirically, risk taking behavior of individual investors hasbeen studied using different approaches and datasets. Vissing-Jorgensen (2003) analyzes a US individual investor survey byUBS/Gallup and nds a strong positive effect of expected returnon equity share in self-reported investor portfolios. Dorn and

ng & Finance 46 (2014) 372386 373Huberman (2005) report portfolio volatilities for a sample ofGerman brokerage clients and identify risk aversion as most

predictive for portfolio volatility. Moreover, younger, self-employed, less sophisticated, and poorer investors tend to holdmore risky portfolios. Calvet et al. (2007) examine disaggregatedwealth data covering the entire Swedish population and show apositive impact of wealth, income, and education on risk taking

3. Data

We obtain survey responses and transaction data for a sampleof clients at Barclays Stockbrokers, a UK direct brokerage provider.Barclays is one of the largest brokers in the UK and attracts a widevariety of customers (for demographic characteristics of its clientssee below). The accounts are self-directed in the sense that cus-tomers can inform themselves on special webpages provided bythe bank but receive no direct investment advice. Most transac-tions are processed online.

3.1. Survey data

In collaboration with Barclays Wealth, we conduct a repeatedsurvey taking place every three months, beginning in September2008 and ending in September 2010. Fig. 1 shows the developmentof the UK stock market represented by the FTSE all-share index andthe timing of survey rounds. Our panel consists of nine rounds cov-ering a time period of highly volatile market environment. We thusexpect participants to express changing beliefs about market pros-pects; in the standard model of Eq. (4) this would in turn lead tochanges in their portfolios.

In the initial survey a stratied sample of the banks client basewas invited via e-mail to participate in the online questionnaire(for details on the sampling procedure see Weber et al., 2013). Intotal 617 clients of the bank participated in the survey, 394 ofwhichparticipated multiple times. 189 participants have completed atleast ve rounds, and 52 have participated in all nine rounds. Wehave a minimum of 130 observations for each of the nine rounds.

Table 1

374 C. Merkle, M. Weber / Journal of Banking & Finance 46 (2014) 372386measured by portfolio volatility.1 They also break down portfoliorisk in its various components and reveal interesting patterns of risktaking. In a follow-up study, Calvet et al. (2009) present evidence onrebalancing, suggesting that investors actively control their share ofrisky investments and offset changes brought about by passive mar-ket variations.

While this literature addresses risk taking behavior of privateinvestor, it lacks a systematic study of the input variables we areinterested in: individual investor beliefs in form of return and riskexpectations, and investor risk preferences. Closest related to ourstudy is the work by Amromin and Sharpe (2009), Weber et al.(2013), Hoffmann et al. (2013), and Guiso et al. (2011). Similar tous Amromin and Sharpe (2009) use panel data, in their case comingfrom the Michigan Survey of Consumer Attitudes. However, theyanalyze self-reported portfolio shares of survey participants anddo not have access to their transactions or actual portfolios. Theyconcentrate on the interrelation of return expectations and riskexpectations, but also provide some evidence of the inuence ofthese variables on portfolio composition. Consistent with nancialtheory, higher return expectations and lower risk expectationsincrease the share of equity in portfolios of investors. Hoffmannet al. (2013) study an investor survey in the Netherlands, whichis matched to brokerage account data. Their data spans a timeperiod from April 2008 to March 2009 and survey rounds areadministered monthly. By eliciting expectations and portfoliocharacteristics, Hoffmann et al. (2013) establish a link betweenthe beliefs of investors and their investing behavior. They nd apositive impact of risk tolerance, risk perception, and return expec-tations on trading activity, while risk tolerance is identied as amain driver for risk taking behavior.

Guiso et al. (2011) concentrate in their analysis on risk aversionmeasured by a qualitative and a quantitative approach. They reporta substantial increase of risk aversion in the nancial crisis com-pared to pre-crisis levels. Ownership of risky assets is negativelyrelated to risk aversion. Guiso et al. (2011) suggest psychologicalfactors as drivers of risk aversion, as they are able to rule out alter-native explanations such as wealth or background risk.

In a previous analysis of our dataset, Weber et al. (2013) reporta relationship between expectations and investing decisions. Theyanalyze a survey question which asks participants to split a hypo-thetical amount of 100,000 between an investment in the UKstock market and a riskless asset. With this investment task theyare able to show a strong inuence of changes in expectationsand risk attitude on changes in the proportion of risky investment.This inuence is in the expected direction: increases in expectedreturns or risk tolerance lead to an increase in risky investment,while higher risk expectations render investors more cautious.We extend this research by relating return and risk expectationsto the actual trades and portfolios of investors. By analyzing vari-ous aspects of investing behavior, we present a more complete por-trayal of the underlying relationships. We also exploit the full timeseries of the survey which was not available to the earlier study byWeber et al. (2013).

1 The seemingly contradictory results might be explained by the differentcomposition of the datasets. While Dorn and Huberman (2005) analyze stockportfolios, where wealth and nancial sophistication usually lead to a better

diversication (and thus less risk), Calvet et al. (2007) use total wealth portfoliosfor which wealth and sophistication typically lead to a greater equity share (and thusmore risk).Demographics of participants.

n Mean Median Std.dev. Min Max

Age (in years) 613 51.4 53 12.9 21 84Gender (male = 1) 617 0.93 1 0.25 0 1Financial literacy

(% correct)614 3.49 4 0.68 0 4

Wealth (in categories) 502 4.80 5 2.39 1 9Income (in categories) 494 3.88 4 1.80 1 8

Notes: The table shows descriptive statistics about demographics of participants.Age is reported in years, gender as a dummy variable taking a value of 1 for maleparticipants. Financial literacy is the number of correct responses in a 4-itemWe will discuss potential selection effects in Section 4.4.Table 1 shows some demographic characteristics of survey par-

ticipants. Investors are predominantly male, and they are older andmore afuent than the general population (for an explicit

Fig. 1. FTSE all-share index and survey rounds. Development of the FTSE all-shareindex (covers 98% of UK market capitalization) between June 2008 and December2010. Vertical lines represent the timing of the nine survey rounds.nancial literacy test (see Appendix A). Wealth and income are self-reported andmeasured in categories (see Appendix A). Number of observations varies due torefusals.

Risk tolerance of investors is measured as agreement to thestatement It is likely I would invest a signicant sum in a high riskinvestment (on a seven-point scale). The statement is part of amore complete assessment of risk attitude (eight items) in theentry questionnaire to our survey. Factor analysis and Cronbachsalpha show high consistency between the items, and for brevitythe set of statements was reduced to one for the panel survey.The selected statement was chosen not for wording, but for statis-tical properties such as to capture maximal information from themulti-dimensional measure (for the construction of psychometricrisk tolerance scores cp. also Egan et al., 2010; Kapteyn andTeppa, 2011). The correlation between the eight-item risktolerance score and single-item risk tolerance is 0.77 for the entryround when both were elicited. Weber et al. (2013) nd high pre-

Fig. 3). While condence intervals are too narrow in the initial sur-vey round, investors seem to learn from observed outcomes that

anking & Finance 46 (2014) 372386 375comparison see again Weber et al., 2013). However, they closelyresemble typical investor populations in other studies (e.g.,Barber and Odean, 2001). The nancial literacy of survey partici-pants is relatively high with on average 3.5 correct responses outof four questions. This exceeds values usually found for these ques-tions in household surveys (van Rooij et al., 2011).

We elicit beliefs about return and risk expectations in two ways,by a numerical question asking for return expectations in percentageterms and a more subjective evaluation of risk and returnon a bipolar scale. The wording of the numerical question is asfollows:

We would like you to make three estimates of the return of the UKstock market (FTSE all-share) by the end of the next three month.

