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Variance preferences and variance shifts in group investment decisions
ORGANIZATIOI~AL BEIIAVIOR A N D ttlI1VLAiNPERFORMAI~CE ~ 378386 (1970)
Variance Preferences and Variance Shifts in Group Investment Decisions M. KING DEETS University oJ Massachusetts AND
GEORGE C. HO~T
University o/Iowa In this study 58 subjects made five investment decisions first as individuals and then in groups. The subjects were led to believe tha£ they were basing their decisions on actual current stock market data, but in fact they were responding to an investmen£ simulation. The simulation controlled for the probabilities, the pay-offs, and the variances of all choices. It was found that both groups and individuals displayed definite variance preferences, but that groups had substantially greater preference for high variance, high risk securities. It is eonehided that variance is an important variable for both individual and group risk-taking and decision-making s'mdies. The results also tend to confirm and extend the generality of earlier studies of group risk taking by introducing a task which is different from that used in previous stadies and which is, perhaps, more directly related to typical forms of organizational decision making. Since 1961, a n u m b e r o.f studies h.ave 'been addressed ~o the prob.lem of group versus individual preferences on risk taking. T h e most general finding is .that group eonsen'sus decisions tend to be riskier than the mean of the pre,feren'ees of the individuals who m a k e up the group. This finding has been widely replicated (see, for example, Stone r , 19'6.1; Marquis, 1962; Wallach, Kogan, & B e m , 1962; I~im, 1963; H o y t & Stoner, 1968.). With a few exeep'tions (see K o g a n & Wallach, 1967; Ret~tig, 1966) these studies have employed, as did the original Stoner study, some form of a r i s k - t a k i n g questionnaire first developed b y Wallaeh and K o g a n (1959). This W a l l a e h - K o g a n dilemmas of choice questionnaire requires the decision m a k e r to specify his preference for a favorable bug uncertain event b y comparing it again'st a certain b u t less 'favorable event. B y stating the minimum probability t h a t he would require before recommending or accepting :the preferred but uncertain alternative, the individual m a y be presumed to be sharing this risk preference within tha~ 378
VARIANCE IN GROUP INVESTMENT DECISIONS
379
situation. After first taking the questi.onnaire as ,an individual, and then being placed in an ad hoc group, individuals have been fairly consistently shown to change ~their preferences in the direction of assuming greater risk. Groups, in a consensus decision, have generally Seen shown to display greater preference for risk than do the individuals who make up the group. Bateson (19'66) has been able to show similar results through familiarization .as well as 'through group discussion. Other studies, such as those by Nordhoy (1962), Stoner (1967), and Marquis (1968), have been able to develop some decision i.tems that show a cautious shift under group discussion or group decision. [For summary discussions of these studies and their possi'ble explanation, see Brown (1965) and Kogan and W.allach (19:67).] While such findings are of considerable significance for the study of organizations, they seem to have two limitations which limit their generality. The first of these is the familiar one of the difficulty of replicating the experiments under natural group, real world conditions. The second limitation is that a sufficient variety in task pro,blems has not ,been employed, further res:tric.ting the generality of results. This latter limitation seems of crucial importance in She light of Slovic's (19,62) observation, after careful review, that risk-taking measures lack convergent validity, and .risk-taking ~behavior is highly task specific. The present study is in part an attempt to replicate previous results with a task more anal og,ous to organizational decision pro'blems; thus the generality of task problems would be extended ,at the same time that n~ural group replication would be facilitated. This paper describes an experiment ~hat tested for .both individual and group variance preferences. It provides an example indicating th~at individuals do display variance preferences. It demonstrates a situation where these preferences differ between individuals and groups. As an alternative to the W,allach-Kogan questionnaire, the experiment offers additional insight into group risk-taking behavior 'by reporting a variante shift. THE EXPERIMENT The subjects were finance students having nearly completed trhe investments or security analysis courses at the University .of Iowa. There were 5.8 individual sulbjects l,ater formed into 16 groups (11 four-man groups, 4 three-man groups, and 1 .two-man group). The su~bjects were told the experimenter had compiled a series of historical observations from the stock and Ibond .markets and had .ordered these ~bser~vations according to ~he quality and ~eturn .of the security.
