confounding changes in averages with marginal effects: how anchoring...

Strategic Management JournalStrat. Mgmt. J., 35: 1414–1426 (2014)

Published online EarlyView 14 August 2013 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/smj.2165

Received 18 January 2012 ; Final revision received 18 December 2012

CONFOUNDING CHANGES IN AVERAGES WITHMARGINAL EFFECTS: HOW ANCHORING CANDESTROY ECONOMIC VALUE IN STRATEGICINVESTMENT ASSESSMENTS

ZUR SHAPIRA1 and J. MYLES SHAVER2*1 Department of Management and Organizations, Stern School of Business, NewYork University, New York, New York, U.S.A.2 Department of Strategic Management and Entrepreneurship, Carlson School ofManagement, University of Minnesota, Minneapolis, Minnesota, U.S.A.

Profit maximization requires that decision makers assess marginal profits. We demonstrate thatdecision makers often confound marginal profits with changes in average profits (e.g., changesin return-on-investment). This results in systematic deviations from profit maximization wheredecision makers forgo profit-enhancing investments that reduce average profits or engage in loss-enhancing investments that decrease average losses. In other words, average profit becomes ananchor by which new investments are assessed. We conduct two decision-making experiments thatshow this bias and demonstrate it is pronounced when average profit data are accessible or task-relevant. Moreover, we find within-subject effects across experiments, which helps demonstratethe mechanism that invokes the bias. Copyright © 2013 John Wiley & Sons, Ltd.

INTRODUCTION

Making strategic investment decisions is not atask that should be taken haphazardly. Managersand MBA students spend time studying appro-priate decision criteria such as net present value(NPV) to aid in making profit-maximizing deci-sions. However, in discussing investment deci-sions with practicing managers over the years, wesensed that managers often systematically devi-ated from profit maximization. In particular, wenoticed that managers often equate changes inscaled profit measures (e.g., changes in return oninvestment [ROI]) with changes in total profits(i.e., marginal profits). This causes them to deviate

Keywords: decision making; biases; investments; ROI;profit maximization*Correspondence to: J. Myles Shaver, Carlson School ofManagement, University of Minnesota, 321 19th Ave. S.,Minneapolis, MN 55455, U.S.A. E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

systematically from profit maximization withrespect to strategic investment decisions (e.g.,research and development [R&D] investments,capital investments, acquisitions) by avoidinginvestments that increase total profits yet are lessprofitable than their average current investment.1

In other words, current levels of average profit cre-ate an anchor by which investments are assessed.

In illustration this phenomenon, we asked man-agers enrolled in an Executive Master of Busi-ness Administration (EMBA) class the followingquestion:

Assume that you work for a company thatcurrently, after accounting for the cost ofcapital, has a current return of 10 percent

1 In parallel, this can lead to decisions to make investmentsthat increase total losses yet decrease average losses. Namely,investments that are loss-generating but relatively less loss-generating than the average current investments.

Confounding Changes in Averages with Marginal Effects 1415

on $10 million of invested capital. You areasked to make a recommendation whetherthe company should invest in Project A, inProject B, in both or in neither.Project A, which after accounting for the costof capital, has an expected discounted returnof 10 percent on a $1 million investment.Project B, which after accounting for the costof capital, has an expected discounted returnof five percent on a $1 million investment.

Many of the managers who responded to theabove choice question recommended investing inProject A but not in B. It is clear that ProjectA dominates Project B; however, the positive[albeit lower] return is a sufficient reason toinvest also in B, and profit-maximizing decisionmakers should make the investment. Althoughmanagers might shy away from recommendingB for many “good” reasons, such as holdingthe money for better alternatives or investing themoney in riskless alternatives, the experiments wereport in this paper controlled for such reasons, butthe phenomenon did not go away.