Your best estimate should be your best guess. Your high estimate should very rarely be lower than the actual out-come of the FTSE all-share (about once in 20 occasions).

Your low estimate should very rarely be higher than the actual out-come of the FTSE all-share (about once in 20 occasions).

Please enter your response as a percentage change.

The question asks participants to predict the three-monthreturn of the UK stock market. We use this time horizon to avoidoverlapping observations as the distance between survey roundsis three month as well. One might argue that these short-termexpectations will be irrelevant, if investors have a longer invest-ment horizon. However, we nd them to be highly correlated withone year expectations which were elicited twice during the survey.We suspect that three-month expectations express an investorscurrent optimism or pessimism about the market not limited tothe particular time interval. In addition, high portfolio turnoverreported below implies that short-term expectations shouldcertainly matter.

In a design similar to Glaser and Weber (2005), participants haveto submit a best estimate as well as a high and a low estimate, whichtogether yield a90%-condence interval.We take thebest estimate torepresent an investors returnexpectationabout theUKstockmarket.The high and low estimates allow calculating implicit expected vola-tility of investors which we use as numerical risk estimate applyingthe method of Keefer and Bodily (1983). We use this indirect way asit has been shown that people often have difculties with numericrisk estimates (Windschitl and Wells, 1996; Dave et al., 2010).

Furthermore, numeric estimates may not cover all aspects ofexpected risks and benets which are partly emotional. The risk-as-feelings hypothesis maintains that subjective risk perceptionswill often differ from cognitive assessment of risk (Loewensteinet al., 2001). It is unclear, whether investors primarily act on theirnumerical expected volatility or an affective impression of risk.The nance literature uses many different ways to measure riskexpectations, and it is still debated which best explains investorbehavior (Hoffmann et al., 2013; Weber et al., 2013). We thereforeinclude qualitative questions, which ask people to evaluate returnand risk on a seven-point scale.

How would you rate the returns you expect from an investment inthe UK stock market (FTSE all-share) over the next 3 months?

Over the next 3-months, how risky do you think the UK stock mar-ket (FTSE all-share) is?

In the rst question answer alternatives range from extremelybad to extremely good, in the second question from not risky

C. Merkle, M. Weber / Journal of Bat all to extremely risky. We ask equivalent questions for inves-tors own portfolios heldwith Barclays. In total we thus collect eightbelief items per investor per round.extreme realizations are possible and enlarge their condenceintervals. Expected volatility thus increases, but is still belowimplied option volatility. Furthermore after the initial adjustment,the condence intervals remain insensitive to subsequent marketdevelopments.dictive power of the single-item risk tolerance measure for hypo-thetical investment decisions. Besides the core variables ofbeliefs and preferences, the survey asks for demographics, psycho-logical dispositions, and investment objectives. All variables usedin our analysis are described in Appendix A.

3.2. Survey responses

Average numeric return expectations are relatively low beforethe peak of the nancial crisis, then rise during the crisis and fallagain, when the UK stock market recovers. Fig. 2 shows the patternin detail. In general investors tend to be more optimistic abouttheir own portfolios: the average return expectations are consis-tently higher and the difference is non-trivial (24%-points). Incontrast to market expectations, average portfolio expectationsremain high throughout 2009 and only decline afterwards. Whilemarket expectations are in a reasonable range adding up to anannual return of 812% (compared to a FTSE all-share historicalreturn of about 8%), the absolute level of portfolio expectationsseems unrealistically high (probably explained by overcondencecp. Merkle, 2012).

Investors in our panel (numerically) underestimate stock mar-ket risk (cp. Glaser et al., 2013). The implied volatilities calculatedfrom the condence intervals of investors return expectations aremuch lower than volatility expectations of sophisticated marketparticipants (represented by implied option volatilities, seeFig. 2. Numerical return expectations of investors. Average quarterly returnexpectations of investors for their own portfolio and the UK stock market (FTSEall-share).

trading volume is 72,805. We observe most pronounced tradingactivity in the initial phase of the nancial crisis; investors seemto feel a need to react to the turbulent times on asset markets.

nking & Finance 46 (2014) 372386Compared to the quantitative measure, qualitative risk expecta-tions elicited on a seven-point scale reect more closely impliedmarket risk expectations represented by the FTSE 100 VIX. Whileit is not possible to compare the absolute magnitudes, we nd acorrelation of 0.78 (p < 0:02) between average qualitative riskexpectations and implied option volatilities. Quite intuitively, riskexpectations rise with the peak of the nancial crisis and then fallafterwards. However, there are two further increases in panelistsrisk expectations: one without a corresponding rise in option mar-ket expectations (September to December 2009), and another,which falls together with the onset of the European debt crisis(June 2010). In general, expectations for own portfolio risk followthis trend but are on average slightly lower and more stable thanmarket expectations. It is noteworthy that investors appear tobelieve they can earn higher returns bearing less risk (cp. Kempfet al., 2014).

For investigating trading behavior over time, changes in expec-tations are particularly important. Table 2 shows average changesfor all expectation variables. We observe a signicant increase inaverage return and risk expectations between round one and threefollowed by a very mixed pattern from round three to four (furtherincrease of qualitative return and numerical risk expectations, butsharp drop of qualitative risk expectations). Changes in expecta-tions are less pronounced for the time after the immediate crisis.An exception is the very last survey round for which we observestrongly increasing return expectations and decreasing risk expec-tations. Similar to Weber et al. (2013), we nd that the correlationsbetween changes of numeric and qualitative expectations are often

Fig. 3. Risk expectations of investors. Qualitative risk expectations for market andown portfolio (scale 17, right axis), and numerical risk expectations as implied bycondence intervals (volatilities, left axis). For comparison implied option volatility(FTSE 100 VIX, left axis).

376 C. Merkle, M. Weber / Journal of Balow (return) or insignicant (risk). Stronger correlations existbetween market and portfolio expectations. Average risk toleranceremains fairly stable over the whole survey period.

3.3. Trading data

Our data also include the trading records of all investors activein the panel survey. We include three months prior to our rst sur-vey round and three months after our last survey round. In theresulting period between June 2008 and December 2010 weobserve 49,372 trades with a total trading volume of258,940,694. Of these trades 37,022 or 75% are in stocks (63% oftrading volume). In some parts of the analysis, we will concentrateon these equity transactions as they are closest related to theexpectations we elicit among investors. The remaining tradesinclude bonds, derivatives, mutual funds and ETFs. The average tra-der in the panel trades 84.1 times within the 2.5 year period (aboutthree times per month), with an average trading volume of441,126. However, the distribution is strongly skewed; the med-ian trader trades only 33 times (about once a month), the medianCombining trading data with a snapshot of investors portfolios,we are able to calculate portfolio statistics for our survey period.The median portfolio is worth 41,687 (average 314,663) andmedian portfolio turnover on a per round basis (three months) is19% (mean 77%), which means that the median investor turns overhis portfolio about twice in the survey period of 2.5 years, andsome turn over their portfolio ten times or more.2

We use the transaction records to develop several measures ofrisk taking behavior. As we cannot directly observe the share ofrisky assets as described in Eq. (4), we dene two alternatives thatcover different aspects of risk taking. First, we consider the balanceof purchases and sales of stocks in the trading records of investors,as in most cases, extending ones equity position corresponds to anincrease in nancial risk taking, while a reduction of ones equityposition corresponds to a decrease in risk taking. We form tworatios of buys divided by total trades, based on the number andvolume of investors equity transactions, respectively. The ratiosthus attain values between 0 and 1. Similar buysell ratios havebeen used by Ritter (1988), Grinblatt and Keloharju (2000), andBhattacharya et al. (2012).