380
DEETS AND I~OYT
The term "q~ality" in the field of finance refers to the stability of the expected income from the assets in question. Thus, in these terms, "quality" is directly related to the variance of the distribution of expeered returns. Dividends and realized price appreciation are the two sources of income fl'om securi.ties. The more secure tlhe expected return, the higher is the quality. Thus, a security in the telephone eommunicat.ions indus.try is generally considered to be of higher quality than a similar security in the textile industry. However, quality and expected return are assumed #o be inversely related. Therefore, a security in the textile trade would 'be expected to yield a somewhat higher return on average than one from 'the communications field. It is also generally assumed that when the securities market is rising, 1.ow quality securities will rise more rapidly than high quality securities, but when the securities market is falling, low quali'ty securities will fall more rapidly than high quality securities. The su'b]eets were informed that the e~perimenter had classified 85 securities in such a manner and 'had gathered this information for the last 40 years. The information consisted of investing $100 into a particular quality security for a 5-year period. At the end of each year :the new market value of the investment was "sold," and the annual ra~e of return was calculated. These observations were then random'ly arranged so that the first 5-year observation on a particular quality might rb.e from the 1950-1954 market, the second ofbserva£ion might be for 1944-1948, the third from 1958-1963, and so forth. The names of these 85 securi~ties were then deleted, and they were given quality numbers and assigned to one of five sets. In each set, then, ,there were 17 different securities, which were ranked from 4highest t.o lowest quality. The su'bjeers understood th'at in all cases the experimenter had arranged the qualities so that the highest quality security in each set would yield a certain return. It might, for example, be a 'high quality bond yielding a 5% return or it might simply provide the op~tion of holding cash (the return, in this case, being zero). The lowest quality security in each set, on the o'ther hand, would always be a 'highly speculative common stock. The task. The su'b]ect was to select one of the 17 different qu~ality securities within each of the five sets. He had .the option of selecting a secure, certain return (highest quality) or a volatile, uncertain return (lowest quali'ty), or any of the shades of quality between, t-Ie was informed th,at there was no correct answer, but that his "investment" was an individual pre,ferenee. He was simply to select that quality security with which he fett "most .comfortable." The procedure followed for ea,eh o,f the five decisions was for the experimen.ter to read one 5-year price record and the average annual return for ~he highest quality security (certain return) and one for the lo~vest quality security (.most volatile return). The sub~ect .then requested
VARIANCE IN GROUP INVESTMENT DECISIONS
381
the experimenter to read as m a n y 5-year observations for as many qualities within the set as @e subject desired. After the subject had requested wha£ he felt was a sufficient number of observations upon which to base his decision, h.e would select t h a t quality security with which he felt "most comfortable." His "a,ctual" investment reburn would be the next 5-year observation in sequence. Hence, if the surb]ect had requested three observations on quality 10, he understood his investment would be tLhe fourth 5-year period on quality 10. The simulation. While the students in the experiment were led to believe they were basing their investment decisions on prices and returns from actual historical stock market data, they were in fact responding to a stock market simulation. Evidence exists th,at the varia'ble Y = log(Pt+l/Pt), where Pt is the purchase price .of a securiW and Pt+l the selling pri'ce, is a normally distributed random variable (Osborne, 19'64). The mean and variance of this distribu.tion is the g.eometrie mean and variance. The e:~periment was characterized by a total commitment of funds for a 5-year investment period. To create the stock market d,a~a a normal distribution was assumed and a specific mean and variance assigned. For e,a.ch 5-year period five random normal num~bers were generated by computer. The ensuing value of the initial $100 investment was a function of :the mean and variance of the normal distributio.n from which the simulated sample was taken. There were 17 different quality securities for each investment decision. Each quality was represented ,by a normal distribution each with a different mean and variance. For each of the five investment decisions the variance of the simulated distributi.ons remained the same. There were 17 varian.ee parameters, one for each quaiity. These are given in Table 1. The variance assignmerrts were selee.ted so .as to yield a substantial portion of the .actual range .available to the typical security investor. TaMe 1 ,also gives the return parameter for each distribution. For the first investment decision the mean (geometric rate of return) was zero for the highest quality rating (quality 1) and was .01 for the lowest quality (quality 17). T~e means between these qualities were linear functions of the quality ratings, Ri = C ~ - 1 / 1 6 Qi_~, i = 1, 2, . . . . , 17. For investment decisions 2, 3, 4, 5, the means .of the 17 distributions were simply incremented ~by a constant .0~ return. Thus, fur the ,certain return (variance of zero.) the mean shifted from .00 to .05, .10, .15, .20. Since the .difference between ~he .means of the highest quality and lowest quality rating for any particular investment decision was just .01, in the last decision the .distri~bution o~f ,the highest quality return had .a geometric mean of .20 and the mean of the towest quality (variance .of .15) was .91. The subject who selected quality 9 for his first investment decision