Moreover, we noticed prominent examples ofthis effect in the business press. For example,in 2004 the Coca Cola Company decided toforgo several investments and focus on Coke’score business despite the company’s decliningmarket share. Then-CEO Isdel justified focusingon their core business because “there just aren’tmany businesses for sale that produce the lushmargins-around 30 percent, some analysts esti-mate that Coke makes from selling its proprietaryconcentrate to bottlers.” (Foust and Byrnes, 2004).This statement suggests that Coke’s current per-formance provided a strong anchor that affectedinvestment decisions. Namely, one can imaginethat investments with returns below 30 percentwould be profitable to Coke; however theyappeared not to want to make suc investments.

Likewise, such an affect presents a way toreconcile the discussion of why managers statethat they are unwilling to make acquisitions thatdilute earnings per share (Lynch, 1971 as citedin Matsusaka, 1993), even though there is noevidence that doing so leads to superior marketreactions on announcement (Matsusaka, 1993).Earnings per share is an average performancemeasure and by acquiring a target with lowerearnings per share, a firm lowers earnings pershare of the combined entity. Nevertheless, total

profits can often be increased under this situation.Therefore, the decision bias would be reflected inthe managerial statement and not in the marketreaction [if markets are efficient].

Our goal in this paper is twofold: first, todemonstrate deviations from profit maximizationwhere decision makers anchor on current averageprofit; second, to examine under what conditionssuch anchors are more likely to be pronounced.We do so by conducting two decision-makingexperiments with MBA students.

We find that many of our respondents demon-strate the decision making bias central to our argu-ments. Moreover, we find the likelihood of suchbias increases when average performance data areavailable or when they are task-relevant [i.e., whensubjects have multiple investments to compare].

Before proceeding, we wish to note that weare not stating that average performance dataare meaningless or should be avoided. Averagereturn data are beneficial because they facilitatecomparisons of investment choices. For example,the preference of two investments that result in$10 million profit likely differs if one requiresan investment of $1 million and the other aninvestment of $100 million—and average returndata make this comparison transparent. Our point,however, is that average performance data caninvoke an anchor in the decision-making processthat may lead to nonoptimal choices.

Anchoring in decision making

The mechanisms that underlie the behavior westudy are described in the judgment under uncer-tainty literature. Edwards (1954) did some of thepioneering work in this area by showing thatthe way people process probabilistic informationdeparts from Bayes rule. His major finding wasthat people do not update their prior probabilitiessufficiently when they get additional informationin the way prescribed by Bayes rule; he coined theterm “conservatism” to describe such behavior.

Tversky and Kahneman (1974) followedEdwards’s work and described the representa-tiveness heuristic to show that when makinginferences in situations where prior probabilitiesare given and then additional information isprovided, people do not use Bayes rule and tendto focus on the information elements that representto them the problem in a clearer manner. Theyproposed another heuristic called anchoring and

Copyright © 2013 John Wiley & Sons, Ltd. Strat. Mgmt. J., 35: 1414–1426 (2014)DOI: 10.1002/smj

1416 Z. Shapira and J. M. Shaver

adjustment to describe a situation in which anunrelated numerical figure is mentioned to peopleand may affect their estimate of the frequencyor probability of another uncertain event. Theyshowed that the original numerical stimulusoperates as a strong anchor from which peopledo not adjust enough even though the originalstimulus is unrelated to the question at hand. Themetaphor they used is an anchor, which sailors useto stabilize the position of a boat so that it doesn’tmove. Accordingly, Tversky and Kahnemanhypothesized that once anchored on a specificestimate people find it hard to adjust it when givennew information. Note, however, that while Tver-sky and Kahneman (1974) showed that an anchorcan affect people’s estimates of another unrelatedevent, other researchers used a substantial eventto demonstrate the anchoring effect. This has beendemonstrated often in negotiation research. Forexample, Northcraft and Neale (1987) providedreal estate agents and students with information onlist prices for properties and the subjects anchoredon those prices when estimating the value ofthese properties. The effect was clear even thoughthe real estate agents denied that this affectedtheir estimates. Galinsky and Mussweiler (2001)also show how meaningful anchors affect sub-sequent judgments by manipulating who makesthe first offer within a negotiation. Galinskyet al. (2002) go further and examine the effectsof the extremity of first offers as meaningfulanchors.