We expect buysell imbalance to be related to investors stockmarket expectations: with high return expectations for the stockmarket, the propensity to buy should rise relative to the propensityto sell, while the opposite effect is predicted for high risk expecta-tions and high risk aversion. More precisely, only changes in expec-tations and preferences should be relevant for changes in portfolios(cp. Weber et al., 2013). However, as this is a stark theoreticalassumption, we analyze both levels and changes of expectations.

A second strategy to assess nancial risk taking of investors isby measures of portfolio risk such as volatility and beta (cp. Dornand Huberman, 2005; Calvet et al., 2007; McInish, 1982). Financialtheory posits that the composition of the risky portfolio should notchange, but risk is entirely adjusted via the share of the risky port-folio (fund separation, Tobin, 1958). However, in practice there arelarge differences in composition and risk of portfolios suggestingthat investors manage their overall risk taking at least in part byportfolio risk. Therefore, we apply the theoretical predictions inEq. (4) also to portfolio risk measures, and expect higher portfoliorisk in response to a positive change in return expectations or anegative change in risk expectations.

We calculate volatility of portfolios over one-year and overthree-month horizons. We calculate portfolio beta over a one-yearhorizon using the FTSE all-share index as corresponding marketindex (this choice seems justied as survey participants hold mostof their investments (>90%) in the UK stock market). Taking intoaccount that within a volatile market environment a large part ofthe changes in portfolio volatility will be passively caused bychanges in market volatility, we also measure relative volatilityas the ratio of portfolio volatility divided by market volatility.Dorn and Huberman (2010) argue that portfolio volatility is notthe correct measure of risk, if investors disregard correlationsbetween securities. They propose a value-weighted average ofthe return volatilities of portfolio components (ACV), whichreects risk taking if investors mainly orient themselves at the vol-atility of individual securities rather than portfolio volatility. Again,we consider levels and changes of these variables. Exact denitionsof all variables can be found in Appendix A.

2 Compared to similar studies, portfolio value is high. Glaser and Weber (2007)report a median portfolio value of 15,630, Barber and Odean (2000) of $16,210,

and Dorn and Huberman (2005) of DM55,000 (about 23,000). On a monthly basis,median turnover is in the same range as in Barber and Odean (2000) and Dorn andHuberman (2005) with 6% and 9% respectively.

3.4. Descriptive statistics of investor risk-taking

Table 2Changes in expectations of investors.

Market

Round D risk tolerance D num. return D qual. return D num. ris

2 (December 08) 0.23 0.020 0.12 0.023

3 (March 09) 0.10 0.014 0.20 0.0014 (June 09) 0.07 0.010 0.30 0.0145 (September 09) 0.15 0.008 0.01 0.0086 (December 09) 0.14 0.016 0.03 0.0117 (March 10) 0.03 0.004 0.05 0.0048 (June 10) 0.21 0.008 0.27 0.0019 (December 10) 0.22 0.009 0.45 0.015

Notes: The table states changes in risk tolerance and changes in numerical and qualitati Changes are signicantly different from zero at 10%-level (one-sided t-test). Changes are signicantly different from zero at 5%-level (one-sided t-test). Changes are signicantly different from zero at 1%-level (one-sided t-test).

C. Merkle, M. Weber / Journal of BankiFor all rounds, average buysell ratios exceed 50%, whichimplies that investors are net buyers. There is almost no differencebetween ratios based on number of trades and volume, correlationis 0.94 (p < 0:01). We observe the highest buysell imbalance forlate 2008, at the peak of the nancial crisis, when the ratios reachabout 0.66. This suggests that investors in our sample view the cri-sis as an opportunity to buy at low prices. There is also large cross-sectional variation in buysell ratios between investors, which iscrucial for our analysis of the differential inuence of expectationsand preferences.

Fig. 4 displays portfolio volatilities of the median investor, therst-quartile investor, and third-quartile investor in our panel atthe time of each survey round. The volatility of the FTSE all-shareindex serves for comparison. Median portfolio volatility in ourpanel rises from 0.26 in June 2008 to about 0.40 during the crisis,before falling to values around 0.18 for the last year of the survey.It remains constantly above market volatility, which indicates thata majority of investors hold portfolios that are riskier than the UKmarket portfolio. The difference between median portfolio volatil-ity and market volatility is strongly signicant for all rounds(p < 0:01, Wilcoxon signed-rank test). The third quartile showsthat many investors hold very volatile portfolios compared to themarket index, while the rst quartile is still close to that index.The average component volatility (ACV, not displayed) exceedsthese portfolio volatilities by about 40% as it does not account fordiversication effects.0

0.1

0.2

0.3

0.4

0.5

0.6

0.73rd Qrt Investor

Median Investor

Market

1st Qrt Investor

Fig. 4. Portfolio volatility of investors and UK stock market volatility. Portfoliovolatility is the one-year standard deviation of daily portfolio returns at point intime of survey rounds. Displayed are the median investor, the rst-quartile andthird-quartile investor. UK stock market volatility uses the FTSE all-share index.High portfolio volatility of investors is not due to high levels ofsystematic risk, as the median beta is around 0.8 over the wholesample period and most investors hold portfolios with a beta smal-ler than one. Instead, high volatility is driven by idiosyncratic riskas a result of a low degree of diversication. Relative volatilitiessuggest that investors in the immediate phase of the nancial crisistry to reduce their risk exposure relative to the market, while theyincrease it again afterwards. Changes in beta conrm a reduction insystematic risk for the rst phase of the crisis, while for laterrounds the results remain inconclusive.

4. Results

4.1. Investor trading behavior

We rst investigate whether market expectations drive thedecision of investors to increase or decrease their stock marketexposure, which is measured by buysell ratios. We estimate apanel Tobit model with random effects as the buysell ratios arelimited on the interval between 0 and 1, and values on the bound-aries occur frequently. We consider two specications, one inwhich the absolute levels of expectations are relevant for investors,and another in which investors are supposed to react on changes inexpectations.

Columns 1 and 5 of Table 3 show the results of the buysellratios regressed on expectation levels. More precisely, we measureexpectations at the time of the survey and then observe buysellratios in the three month afterwards until the next survey takesplace. Levels of expectations seem to have little effect on subse-quent buying and selling behavior. Among the few marginally sig-

Own portfolio

k D qual. risk D num. return D qual. return D num. risk D qual. risk

0.43 0.026 0.09 0.023 0.280.03 0.030 0.20 0.007 0.13

0.77 0.003 0.33 0.018 0.240.38 0.019 0.10 0.008 0.020.07 0.014 0.17 0.008 0.06

0.22 0.047 0.11 0.017 0.120.17 0.010 0.09 0.010 0.13

0.29 0.045 0.35 0.011 0.29

ve expectations of investors (compared to the previous survey round).

ng & Finance 46 (2014) 372386 377nicant effects is a negative coefcient for risk tolerance. Anexplanation might be that risk tolerant investors already hold highequity positions and tend to reduce their exposure during thenancial crisis. However, this effect is not robust to the inclusionof additional explanatory variables.

Changes in expectations are dened over the same time horizon(between surveys), for which buysell ratios are calculated. Thelower number of observations in the changes regressions is due tothe fact that for changes in expectations, we need investors to par-ticipate in the survey for two consecutive rounds. Among thechanges variables, changes in numeric return expectations exert asignicant effect on buysell behavior (columns 2 and 6). If returnexpectations improve, investors tend to move to the buying side ofthe market, which is consistent with the theoretic prediction. Foradditional equity purchases thus not the absolute level of returnexpectations is relevant, but instead changes in these expectations.This result is robust to the inclusion of the levels variables (columns3 and 7) and of demographic variables: age, gender, wealth, income,and nancial literacy (columns 4 and 8). Income quite intuitively

Table 3Buying and selling behavior.