382
DEETS AND I-IOYT
TABLE 1 MEAN AND VARIANCE :PARAMETERS DETERMINING QUALITY ASSIGNMENTS
Mean return
Investment Investment Investment Investment Investment
Quality
Variance
decision 1
decision 2
decision 3
decision 4
decision 5
1 2 3 4 5 6 7 8 9 10 11 12 18 14 15 16 17
.000000 .000001 .000010 .001000 .002000 .004100 .007500 .012000 .018000
.000000 .000625 .001250 .001875 .002500 .003125 .003750 .004375 .005000 .005625 .006250 .006875 .007500 .008125 .008750 .009375 .010000
.050000 .050625 .051250 .051875 .052500 .053125 .053750 .054375 .055000 .055625 .056250 .056875 .057500 .058125 .058750 .059375 .060000
.100000 .100625 .101250 .101875 .102500 .103125 .103750 .104375 .105000 .105625 .106250 .106875 .107500 .108125 .•08750 .109375 .110000
.150000 .150625 .151250 .•51875 .152500 .153125 .153750 .154375 .155000 .155625 .156250 .156875 .157500 .158125 .158750 .159375 .160000
.200000 .200625 .201250 .201875 .202500 .203125 .203750 .204375 .205000 .205625 .206250 .206875 .207500 .208125 .208750 .209375 .210000
.027000
.037000 .047000 .060000 .074000 .090000 .115000 .150000
felt " m o s t .comfor~a~ble" with the five r a n d o m numbers generated from a n o r m a l distribution with a geometric m e a n of .005 and a varian'ce sf .018. While the empirical r e t u r n generated 'by this process fluctu,ated about the true mean, the more 5 - y e a r observations requested on a p a r t i c u l a r quality, the closer She subject was able to estimate the 'true return of the distribution. T h e greater the v a r i a n c e of the distribution, the greater was the fluctuation in ,the empirical return. I t should be noted t h a t while tJhe return is given as a percentage, it could also Ibe given as a fixed dollar amount. Thus, ,a $100 " i n v e s t m e n t " on quali'ty 9 for decision 1 would yield an average $.50 per year. I n a similar fashion the increment fro.m decision 1 to decision 2 is $5.00. T h e m e a n of the n o r m a l distribution for q u a l i t y 9 for decision 2, then, is $5.50. W h a t has been done essentially is .to inc.rement each of the 17 n o r m a l distributions b y a constant. I t is i m p o r t a n t to note .that neither the variances nor t h e psoba'bilities are changed b y this procedure. I t is sometimes a s s u m e d in decision t h e o r y t h a t adding or subtracting a constant in a p a y o f f m a t r i x has no effect on an individual's preferences (Edwards, L i n d m a n , & P,hillips, 19,6.5). All of the 88 subjects were administered the investmen~ p r o b l e m first as individuals and then later assemrbled into groups and required to
VARIANCE IN GROI~P I N V E S T M E N T DECISIONS
383
arrive a~ a group solution by e.onsensus. To neutralize possible effects due ~o sequentia'l deeisi,on making, half of the individuals and groups made the five investment decisions as the return was incremented from 0 to 20%. The .other half made their .decisions as the returns were decreased. I~ESULTS
The means of the five investment decisions were computed for the 58 individuals participating in the experiment on both individu,al and group decisions. A linear curve was fitted to the data, and the results are illustrated in Fig. 1. In no ease did individuals select investment Quality 17 16
15 X
14 13 12
~
roups
\Individual~
O=lndividual quality selections X = Group quality selections Individual regression Y= 12.54 - 15.76x Group regression Y= 13.46 - 11.37x I
0.00
0,05
O: 10 Return
1
0.15
I
0.20
FIG. 1. Individual and group quality selections (see Appendix Table A for data supporting Fig. 1).
decisions that yielded the maximum return avaiLa'ble but rather traded some return for a less volatile, more predictable return and price pattern. Secondly, as the expected return increased from lower to higher returns, individuals selected mo.re conservative investments (qualities containing less variance). When the means of the individual quality selections are compared .to their respective group quality selections, we find %hat groups
384
DEETS AND I-IOYT
o n average selected investments that yielded greater variance. The group regression indicates that on the whole the group quality selections lie above those of the individual selee.tions. Secondly, while the slop.e of the group regression is negative, its .slope is less than ~h,at of the regression on individual means. That is, while groups 'were influenced by increasing returns, they were less influenced than were individu'als. T~he t values have been computed for each investment decision, the over-all investment decisions, and for 'the slope .of the regressions. The results of these calculations are shown in Ta'ble 2.