Following Tversky and Kahneman (1974) manyresearchers studied the effect of unrelated anchorson judgment under uncertainty, where unrelatedanchors operate as a priming mechanism. Webelieve that a clear and meaningful anchor suchas firm’s average profits provides an even strongeranchor from which managers find it hard todeviate. The effect can be stronger and last longerthan what Tversky and Kahneman observed.

Anchor accessibility

Epley and Giolvich (2006) argued that anchorsthat come easily to mind tend to develop resistanceto adjustment due to new data, as compared withanchors that require some effort to come by. Fur-thermore, the ease with which people can come upwith an initial estimate is inversely related to thedegree to which they would engage in adjustment,which is usually effortful. For instance, Epley and

Giolvich (2006) argue that when asked to estimatethe year when Washington became president,people can easily generate an anchor, 1776, whichseems plausible, and therefore their inclinationto make an adjustment is smaller compared withother cases where generating an anchor is effortful,or when an anchor is provided by an experimenternot easily accessible to the subject. In this respect,the context of our study is a natural candidatefor such an effect since a company’s averageprofits are very accessible to managers. Marginalexpected profits, even if their expected NPV is pos-itive, may be less accessible since they may changeoften. Average profits are usually stated for a cer-tain period, such as in annual reports and thus aremore accessible. Consequently, we argue that man-agers anchor on average performance figures andtend to equate changes in average performance asmarginal effects leading them to make suboptimaldecisions.

We argue that average performance figures areboth relevant and accessible, and these com-bined features are likely to affect managers toanchor on these averages and not adjust themfor better estimates when they make investmentdecisions.

In the domain that we study, we expect thatthe degree to which average profit measures areaccessible or task relevant will affect the likelihoodthat decision makers anchor on the current level ofaverage performance and fail to assess marginalperformance. When faced with a single decision,we predict that decision makers will more likelyanchor on current average performance when wepresent profit data as averages (e.g., ROI) versustotals. Namely, accessibility to average profit datainvokes the bias.

We also predict that task benefits of usingaverages will invoke the bias. In particular, wepredict that decision makers will be more likelyto anchor on average current performance whenthey have multiple investments to compare. Thereason is that average performance measuresfacilitate the comparison of investments andthis heightens the task relevance of using aver-age performance—and hence the likelihood ofobserving the bias. Therefore, under either of theseconditions we predict that average performancewill loom much larger in the decision maker’smind and she will be more likely to assess the newproject based on changes in average performanceversus marginal performance.



METHOD

Pilot study

With the general topic in mind, we went througha process of piloting the experiments we wishedto perform. The focus of the pilot study was tosee if we could document the bias and ensurethat subjects were not misled in our descriptionof the investment. We provided subjects withan investment decision and a set of additionalinformation to aid their assessment. We askedthem to make the decision and explain what theydid. We also asked them if they had to makeassumptions or required additional data to maketheir assessment. We wanted them to find thematerial clear, unambiguous, and complete.

We went through four waves to refine and honethe instrument. Three of these waves involvedclasses of full-time MBA students and the fourthwas a class of executive MBA students. Throughthese iterations we altered the instrument so thatby the end of the process subjects indicated littleevidence of ambiguity or need for additional infor-mation. Moreover, the effectiveness of the pilottests provided us confidence that we could conductthe experiments in a classroom setting becausethe instructions were clear and unambiguous tothe subjects and because the experimental manip-ulations were effective. An advantage of using aclassroom setting is that it allowed us to sam-ple a large number of MBA students—many ofwhom were working professionals—rather thanhaving to rely on a small sample and subjects withless business experience such as undergraduatestudents.

Experiment overview

To assess the existence of this bias we designedtwo decision-making experiments. The goal of theexperiments was to assess if the predicted con-ditions in which decision makers would likelyanchor on existing average performance, systemat-ically led to decisions based on changes in averageprofits, rather than marginal profits. Due to thenature of these experiments, it was possible tohave subjects take both experiments at one time.Having subjects take two experiments allows us toassess within-subject effects. Namely, we are ableto assess if subjects are sensitive to the manipu-lations across the experiments. This aids in ruling

out alternative explanations to our findings, as wedemonstrate below.