Buysell ratio Buysell volume ratio

(4

0.0.0.0.0.0.0.

0.0.0.

76

unddinglanainclucK

378 C. Merkle, M. Weber / Journal of Banki & Finance 46 (2014) 372386has a positive effect on buysell ratios as it is a proxy for additionalliquidity investors might want to invest. For the remaining demo-graphic variables we nd no signicant effect. Overall the lowpseudo-R2 in the regressions suggests that the predictive powerof beliefs for immediate trading behavior is rather low.

The coefcients in Table 3 represent marginal effects (the coef-cients for the latent variable), which directly allow an interpreta-

(1) (2) (3)

Num. return 0.068 0.275

Num. risk 0.059 0.043Qual. return 0.014 0.009Qual. risk 0.007 0.018Risk tolerance 0.010 0.010D num. return 0.150 0.293

D num. risk 0.058 0.074D qual. return 0.010 0.014D qual. risk 0.007 0.016D risk tolerance 0.012 0.007

AgeGender (male = 1)WealthIncomeFin. literacy

Pseudo-R2 0.039 0.035 0.049

n 1376 769 769

Notes: The table shows results of a panel Tobit regression with random effects and robuys/# of total trades) for columns 14 and buysell volume ratio dened over trainclude levels of expectations and columns 2 and 6 changes of expectations as expcolumns 4 and 8 additionally controlled for demographics. Demographic variableswhich are the coefcients of the uncensored dependent variable. The pseudo-R2 is M They are signicant at 10%-level. They are signicant at 5%-level. They are signicant at 1%-level.tion in terms of economic signicance. A 10%-point increase inreturn expectations will raise buysell ratios by about three per-cent. For comparison, moving upward one category in incomehas about the same effect. In unreported results, we exclude heavytraders (the top 10% in number of trades and trading volume), asthese investors might be engaged in trading activity independentof their current beliefs or other situational factors. When investors,who trade less frequently, place an order, this order might be moreclosely related to personal return and risk expectations. However,there is almost no change in the results under this restriction.For robustness, as the presented panel Tobit model cannot accountfor potential heteroscedasticity, we test several alternatives: A lin-ear panel regression with clustered standard errors by individual, axed effects regression, and a regression with least absolute devi-ation (LAD) estimators. The results are reported in Table 4.

Clustered standard errors take into account the non-indepen-dence of observations within our sample. Columns 1 and 4 conrmthe strongly positive impact of changes in return expectations. In axed effectsmodel, results are less pronounced and onlymarginallysignicant as much of the cross-sectional variation is eliminated.Part of the effect is picked up by changes in qualitative expecta-tions.3 Finally, the LAD regression (columns 3 and 6) has favorablesmall sample properties in reducing the importance of outliers. Theeffect of changes in return expectations is robust to this specication.

3 The correlation between changes in numerical and qualitative expectations ispositive but low (0.26), suggesting that multicollinearity is not an issue. Anexplanation for the emergence of the qualitative rating effect is that the used scalelacks inter-subject comparability, but is a good predictor within subjects (xed-effects model).4.2. Investor portfolio risk

We now turn to investor portfolio risk, which might be a morestable measure of investor risk taking. In our analysis, we interpretthe volatility levels of investors portfolios when the survey takesplace as the level of risk an investor is taking at this point in time.Consequently, changes in volatility correspond to changes in risk

) (5) (6) (7) (8)

257 0.040 0.251 0.2340.029 0.040 0.124 0.106013 0.014 0.011 0.015022 0.008 0.020 0.0240.010 0.012 0.011 0.009288 0.186 0.321 0.316

0.070 0.063 0.115 0.111017 0.012 0.016 0.019018 0.010 0.020 0.022

007 0.011 0.005 0.006

002 0.0020.089 0.1080.013 0.010034 0.028

0.034 0.034067 0.035 0.035 0.049 0.064

7 1376 769 769 767

dummies. Dependent variable is buysell ratio dened over number of trades (# ofvolume (buying volume/total trading volume) for columns 58. Columns 1 and 5tory variables. Columns 3 and 7 show regressions on both, levels and changes, inde age, gender, wealth, and nancial literacy. The table displays marginal effects,elvey and Zavoinas R2.ngtaking.4 Similarly, we use levels and changes of other portfolio riskmeasures (beta, relative volatility, average component volatility).

Panel A of Table 5 shows correlations between the levels of thesemeasures; all correlations are positive as they share a common con-cept of risk, but the variables also capture different aspects of risk ascorrelations are not perfect. In particular, portfolio beta shows theweakest relation to other risk measures with coefcients between0.23 and 0.43. When considering changes (Panel B) the picturebecomes even more mixed. All but one correlation are still positive,but especially for beta and three-month volatility (which is the onlymeasure calculated over a shorter time horizon) coefcients arelow. As portfolio risk measures differ, we consider most of themin our regression analysis (except relative volatility which is redun-dant in the levels analysis). We take the natural logarithm of thevolatility variables, as volatilities are skewed within our sample.

We use market expectations as explanatory variables to avoidreverse causality inherent with portfolio expectations, as currentportfolio volatility will determine expectations for future portfolioreturns and volatility. Table 6 shows the results of a panel GLSregression with random effects and clustered standard errors (col-umns 14) and a xed effects regression (columns 58). We ndthat the risk level investors take on in their portfolios dependson their expectations. In all regressions, a positive impact ofnumerical return expectations on volatilities and a negative impact

4 This is a deliberate analogy to levels and changes in the hypothetical risk takingtask analyzed by Weber et al. (2013). In this task investors had to divide 100,000between the FTSE all-share and a riskless asset. If we assume a volatility of 0 for theriskless asset, the volatility of the chosen portfolio is monotonically increasing withthe fraction invested in the FTSE.

Table 4

Buysell volume ratio

(3) (4) (5) (6)LA

0.0.0.0.0.

C. Merkle, M. Weber / Journal of anking & Finance 46 (2014) 372386 379Robustness tests: Buying and selling behavior

Buysell ratio

(1) (2)clus. SE FE

Num. return 0.199 0.134Num. risk 0.025 0.090Qual. return 0.014 0.038

Qual. risk 0.017 0.025Risk tolerance 0.007 0.023D num. return 0.230 0.179D num. risk 0.034 0.006D qual. return 0.019 0.033of numerical risk expectations can be observed. Both effects aresignicant in most specications, the effects are weakest for port-folio beta (also conrmed by low R2). Risk tolerance and qualitativeexpectations mostly have no predictive power for portfolio riskAmong the demographic variables, we nd signicant effects forage, wealth, and nancial literacy. Younger investors hold morevolatile portfolios, while wealthier investors tend to own less riskyportfolios.5 This result is consistent with the ndings of Dorn andHuberman (2005).

Even though using market expectations addresses the mostobvious endogeneity problem, there might still be concerns that

D qual. risk 0.013 0.015D risk tolerance 0.006 0.005Age 0.002Gender (male = 1) 0.088Wealth 0.013Income 0.029

Fin. literacy 0.029R2 0.055 0.073

n 767 769

Notes: The table shows results of a panel GLS regression with random effects andeffects (columns 2 and 5), and a regression using least absolute deviation and bootover number of trades (# of buys/# of total trades) for columns 13 and buysell vo46. Independent variables are as specied in Table 3. For random effects regrespseudo-R2. Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.

Table 5Correlation of portfolio risk measures.