TABLE 2 INDIVIDUAL
Decision number Overall 1 2 3 4 5 I n d i v i d u a l slope G r o u p slo pe
AND GROUP
QUALITY
S]~LECTIONS
M e a ndifference Number groups 1.7 -. 3 2.0 3.5 -. 1 1.8
80 16 16 16 16 16 288 80
t
p
2. 7178 - . 4316 2. 5969 4.7017 - . 1764 1. 3424 - 4.45 - 1.98
<.005 n.s < . 005 < . 0005 n.s < . 10 < . 0005 < . 025
Although not directly measured, it was noted t'hat groups request more information (observations) on the average 'than did individuals. As also might 'be expected, the amount of information requested by individuals before making their investment selection showed considerable variation from subject to subject. The .reversal of sequence (from lower to higher returns for one set of subjects, and from higher to lower returns for' the other set, as noted ,a~b.ove) showed some effect but not a significant one. When moving from lower to higher returns the slope of 'the regression tends to be steeper for both individuals and groups. DISCUSSION We conclude that our experiment has provided additional evidence for the Stoner risky shift phenomenon. Since the task pro%tern employed in this experiment involves financial .decision making, sguden;ts of organization may find the results more convincing, or at least more relevant, th,an those derived from the original Wallach-Kogan instrument. Further, we have found that adding and subtracting a constant to the payoffs in our problem does indeed make a difference in the decision behavior of both individuals and groups--contrary to the assumption sometimes made in decision theory. Secondly, we conclude that variance has properties that are associated
VARIANCE IN GROUP INVESTMENT DECISIONS
385
w i t h risk. B y s t r u c t u r i n g o u r i n v e s t m e n t prGblem as we h a v e done, we a r e a~ble t o i n d u c e a v a r i a n c e s h i f t b y groups f r o m t h e i r .prior i n d i v i d u a l m e a n s . W e suggest t h a t in t h e sea,rch for e x p l a n a t i o n s of t h e group r i s k p h e n o m e n o n , v a r i a n c e m u s t be c o n s i d e r e d to be a a i m p o r t a n ~ v a r i a b l e . APPENDIX TABLE A Data for Figure 1
Decision
Return
Mean individual quality selections
1 2 3 4 5
.00 .05 .10 .15 .20
13.4 10.8 10.5 10.4 9.7
Mean group quality selections
Individual regression values
Group regression values
13.1 12.8 14.0 10.3 11.5
12.54 11.75 10.96 10.18 9.42
13.46 12.87 12.32 11.76 11.19
REFERENCES
BATESON, N. Familiarization, group discussion, and risk-taking. Journal of Experimental Social Psychology, 1966, 2, 119-129. BROWN, R. Social psychology. New York: Free Press, 1965. Coo~Bs, C. H., & Puurrr, D. G. Components of risk in decision making: Probability and variance preferences. Journal o] Experimental Psychology, 1960, 60, 265-277. EDWARDS, W. Variance preferences in gambling. American Journal o/ Psychology, 1954, 67, 68-95. EDWARDS, W., LINDMAN, H., • PICIILYPS,L. D. In F. Barron, J. M. Olds, W. D. Dement, W. Edwards, M. Lindman, and L. D. Philips (Eds.), New directions in psychology II. New York : Holt, Rinehart, and Winston, 1965. HOYT, G. C., • STONER, J. A. F. Leadership and group decisions involving risk. Journal o/Experimental Social Psychology, 1968, 4, 275-284. KORAN, N., & WALLACH,M. A. Risk taking as a function of the situation, the person, and the group. I a G. Mandler (Ed.), New directions in psychology III. New York: Holt, 1967. LICHTENSTEIN, S. Bases for preferences among three-outcome bets. Journal o] Experimental Psychology, 1965, 69, 162-169. MARX0WITZ, H. M. Port]clio selection. New York: Wiley, 1959~. MARQUIS, D. G. Individual responsibility and group decisions involving risk. Industrial Management Review, 1962, 3, 8-23. MARQUIS, D. G. Individual and group decisions involving risk. Industrial Management Review, 1968, 9, 69~-75. NORDH~Y, F. Group interaction in decision-making under risk. Unpublished Master's thesis, Massachusetts Institute of Technology, School of Industrial Management, 1962. OSBORNS, M. F. M. Brownian motion in the stock market. In P. H. Cootner (Ed.), The random character o] stock market prices. Cambridge: The M. I. T. Press, 1964. Pp. 100-131. l%a~Tm, S. Group discussion and predicted ethical risk taking. Journal o] Personality and Bocial Psychology, 1966, 3~ 629-633.
386
DEETS AND HOYT
RI~, Y. P~isk-taking and need for achievement. Acta Psychologica, 1963, 21, 108115. S~ovIc, P. Convergent validation of risk taking measures. Journal of Abnormal and Social Psychology, 1962, 65, 68-71. SToNIng, J. A. F. A comparison of individual and group decisions involving risk. Unpublished Master's thesis, Massachusetts Institute of Technology, School of Industrial Management, 1961. STONER, J. A. F. The effect of general values on cautious and risky shifts in group decisions. Unpublished Doctor's thesis, Massachusetts Institute of Technology, School of Industrial Management, 1967. SUYDA~, M. M., & MYERS, J. L. Some parameters of risk taking behavior. Psychological Reports, 1962, 10, 559-562. VAx D~a ME~% H. C. Decision making: The influence of probability preference, variance preference, and expected value on strategy in gambling. Acta Psychologia, 1963, 21, 231-259. WA~Ac~, M. A., & I
Variance Preferences and Variance Shifts in Group Investment Decisions M. KING DEETS University oJ Massachusetts AND
GEORGE C. HO~T
University o/Iowa In this study 58 subjects made five investment decisions first as individuals and then in groups. The subjects were led to believe tha£ they were basing their decisions on actual current stock market data, but in fact they were responding to an investmen£ simulation. The simulation controlled for the probabilities, the pay-offs, and the variances of all choices. It was found that both groups and individuals displayed definite variance preferences, but that groups had substantially greater preference for high variance, high risk securities. It is eonehided that variance is an important variable for both individual and group risk-taking and decision-making s'mdies. The results also tend to confirm and extend the generality of earlier studies of group risk taking by introducing a task which is different from that used in previous stadies and which is, perhaps, more directly related to typical forms of organizational decision making. Since 1961, a n u m b e r o.f studies h.ave 'been addressed ~o the prob.lem of group versus individual preferences on risk taking. T h e most general finding is .that group eonsen'sus decisions tend to be riskier than the mean of the pre,feren'ees of the individuals who m a k e up the group. This finding has been widely replicated (see, for example, Stone r , 19'6.1; Marquis, 1962; Wallach, Kogan, & B e m , 1962; I~im, 1963; H o y t & Stoner, 1968.). With a few exeep'tions (see K o g a n & Wallach, 1967; Ret~tig, 1966) these studies have employed, as did the original Stoner study, some form of a r i s k - t a k i n g questionnaire first developed b y Wallaeh and K o g a n (1959). This W a l l a e h - K o g a n dilemmas of choice questionnaire requires the decision m a k e r to specify his preference for a favorable bug uncertain event b y comparing it again'st a certain b u t less 'favorable event. B y stating the minimum probability t h a t he would require before recommending or accepting :the preferred but uncertain alternative, the individual m a y be presumed to be sharing this risk preference within tha~ 378
VARIANCE IN GROUP INVESTMENT DECISIONS
379
situation. After first taking the questi.onnaire as ,an individual, and then being placed in an ad hoc group, individuals have been fairly consistently shown to change ~their preferences in the direction of assuming greater risk. Groups, in a consensus decision, have generally Seen shown to display greater preference for risk than do the individuals who make up the group. Bateson (19'66) has been able to show similar results through familiarization .as well as 'through group discussion. Other studies, such as those by Nordhoy (1962), Stoner (1967), and Marquis (1968), have been able to develop some decision i.tems that show a cautious shift under group discussion or group decision. [For summary discussions of these studies and their possi'ble explanation, see Brown (1965) and Kogan and W.allach (19:67).] While such findings are of considerable significance for the study of organizations, they seem to have two limitations which limit their generality. The first of these is the familiar one of the difficulty of replicating the experiments under natural group, real world conditions. The second limitation is that a sufficient variety in task pro,blems has not ,been employed, further res:tric.ting the generality of results. This latter limitation seems of crucial importance in She light of Slovic's (19,62) observation, after careful review, that risk-taking measures lack convergent validity, and .risk-taking ~behavior is highly task specific. The present study is in part an attempt to replicate previous results with a task more anal og,ous to organizational decision pro'blems; thus the generality of task problems would be extended ,at the same time that n~ural group replication would be facilitated. This paper describes an experiment ~hat tested for .both individual and group variance preferences. It provides an example indicating th~at individuals do display variance preferences. It demonstrates a situation where these preferences differ between individuals and groups. As an alternative to the W,allach-Kogan questionnaire, the experiment offers additional insight into group risk-taking behavior 'by reporting a variante shift. THE EXPERIMENT The subjects were finance students having nearly completed trhe investments or security analysis courses at the University .of Iowa. There were 5.8 individual sulbjects l,ater formed into 16 groups (11 four-man groups, 4 three-man groups, and 1 .two-man group). The su~bjects were told the experimenter had compiled a series of historical observations from the stock and Ibond .markets and had .ordered these ~bser~vations according to ~he quality and ~eturn .of the security.