Levels of portfolio risk

Vol 1y Vol 3m Rel. Vol Beta ACV

Panel AVolatility 1y 1.00Volatility 3m 0.76 1.00Rel. volatility 0.89 0.59 1.00Portfolio beta 0.42 0.28 0.43 1.00ACV 0.64 0.54 0.50 0.23 1.00

Changes of portfolio risk

D Vol 1y D Vol 3m D Rel. Vol D Beta D ACV

Panel BD Volatility 1y 1.00D Volatility 3m 0.60 1.00D Rel. volatility 0.39 0.11 1.00D Portfolio beta 0.13 0.05 0.40 1.00D ACV 0.60 0.32 0.06 0.05 1.00

Notes: The table shows pairwise Pearson correlations of levels (Panel A) and changes(Panel B) of portfolio risk measures. All correlations are signicant at 1%-level.

5 We do not nd signicant results for portfolio value / wealth as a measure orelative importance of investors portfolios for their overall wealth.B.

0.0.

0.0.0.

76

standastrapplumesions

fown portfolio risk determines also market expectations. Therefore,we repeat the previous analysis using lagged expectations andlagged preferences. The timing now is such that we use the expec-tations of each survey date to explain portfolio risk three month

D clus. SE FE LAD

343 0.173 0.132 0.1740.151 0.130 0.106 0.162008 0.018 0.034 0.011019 0.021 0.031 0.0160.006 0.006 0.022 0.009252 0.276 0.239 0.255

0.025 0.091 0.127 0.020026 0.024 0.035 0.028

004 0.019 0.023 0.010006 0.004 0.006 0.002001 0.002 0.0020.146 0.118 0.1360.006 0.009 0.012032 0.022 0.030

0.010 0.030 0.023047 0.053 0.075 0.043

7 767 769 767

rd errors clustered by participant (columns 1 and 4), a panel regression with xeded standard errors (columns 3 and 6). Dependent variable is buysell ratio denedratio dened over trading volume (buying volume/total trading volume) for columnsoverall R2 is reported, for xed effects regressions within R2, for LAD-regressionslater. Results in Table 7 conrm the impact of numerical returnand risk expectations on portfolio risk. The most notable differenceis that in the lagged regression risk tolerance has a more consistentpositive effect on risk taking, suggesting that it takes some time forinvestors to implement their risk preferences.6

The interpretation in terms of economic signicance is straight-forward, as the dependent variable is log transformed. 10%-pointshigher return expectation will induce investors to hold a portfoliowith 1.65% higher volatility (1.27% for lagged expectations). Analo-gously, a 10%-points higher expected volatility relates to a 1.31%decrease in portfolio volatility (1.16% for lagged expectations).

Up to this point, we dealt with state variables that give us someinformation which portfolio risk investors choose depending ontheir expectations, risk tolerance, and demographics. The panestructure of our data allows us to investigate in more detail thedynamics of these relationships. We now analyze changes of port-folio risk in response to contemporaneous changes in investorexpectations and preferences. The assumption is that investors inaddition to adjusting their risky share as suggested by Eq. (4) alsochange portfolio composition. We adopt a parallel approach to thelevels regression and again estimate a random effects and a xedeffects model.

Table 8 shows the results of these regressions. With changes inone-year portfolio volatility (columns 1 and 6) we observe thesame patterns as in the levels regression. Positive changes in

6 As a further test we instrument contemporaneous expectations by laggedexpectations. While the results are consistent in direction, signicance is weakHowever, instrumentation is costly in terms of statistical power, as it requiresconsecutive observations. Additionally, there are concerns about weak instruments ascorrelations between expectations and lagged expectations are only around 0.3(common tests for weak instruments attain borderline results).l

.

l(

000

0

nkiTable 6Portfolio risk and expectations.

Random effects model

ln(Vol 1y) ln(Vol 3m) Beta(1) (2) (3)

Num. return 0.165 0.165 0.070

Num. risk 0.131 0.187 0.030Qual. return 0.001 0.000 0.002Qual. risk 0.000 0.013 0.003Risk tolerance 0.001 0.007 0.004Age 0.006 0.006 0.002Gender (male = 1) 0.085 0.115 0.104

Income 0.016 0.014 0.004Wealth 0.031 0.030 0.016Fin. literacy 0.066 0.066 0.054

380 C. Merkle, M. Weber / Journal of Banumerical return expectations are accompanied by increased risktaking, while higher numerical risk expectations result indecreased risk taking. In the regressions of changes in three-monthvolatilities on changes in expectations (see Table 8), the coef-cients for numerical expectations maintain their direction but nolonger reach statistical signicance. This may be due to the dimin-ished statistical power of the changes regressions, as we can onlyconsider investors who participate in two consecutive surveyrounds. However, another interpretation is that investors haverather long-term objectives and do not manage their portfoliosaccording to three-month volatilities. In our questionnaire, mostinvestors state an investment horizon of 35 years.

For relative volatility and average component volatility similarpatterns as for volatility emerge. In particular numerical returnexpectations positively inuence risk taking. Changes in relativevolatility most closely reect investors active interventions to

R2 0.368 0.495 0.036 0

n 1924 1911 1926 1

Notes: The table shows results of a GLS panel regression with random effects and clustecontain round dummies. Dependent variables are portfolio risk measures: the natural logbeta and the log of average component volatility (ACV). Expectation variables and demogfor xed effects regressions within R2. Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.

Table 7Portfolio risk and lagged expectations.

Random effects model

ln(Vol 1y) ln(Vol 3m) Beta ln(1) (2) (3) (

Lagged num. return 0.127 0.101 0.060 0Lagged num. risk 0.116 0.136 0.048 Lagged qual. return 0.005 0.006 0.008 0Lagged qual. risk 0.007 0.022 0.001 Lagged risk tolerance 0.006 0.013 0.003 0Age 0.006 0.006 0.002 Gender (male = 1) 0.080 0.075 0.069 0Income 0.019 0.025 0.007 Wealth 0.030 0.025 0.016 Fin. literacy 0.058 0.036 0.047 R2 0.400 0.542 0.027 0

n 1923 1908 1925 1

Notes: The table shows results of a GLS panel regression with random effects and clustecontain round dummies. Dependent variables are portfolio risk measures: the natural logbeta and the log of average component volatility (ACV). Expectation variables are includeeffects regressions within R2. Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.Fixed effects model

n(ACV) ln(Vol 1y) ln(Vol 3m) Beta ln(ACV)4) (5) (6) (7) (8)

.135 0.129 0.102 0.042 0.098

0.086 0.106 0.154 0.006 0.048.002 0.003 0.003 0.004 0.0010.010 0.000 0.012 0.003 0.010.011 0.002 0.002 0.003 0.0060.003

.0590.018

0.022

0.059

ng & Finance 46 (2014) 372386alter portfolio risk, as raw portfolio volatility is in large part drivenby changes in market volatility. As already documented for levels,beta is the risk measure least related to expectations. It is likelythat beta has little relevance to participants in managing the riskof their portfolios. Many private investors may not even knowabout this concept.

In unreported results, we substitute round dummies by marketvolatility, which is constant across participants and will thus cap-ture the part of changes in portfolio volatility caused by a passivechange in overall market volatility. In portfolio volatility regres-sions, the coefcient of market volatility is about 0.7, which meansthat about 70% of changes in portfolio volatilities are driven bychanges in market volatility. Interestingly, changes in market vol-atility have a negative impact on relative volatility, suggestinginvestors attempt to counteract rising market volatility by reduc-ing their portfolio risk relative to the market.