380
DEETS AND I~OYT
The term "q~ality" in the field of finance refers to the stability of the expected income from the assets in question. Thus, in these terms, "quality" is directly related to the variance of the distribution of expeered returns. Dividends and realized price appreciation are the two sources of income fl'om securi.ties. The more secure tlhe expected return, the higher is the quality. Thus, a security in the telephone eommunicat.ions indus.try is generally considered to be of higher quality than a similar security in the textile industry. However, quality and expected return are assumed #o be inversely related. Therefore, a security in the textile trade would 'be expected to yield a somewhat higher return on average than one from 'the communications field. It is also generally assumed that when the securities market is rising, 1.ow quality securities will rise more rapidly than high quality securities, but when the securities market is falling, low quali'ty securities will fall more rapidly than high quality securities. The su'b]eets were informed that the e~perimenter had classified 85 securities in such a manner and 'had gathered this information for the last 40 years. The information consisted of investing $100 into a particular quality security for a 5-year period. At the end of each year :the new market value of the investment was "sold," and the annual ra~e of return was calculated. These observations were then random'ly arranged so that the first 5-year observation on a particular quality might rb.e from the 1950-1954 market, the second ofbserva£ion might be for 1944-1948, the third from 1958-1963, and so forth. The names of these 85 securi~ties were then deleted, and they were given quality numbers and assigned to one of five sets. In each set, then, ,there were 17 different securities, which were ranked from 4highest t.o lowest quality. The su'bjeers understood th'at in all cases the experimenter had arranged the qualities so that the highest quality security in each set would yield a certain return. It might, for example, be a 'high quality bond yielding a 5% return or it might simply provide the op~tion of holding cash (the return, in this case, being zero). The lowest quality security in each set, on the o'ther hand, would always be a 'highly speculative common stock. The task. The su'b]ect was to select one of the 17 different qu~ality securities within each of the five sets. He had .the option of selecting a secure, certain return (highest quality) or a volatile, uncertain return (lowest quali'ty), or any of the shades of quality between, t-Ie was informed th,at there was no correct answer, but that his "investment" was an individual pre,ferenee. He was simply to select that quality security with which he fett "most .comfortable." The procedure followed for ea,eh o,f the five decisions was for the experimen.ter to read one 5-year price record and the average annual return for ~he highest quality security (certain return) and one for the lo~vest quality security (.most volatile return). The sub~ect .then requested
VARIANCE IN GROUP INVESTMENT DECISIONS
381
the experimenter to read as m a n y 5-year observations for as many qualities within the set as @e subject desired. After the subject had requested wha£ he felt was a sufficient number of observations upon which to base his decision, h.e would select t h a t quality security with which he felt "most comfortable." His "a,ctual" investment reburn would be the next 5-year observation in sequence. Hence, if the surb]ect had requested three observations on quality 10, he understood his investment would be tLhe fourth 5-year period on quality 10. The simulation. While the students in the experiment were led to believe they were basing their investment decisions on prices and returns from actual historical stock market data, they were in fact responding to a stock market simulation. Evidence exists th,at the varia'ble Y = log(Pt+l/Pt), where Pt is the purchase price .of a securiW and Pt+l the selling pri'ce, is a normally distributed random variable (Osborne, 19'64). The mean and variance of this distribu.tion is the g.eometrie mean and variance. The e:~periment was characterized by a total commitment of funds for a 5-year investment period. To create the stock market d,a~a a normal distribution was assumed and a specific mean and variance assigned. For e,a.ch 5-year period five random normal num~bers were generated by computer. The ensuing value of the initial $100 investment was a function of :the mean and variance of the normal distributio.n from which the simulated sample was taken. There were 17 different quality securities for each investment decision. Each quality was represented ,by a normal distribution each with a different mean and variance. For each of the five