.290 0.746 0.753 0.089 0.608

817 1924 1911 1926 1817

red standard errors (columns 14) and xed effects (columns 58). All regressionsarithm of portfolio volatility calculated over a 1-year and 3-month horizon, portfolioraphics are as dened before. For random effects regressions overall R2 is reported,

Fixed effects model

(ACV) ln(Vol 1y) ln(Vol 3m) Beta ln(ACV)4) (5) (6) (7) (8)

.188 0.092 0.012 0.036 0.144

0.147 0.095 0.080 0.034 0.119.002 0.007 0.008 0.010 0.0020.008 0.006 0.020 0.000 0.006.014 0.005 0.009 0.002 0.011

0.003

.0780.0170.018

0.059

.297 0.794 0.772 0.134 0.641

808 1923 1908 1925 1808

red standard errors (columns 14) and xed effects (columns 58). All regressionsarithm of portfolio volatility calculated over a 1-year and 3-month horizon, portfoliod as lagged variables. For random effects regressions overall R2 is reported, for xed

Table 8Changes in portfolio risk.

Random effects model

DVol 1y DVol 3m DRel. Vol DBeta D(1) (2) (3) (4) (

D num. return 0.062 0.114 0.059 0.000 0D num. risk 0.079 0.128 0.073 0.017 0D qual. return 0.003 0.005 0.000 0.005 D qual. risk 0.001 0.008 0.000 0.002 D risk tolerance 0.005 0.008 0.004 0.000 Age 0.001 0.001 0.000 0.001 Gender (male = 1) 0.005 0.018 0.012 0.001 Income 0.003 0.012 0.005 0.002 0Wealth 0.001 0.008 0.002 0.003 Fin. literacy 0.008 0.012 0.003 0.009 0.005

R2 0.682 0.652 0.246 0.141 0

n 1038 1031 1038 1009 1

stercha(ACts re

C. Merkle, M. Weber / Journal of Banking & Finance 46 (2014) 372386 3814.3. Volatility of trades

We combine the two approaches of measuring nancial risktaking and examine the volatility of securities investors are trad-ing. For this purpose, all securities traded by survey participants(and for which a sufcient time series of returns is available) aresorted by return volatility throughout the survey period. We formten volatility deciles and hereby establish a ranking of securities bytheir relative riskiness. We then calculate the value-weighted aver-age of volatility decile each investor trades in. We also compute thevolatility of purchases and the volatility differential between pur-chases and sales. The latter two measures we interpret as indica-tors of nancial risk taking as investors shift money to volatilesecurities.

Notes: The table shows results of a GLS panel regression with random effects and clucontain round dummies. Dependent variables are changes in portfolio risk measures:relative volatility and portfolio beta, and changes in average component volatilitydened before. For random effects regressions overall R2 is reported, for xed effec Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.Table 9 shows population averages of volatility of trades, of vol-atility of purchases, and the average buysell volatility differential.We observe that investors trade securities that are slightly morevolatile than the total sample of securities (which of course hasan average decile rank of 5.5). This is due to the fact that mutualfunds and ETFs are less frequently traded than more volatile secu-rities such as stocks and options. Volatility of trades and purchasesis highest in the rst two rounds of the survey; these are also the

Table 9Volatility of securities traded.

Round Tradevolatility

Buyvolatility

Buysellvol. diff.

Pre-survey (June 08September 08) 6.20 6.42 0.33

Round 1 (September 08December 08) 6.23 6.37 0.29

Round 2 (December 08March 09) 6.02 6.05 0.24Round 3 (March 09June 09) 5.99 5.79 0.39Round 4 (June 09September 09) 6.00 5.88 0.32Round 5 (September 09December 09) 5.96 6.07 0.02Round 6 (December 09March 10) 6.03 6.04 0.06Round 7 (March 10June 10) 5.75 5.60 0.36Round 8 (June 10September 10) 5.86 5.84 0.29Round 9 (September 10December 10) 5.82 5.76 0.23

Notes: The table shows for all survey rounds the average volatility decile of tradesand purchases, and the average volatility differential between purchases and sales. This difference is signicant by a Wilcoxon signed-rank test at 10%-level. This difference is signicant by a Wilcoxon signed-rank test at 5%-level. This difference is signicant by a Wilcoxon signed-rank test at 1%-level.only rounds where the buysell volatility differential is positivewhich conrms the earlier nding that private investors in oursample seem to view the crisis as an opportunity to buy risky secu-rities. This behavior then turns around, in particular for a period ofhigh stock market gains in mid-2009 (cp. also Fig. 1). Investorsmove back into safer securities, a behavior that repeats itself forthe nal survey rounds, for which the average volatility of tradesis lowest.

When we regress the three measures dened above on the lev-els of investors expectations and risk tolerance (Table 10), we ndno effect on overall trade volatility, a slight effect on the volatilityof purchases and a pronounced impact on the buysell volatilitydifferential. This means that investors shift capital towards riskiersecurities when they have high return expectations. This extends

.417 0.733 0.682 0.275 0.170 0.394

018 1038 1031 1038 1009 1018

ed standard errors (columns 15) and xed effects (columns 610). All regressionsnges in portfolio volatility calculated over a 1-year and 3-month horizon, changes inV). Independent variables are demographics and changes in expectations, both asgressions within R2.Fixed effects model

ACV DVol 1y DVol 3m DRel. Vol DBeta DACV5) (6) (7) (8) (9) (10)

.080 0.051 0.107 0.047 0.009 0.083

.020 0.072 0.149 0.069 0.005 0.0140.006 0.007 0.014 0.004 0.001 0.0080.003 0.000 0.010 0.000 0.000 0.0050.004 0.004 0.009 0.002 0.000 0.0040.0000.018.0040.001the results of the previous section, as we now learn how investorsadjust their portfolio volatility in response to positive expecta-tions: they buy high volatility securities and sell low volatilitysecurities. We also nd that less risk-averse investors buy securi-ties with higher volatility, in line with risk habitat theory whichstates that investors select securities of which volatilities are com-mensurate with their risk aversion (Dorn and Huberman, 2010).7

Again older, wealthier, and more sophisticated investors trade lessvolatile securities. We do not report results for a regression onchanges in expectations in this case, as we nd no signicant results

4.4. Selection effects

Our sample is clearly not representative, neither for the total UKpopulation, nor for UK stock market investors, maybe not even forBarclays online brokerage clients. We make no claim in thisregard. However, we do believe that our data are meaningful andallow to draw some inferences about investing behavior inresponse to personal expectations and preferences. While onehas to be careful not to overgeneralize our ndings, we have noevidence of systematic selection in our sample, which would inval-idate our results. In this section we analyze selection issues in aformal way.

7 There is no such effect for buysell volatility differentials, but this is nosurprising as both risk-averse and risk tolerant investors will sometimes augment andsometimes reduce risk (though on different levels)..

t

Table 10Volatility of trades explained by expectations

Random effects model

ll vo

1467 1343 890

d stcha

382 C. Merkle, M. Weber / Journal of Banki & Finance 46 (2014) 372386Given the relatively low (but not uncommon8) response rate andthe presence of attrition in our panel, there are two potential chan-nels of selection. Specic investors might be more attracted to par-ticipate in the survey, or they leave and rejoin the sample in anon-random way, both potentially biasing our results. We have onlylimited data on non-participants, including age and gender, as wellas some portfolio information (portfolio value, number of positions,number of transactions).9 We use these items as explanatory vari-ables in a participation regression, results are reported in column 1of Table 11. We nd that male investors and investors with a highernumber of holdings and transactions are more likely to participate inthe survey. The latter are potentially more active and interested innancial markets, which would explain this result.

While this supports the presence of selection on observables inour sample, it may remain inconsequential for our results. We runa two-stage Heckmann selection model to test for this possibility.

Trade volatility Buy volatility Buyse(1) (2) (3)

Num. return 0.467 0.840 1.374

Num. risk 0.042 0.431 0.377Qual. return 0.003 0.002 0.001Qual. risk 0.038 0.031 0.049Risk tolerance 0.045 0.082 0.050Age 0.017 0.017 0.010Gender (male = 1) 0.704 0.604 0.077Income 0.047 0.048 0.023Wealth 0.102 0.116 0.031Fin. literacy 0.391 0.376 0.005

R2 0.085 0.108 0.041

n 1467 1343 890

Notes: The table shows results of panel regression with random effects with clustereround dummies. Dependent variables are the volatility of trades, the volatility of purregressions overall R2 is reported, for xed effects regressions within R2. Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.In columns 2a and 2b, we reproduce the regression of portfoliovalue on expectations including the inverse Mills ratio of the rststage. The inverse Mills ratio is highly signicant, again suggestinga selection effect. However, our main result regarding the inuenceof expected return and expected risk on risk taking remains intact.It is also robust to an inclusion of the set of variables from the par-ticipation regression (column 2b). Not surprisingly, portfolio valueand number of positions are strongly negatively related to portfoliovolatility, as they come along with a diversication effect. In con-trast, number of transactions has a positive effect on volatility. Inthis specication, the signicance of the inverse Mills ratio is muchreduced, as the additional variables capture part of the selectioneffect.

We nd similar results for the other levels specications, mean-ing that despite selection is present in our sample, our results aremainly unaffected by it. The changes regressions, by making useof the in-sample variation over time, are per se less vulnerableagainst this type of selection.

Next, we analyze the participation in the panel over time todetect any signs of systematic attrition. To make sure that this type

8 In similar survey studies Graham and Harvey (2001) report a response rate of 9%,Glaser and Weber (2007) of 7%, Dorn and Sengmueller (2009) of 6%, compared to our3% for a repeated survey.

9 The remaining demographic variables such as income and wealth were self-reported survey items.of selection does not bias our main results we again use a Heckmanselection model. We follow Wooldridge (1995) in estimating theparticipation equation separately for each round of the panel,including demographics and lagged survey variables. Instead ofdisplaying these roundwise rst stage regressions, Table 11 showsa panel probit version of the participation regression (column 3). Itdemonstrates that wealthier investors are more likely to partici-pate, while higher income investors are less likely to participate.Intuitively, those with higher income might be more time-con-straint. More importantly, lagged expectations do not explain sub-sequent participation, which means that it is not the case that e.g.,optimistic or more risk tolerant investors are more likely to con-tinue the survey.

We then re-estimate in the second stage the panel regression asbefore, including now inverse Mills ratios from the roundwise par-ticipation regressions. This time,wendno signicance for theMills

andard errors (columns 13) or xed effects (columns 46), all regressions containses and the difference between volatility of purchases and sales. For random effectsFixed effects model

l. diff. Trade volatility Buy volatility Buysell vol. diff.(4) (5) (6)

0.127 0.514 2.367

0.201 0.199 0.4210.027 0.038 0.0510.035 0.037 0.0890.015 0.001 0.065

0.010 0.021 0.049ngratio, suggesting no strong evidence for selection effects in the senseof systematic panel attrition. Our main results are unchanged inboth specications, whether using random effects (4a) or xedeffects (4b). We also nd no evidence that the changes regressionof Table 8 is affectedby selection.We thus conclude thatwhile selec-tion is present in our sample, it seems to have little inuence on theeffect of expectations and preferences on risk taking behavior.

5. Discussion

A main problem any research in beliefs and expectationsencounters is whether responses in a survey are valid representa-tions of the internal beliefs of participants. The challenge is two-fold, questions need to be stated in a way that participants areable to answer them in a sensible way, and participants need tobe motivated to do so. For the latter we rely on the intrinsic moti-vation of participants as they completed the survey voluntarily,and many found it interesting enough to take part multiple times.As in most large-scale surveys, monetary incentives were not fea-sible, but we are in this case not aware of any obvious reason toconceal or distort beliefs in their absence.10 Additionally, we build

10 For a discussion about when monetary incentives are useful see Camerer andHogarth (1999). Other surveys that do not incentivize participants include theMichigan Survey of Consumer Finances, the German Socioeconomic Panel and mostsurveys on investing behavior.

Table 11

(2b

0.130.0.000.000.00

0.0.110.0.0.0.0.0.04

0.35

151

the sll login s

C. Merkle, M. Weber / Journal of anking & Finance 46 (2014) 372386 383on the nding of Weber et al. (2013)who use the same surveythat the elicited expectations are effective and consistent predictorsof decisions, which should attenuate concerns about their validity.

The other concern that participants might not be able to expresstheir beliefs in the question format provided to them is taken intoaccount by the use of both, numerical and qualitative elicitation ofexpectations. While the numerical estimates are more demanding,in particular with respect to condence intervals, they have theadvantage of being comparable across participants. On the other

Sample selection.

Participation

Part. ln(Vol 1y)

(1) (2a)

Num. return 0.131

Num. risk 0.128Qual. return 0.005Qual. risk 0.004Risk tolerance 0.002

Age 0.000 0.006Gender (male = 1) 0.168 0.219

Income 0.014Wealth 0.031Fin. literacy 0.040Portfolio value 0.015Portfolio positions 0.062

Transactions 0.064

Inv. Mills ratio 0.594

n 19,609 1536

Notes: The table shows two-stage Heckman selection models for participation inincluding age and gender, and portfolio value, portfolio positions, and transactions (aMills ratio of the rst stage. Column 3 shows a probit regression for participation with(4a) and xed effects (4b). Coefcients are signicant at 10%-level. Coefcients are signicant at 5%-level. Coefcients are signicant at 1%-level.hand, qualitative estimates may capture aspects of value and risknot comprised in the rst two moments of a distribution. Interest-ingly, we nd with rare exceptions that only numerical expecta-tions are relevant for actual nancial risk taking decisions, whichis in contrast to the results of Weber et al. (2013) who establisha strong inuence of qualitative expectations on allocations inthe hypothetical investment task. We test whether the explanatorypower of numerical expectations changes over to qualitativeexpectations if we drop numerical expectations from the regres-sions. In general, this is not the case and the impact of qualitativeexpectations remains weak. When in turn qualitative expectationsare excluded, our results are unchanged.

An explanation for this nding has to consider the decision pro-cess in the hypothetical investment task compared to actuainvesting. First of all, our measures of nancial risk taking are onlyweakly correlated with the proportion of risky investment in thesurvey task, which already hints at the two being different. In par-ticular, the changes of risk taking in the task and investors portfo-lios are unrelated. We conjecture that the qualitative expectationsare affective evaluations of the market situation, while the numer-ical estimates draw more on cognitive resources (cp. Kuhnen andKnutson, 2011). We would then expect these evaluations to be pre-dictive for decisions that are made in the same mode ofthinking.11 If the actual investment decisions of investors are pre-ceded by a more deliberate thought process than the allocations inthe hypothetical task, this would at least partly explain the greater

11 Support for this dual-process theories of information processing and decisionmaking can be found, e.g., in Kahneman (2003).Blpredictive power of numerical expectations for these decisions. Aswe cannot fully explore the underlying mechanisms, this might bean interesting avenue for future research.

We also consider the time structure of expectations and trading,and throughout the paper we opted for an approach that tries toexplain changes in investing behavior by contemporaneouschanges in expectations. Another possibility would be that inves-tors need some time to react on changes in expectations, for exam-ple because of inertia. When we use lagged level variables many of

Panel attrition

Part. ln(Vol 1y)

) (3) (4a) (4b)

6 0.065 0.129 0.106136 0.315 0.152 0.1217 0.006 0.003 0.0042 0.010 0.001 0.0001 0.002 0.005 0.003004 0.004 0.004 7 0.192 0.098 015 0.122 0.007 016 0.115 0.042 033 0.043 0.022 046

109

4

4 0.001 0.0088 1825 1033 1033

urvey and panel attrition. Column 1 displays a probit regression of participationarithmized). Columns 2a and 2b reproduce results of Table 6 including the inversedurvey, columns 4a and 4b the associated second stage estimated with random effectsthe described relationships between expectations and investmentbehavior can still be observed (cp. Table 7).12 However, the effectsare in general about equal or weaker than for contemporaneousexpectations. We thus conclude that investors tend to implementtheir beliefs in a timely manner.