investment decisions the variance of the simulated distributi.ons remained the same. There were 17 varian.ee parameters, one for each quaiity. These are given in Table 1. The variance assignmerrts were selee.ted so .as to yield a substantial portion of the .actual range .available to the typical security investor. TaMe 1 ,also gives the return parameter for each distribution. For the first investment decision the mean (geometric rate of return) was zero for the highest quality rating (quality 1) and was .01 for the lowest quality (quality 17). T~e means between these qualities were linear functions of the quality ratings, Ri = C ~ - 1 / 1 6 Qi_~, i = 1, 2, . . . . , 17. For investment decisions 2, 3, 4, 5, the means .of the 17 distributions were simply incremented ~by a constant .0~ return. Thus, fur the ,certain return (variance of zero.) the mean shifted from .00 to .05, .10, .15, .20. Since the .difference between ~he .means of the highest quality and lowest quality rating for any particular investment decision was just .01, in the last decision the .distri~bution o~f ,the highest quality return had .a geometric mean of .20 and the mean of the towest quality (variance .of .15) was .91. The subject who selected quality 9 for his first investment decision
382
DEETS AND I-IOYT
TABLE 1 MEAN AND VARIANCE :PARAMETERS DETERMINING QUALITY ASSIGNMENTS
Mean return
Investment Investment Investment Investment Investment
Quality
Variance
decision 1
decision 2
decision 3
decision 4
decision 5
1 2 3 4 5 6 7 8 9 10 11 12 18 14 15 16 17
.000000 .000001 .000010 .001000 .002000 .004100 .007500 .012000 .018000
.000000 .000625 .001250 .001875 .002500 .003125 .003750 .004375 .005000 .005625 .006250 .006875 .007500 .008125 .008750 .009375 .010000
.050000 .050625 .051250 .051875 .052500 .053125 .053750 .054375 .055000 .055625 .056250 .056875 .057500 .058125 .058750 .059375 .060000
.100000 .100625 .101250 .101875 .102500 .103125 .103750 .104375 .105000 .105625 .106250 .106875 .107500 .108125 .•08750 .109375 .110000
.150000 .150625 .151250 .•51875 .152500 .153125 .153750 .154375 .155000 .155625 .156250 .156875 .157500 .158125 .158750 .159375 .160000
.200000 .200625 .201250 .201875 .202500 .203125 .203750 .204375 .205000 .205625 .206250 .206875 .207500 .208125 .208750 .209375 .210000
.027000
.037000 .047000 .060000 .074000 .090000 .115000 .150000
felt " m o s t .comfor~a~ble" with the five r a n d o m numbers generated from a n o r m a l distribution with a geometric m e a n of .005 and a varian'ce sf .018. While the empirical r e t u r n generated 'by this process fluctu,ated about the true mean, the more 5 - y e a r observations requested on a p a r t i c u l a r quality, the closer She subject was able to estimate the 'true return of the distribution. T h e greater the v a r i a n c e of the distribution, the greater was the fluctuation in ,the empirical return. I t should be noted t h a t while tJhe return is given as a percentage, it could also Ibe given as a fixed dollar amount. Thus, ,a $100 " i n v e s t m e n t " on quali'ty 9 for decision 1 would yield an average $.50 per year. I n a similar fashion the increment fro.m decision 1 to decision 2 is $5.00. T h e m e a n of the n o r m a l distribution for q u a l i t y 9 for decision 2, then, is $5.50. W h a t has been done essentially is .to inc.rement each of the 17 n o r m a l distributions b y a constant. I t is i m p o r t a n t to note .that neither the variances nor t h e psoba'bilities are changed b y this procedure. I t is sometimes a s s u m e d in decision t h e o r y t h a t adding or subtracting a constant in a p a y o f f m a t r i x has no effect on an individual's preferences (Edwards, L i n d m a n , & P,hillips, 19,6.5). All of the 88 subjects were administered the investmen~ p r o b l e m first as individuals and then later assemrbled into groups and required to
VARIANCE IN GROI~P I N V E S T M E N T DECISIONS
383
arrive a~ a group solution by e.onsensus. To neutralize possible effects due ~o sequentia'l deeisi,on making, half of the individuals and groups made the five investment decisions as the return was incremented from 0 to 20%. The .other half made their .decisions as the returns were decreased. I~ESULTS
The means of the five investment decisions were computed for the 58 individuals participating in the experiment on both individu,al and group decisions. A linear curve was fitted to the data, and the results are illustrated in Fig. 1. In no ease did individuals select investment Quality 17 16
15 X
14 13 12
~
roups
\Individual~
O=lndividual quality selections X = Group quality selections Individual regression Y= 12.54 - 15.76x Group regression Y= 13.46 - 11.37x I
0.00
0,05
O: 10 Return
1
0.15
I
0.20
FIG. 1. Individual and group quality selections (see Appendix Table A for data supporting Fig. 1).
decisions that yielded the maximum return avaiLa'ble but rather traded some return for a less volatile, more predictable return and price pattern. Secondly, as the expected return increased from lower to higher returns, individuals selected mo.re conservative investments (qualities containing less variance). When the means of the individual quality selections are compared .to their respective group quality selections, we find %hat groups
384
DEETS AND I-IOYT
o n average selected investments that yielded greater variance. The group regression indicates that on the whole the group quality selections lie above those of the individual selee.tions. Secondly, while the slop.e of the group regression is negative, its .slope is less than ~h,at of the regression on individual means. That is, while groups 'were influenced by increasing returns, they were less influenced than were individu'als. T~he t values have been computed for each investment decision, the over-all investment decisions, and for 'the slope .of the regressions. The results of these calculations are shown in Ta'ble 2.
TABLE 2 INDIVIDUAL
Decision number Overall 1 2 3 4 5 I n d i v i d u a l slope G r o u p slo pe
AND GROUP
QUALITY
S]~LECTIONS
M e a ndifference Number groups 1.7 -. 3 2.0 3.5 -. 1 1.8
80 16 16 16 16 16 288 80
t
p
2. 7178 - . 4316 2. 5969 4.7017 - . 1764 1. 3424 - 4.45 - 1.98
<.005 n.s < . 005 < . 0005 n.s < . 10 < . 0005 < . 025
Although not directly measured, it was noted t'hat groups request more information (observations) on the average 'than did individuals. As also might 'be expected, the amount of information requested by individuals before making their investment selection showed considerable variation from subject to subject. The .reversal of sequence (from lower to higher returns for one set of subjects, and from higher to lower returns for' the other set, as noted ,a~b.ove) showed some effect but not a significant one. When moving from lower to higher returns the slope of 'the regression tends to be steeper for both individuals and groups. DISCUSSION We conclude that our experiment has provided additional evidence for the Stoner risky shift phenomenon. Since the task pro%tern employed in this experiment involves financial .decision making, sguden;ts of organization may find the results more convincing, or at least more relevant, th,an those derived from the original Wallach-Kogan instrument. Further, we have found that adding and subtracting a constant to the payoffs in our problem does indeed make a difference in the decision behavior of both individuals and groups--contrary to the assumption sometimes made in decision theory. Secondly, we conclude that variance has properties that are associated
VARIANCE IN GROUP INVESTMENT DECISIONS
385
w i t h risk. B y s t r u c t u r i n g o u r i n v e s t m e n t prGblem as we h a v e done, we a r e a~ble t o i n d u c e a v a r i a n c e s h i f t b y groups f r o m t h e i r .prior i n d i v i d u a l m e a n s . W e suggest t h a t in t h e sea,rch for e x p l a n a t i o n s of t h e group r i s k p h e n o m e n o n , v a r i a n c e m u s t be c o n s i d e r e d to be a a i m p o r t a n ~ v a r i a b l e . APPENDIX TABLE A Data for Figure 1
Decision
Return
Mean individual quality selections
1 2 3 4 5
.00 .05 .10 .15 .20
13.4 10.8 10.5 10.4 9.7
Mean group quality selections
Individual regression values
Group regression values
13.1 12.8 14.0 10.3 11.5
12.54 11.75 10.96 10.18 9.42
13.46 12.87 12.32 11.76 11.19
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386
DEETS AND HOYT
RI~, Y. P~isk-taking and need for achievement. Acta Psychologica, 1963, 21, 108115. S~ovIc, P. Convergent validation of risk taking measures. Journal of Abnormal and Social Psychology, 1962, 65, 68-71. SToNIng, J. A. F. A comparison of individual and group decisions involving risk. Unpublished Master's thesis, Massachusetts Institute of Technology, School of Industrial Management, 1961. STONER, J. A. F. The effect of general values on cautious and risky shifts in group decisions. Unpublished Doctor's thesis, Massachusetts Institute of Technology, School of Industrial Management, 1967. SUYDA~, M. M., & MYERS, J. L. Some parameters of risk taking behavior. Psychological Reports, 1962, 10, 559-562. VAx D~a ME~% H. C. Decision making: The influence of probability preference, variance preference, and expected value on strategy in gambling. Acta Psychologia, 1963, 21, 231-259. WA~Ac~, M. A., & I