Instead of studying return and risk expectations separately, Eq(4) can also be interpreted in terms of Sharpe ratios. A higherexpected Sharpe ratio then implies a higher share in the riskyinvestment. We calculate expected Sharpe ratios using investorsmarket return expectations, the three-month risk-free rate (repre-sented by the LIBOR), and the expected market volatility frominvestors condence intervals.13 We nd that higher levels ofSharpe ratios are related to higher portfolio risk, supporting ourresults from Tables 6 and 7. However, there are in general no signif-icant results for changes in Sharpe ratios. We attribute this to the factthat Sharpe ratios are a combination of several survey items, eachsubject to noise and measurement error. In particular for changessuch constructs may become unreliable.

As a complement to our research, the investor survey ofHoffmann et al. (2013) has an overlap of seven month with ourdata. Elicited expectations and portfolio characteristics show somesimilarities: For instance return expectations of Dutch investorsalso rise from September to December 2008 and further to March2009, and trading and buying activity initially increases inresponse to the crisis. Similarly to us, Hoffmann et al. (2013) nd

12 A similar analysis for changes is precluded by the fact, that a change Dt1;t ismechanically (negatively) correlated with Dt;t1 over the shared observation in t.13 As negative Sharpe ratios are not well-dened, we have to exclude observationswhere Ers < rf ..

,

that median portfolio volatility is higher than market volatility andclosely tracks the market index. However, there are some differ-ences as well, e.g., risk perceptions fall gradually after a peak inSeptember 2008, while in our data they rise and then stay on a highlevel until March 2009. This might be due to the different wordingof the question, which in Hoffmann et al. (2013) refers to currentrisk perception, while our approach is more forward looking. Nev-ertheless, taken together the ndings suggest that there exist somemore general properties in expectations of private investors thatare not limited to a particular dataset.

In a regression of buysell ratios on beliefs and preferences,Hoffmann et al. (2013) use qualitative measures of expectations asexplanatory variables (which in our case remained insignicant).They demonstrate a signicantly positive inuence of risk toleranceon buying activity, but nd little effect of return and risk expecta-tions (levels and changes). This contributes to our impression that

6. Conclusion

relative to the market. In general, the best t of our model isachieved for long-term portfolio volatility. Changes in short-termportfolio volatility and changes in portfolio beta are less well ornot at all predicted by changes in expectations. This relates directlyto the question how private investors manage their portfolio riskand which risk measure is closest to their subjective experienceof risk. As long-term volatility measures react strongest to investorexpectations, we take this as tentative evidence that they are agood proxy for experienced risk.

Expectations have less predictive power for immediate tradingactivity of investors. We nd a positive effect of return expecta-tions on equity buying activity, which proxies for an adjustmentof the (unobserved) risky share. However, trading is often noisy,inuenced by liquidity and other exogenous trading motives,which might be a reason why we nd no inuence of risk expecta-tions and preferences. Investors also engage in risk shifting within

uesthe

cen endalcomqu

384 C. Merkle, M. Weber / Journal of Banking & Finance 46 (2014) 372386We investigate the functional relationship between beliefs andpreferences of investors and their trading behavior. While we arestill far from suggesting a denite functional form in the spirit ofEq. (4), our ndings are a rst step to improve the understandingof this complicated but fundamental relationship. We provide evi-dence that expectations are relevant for risk taking of investors,and that they areused in apredominantly rational and intuitiveway.

Higher return expectations lead to increased risk taking interms of portfolio volatility among investors, while higher riskexpectations have the opposite effect. Even more, changes in port-folio risk are predicted by contemporaneous changes in return andrisk expectations. We nd evidence that investors counteractchanges in market volatility by adjusting their portfolio volatility

Appendix A

Description of variables

Variable Origin Description

Num. return Survey Return in % in response to survey qUK stock market (FTSE all-share) byguess

Num. risk Survey Volatility calculated from condenusing responses to survey questiostock market (FTSE all-share) by thethan the actual outcome of the FTSErarely be higher than the actual out

Qual. return Survey Rating on scale 17 in response toimmediate trading behavior is hard to predict from elicited beliefs.For portfolio volatility, both datasets share the intuitive positiveresult for risk tolerance and the insignicant result for qualitativereturn expectations. However,Hoffmann et al. (2013) identify a posi-tive effect of risk perception on portfolio volatility. They explain thisresult by investors being aware of the risk of their investment port-folio, which suggests a reverse causality from portfolio risk to riskperception. Our ndings for numerical risk expectations stronglypoint in an opposite direction, i.e., investors taking less risk whenthey perceive risk to be higher. This discrepancy might again be aresult of different measurement, as we strictly distinguish betweenportfolio and market expectations, and use the latter in our regres-sions to avoid reverse causality. Risk perception in Hoffmann et al.(2013) refers more general to riskiness of investing.investment in the UK stock market (FTtheir portfolio, replacing less volatile securities by more volatileones. We infer that contrary to two-fund separation investors useseveral channels to adjust their risky position. They not onlyincrease or decrease a xed risky portfolio, but also change thisrisky portfolio according to their expectations.

Taken together, our results suggest that nancial theory in gen-eral correctly predicts the role of return and risk expectations foractual trading behavior. Private investors take their expectationsinto account to determine whether to buy or sell and whether toincrease or decrease portfolio risk. But at the same time investorsreaction to expectations and preferences is more nuanced andmore ambiguous than in the theoretical model. Not only do indi-vidual investors use different ways to alter their investment risk,but also some nancial risk measures such as equity beta seemto bear little relevance for them. Instead, we conjecture that a mul-titude of other factors, which to describe and identify is beyond thescope of this paper, play a role in investment decisions.

Acknowledgements

We are grateful to Barclays Stockbrokers for providing access totheir online investor client base, and to Barclays BehaviouralFinance team for joint design and execution of the survey. Wethank Daniel Egan, Christian Ehm, Greg Davies, Victor Fleisher,Alen Nosic, participants of the 2011 Boulder Summer Conferenceon Consumer Financial Decision Making and the 2011 SPUDM Con-ference, and seminar participants in Mannheim and Luxemburg.For research assistance we thank Robin Cindori. Research reportedin this article was supported by the Observatoire de lEpargneEuropenne (OEE) and Deutsche Forschungsgemeinschaft (DFG,Grant We993).

tion We would like you to make three estimates of the return of theend of the next three month. Your best estimate should be your best

intervals using the methodology of Keefer and Bodily (1983)We would like you to make three estimates of the return of the UKof the next 3 month. Your high estimate should very rarely be lower

l-share (about once in 20 occasions). Your low estimate should verye of the FTSE all-share (about once in 20 occasions)estion How would you rate the returns you expect from an

SE all-share) over the next 3 months?

IfftatHighlight

IfftatHighlight

que

sta

1)

1)

(t

ankiAppendix A (continued)

Description of variables

Variable Origin Description

Qual. risk Survey Rating on scale 17 in response tomarket (FTSE all-share) is?

Risk tolerance Survey Agreement on Likert scale 17 toinvestment

D num. return Survey Num. return (t) num. return (t D num. risk Survey Num. risk (t) num. risk (t 1)D qual. return Survey Qual. return (t) qual. return (t D qual. risk Survey Qual. risk (t) qual. risk (t 1)D risk tolerance Survey Risk tolerance (t) risk toleranceAge Bank data Age of participants in years

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