One experiment [what we subsequently referto as the single-decision experiment] has onlyone manipulation. We present the profile of aninvestment and a description of the firm’s currentperformance. In one condition subjects see theperformance data presented as averages [i.e., returnon investment]. In the other condition, subjectssee the performance data presented as totals[i.e., profits or loss]. Appendix 1 presents theinstrument. Our expectation is that subjects whosee the data as averages will more likely anchoron changes in average performance than those whosee the data presented as totals.2

As mentioned previously, averages are animportant decision aid when decision makers haveto compare investments. As a result, the otherexperiment presents subjects with two investmentsto make [we subsequently refer to this as the mul-tidecision experiment]. We design this experimentsuch that both investments increase firm prof-its. With the complexity of two investments fromwhich to decide, we can introduce more manipula-tions and produce a 2 × 2 × 2 design. Appendix 2presents this instrument.

The key manipulation we use is how the twoinvestments relate in average performance (i.e.,ROI) to the firm’s current performance. Keepingin mind that both investments increase profits, inone manipulation (1) one of the investments equalsthe firm’s current ROI and the other exceeds thecurrent ROI; and in the other manipulation (2) oneof the investments equals the current ROI but theother is lower than current ROI. Our expectationis that because subjects have two investments tocompare, they will tend to scale the investments[namely, use averages]. Therefore, we expectsubjects will tend to make both investments whenthe investments equal and exceed current ROI andwill be less likely to make both investments whenthe investments have equal and lower ROI.

The other two manipulations in the 2 × 2 × 2design provide conditions that will magnify theanchor in the event that subjects are not sensi-tive to the focal manipulation. These additional

2 We recognize that there are plausible alternative interpretationsfor the results we discuss (e.g., presenting averages leadssubjects to believe this is how they would personally beevaluated). The subsection entitled, alternative explanations inthe discussion section, discusses why we do not believe suchfactors drive the results across studies.



two manipulations (1) present the data as ROIversus profit levels and (2) present investmentsof equal versus different magnitude. The ratio-nale for manipulating the presentation in terms ofROI, or profit levels—as in the single-decisionexperiment—to induce was the consideration ofaverages. The rationale of varying the magnitudesof the investments was that investments of differ-ent magnitude would be more difficult to compare,subjects would be more inclined to calculate aver-ages to compare the investments, and calculatingthe averages would induce the anchor.

Experiment

Subjects

The experiment included 218 MBA students fromfive MBA classes at a Midwestern university: 81full-time MBA students and 137 evening MBAstudents. The average age of students in theseprograms was approximately 28 years. Participantshad an average of 5.27 years of experience in theirlast two full-time positions.

Procedure

The experiment took place at the beginning ofa class session. Prior to the experiment it wasverified that no student was in multiple classesin which the experiment was run. Students wereintroduced to the experiment by a standardizedscript prepared for Institutional Review Board(IRB) approval of the experiment and were assuredthat this was not a graded element of their classand that their responses would be anonymous.Students were able to opt out by simply notcompleting the experiment. The instructor of theclass was not in the room at the time theexperiment was run. Once all students had finishedthe experiments—approximately 15 minutes—thepackets were collected and the students weredebriefed.

We assembled packets that contained the twoexperiments. The conditions for the single-decisionexperiment and for the multidecision exper-iment were randomly matched—namely, themanipulation of the single-decision experimentthat a subject received was not related to themanipulation of the multidecision experiment thesame subject received. Likewise, the order of pre-sentation was randomly assigned—some saw the

Table 1. Single-decision experiment

Presented as totalprofit. Total

profitbecomes $-1.08M

from $-1.00M

Presented asaverage profit

(i.e., ROI). ROIbecomes −9%

from −10%

Recommend not tomake theinvestment[percentage]

93 [81.6] 71 [69.6]

Recommendmaking theinvestment[percentage]

21a [18.4] 31 [30.4]

n = 216.p = 0.029, one-tailed Fisher exact test.The profit-maximizing decision is not to make the investment.The investment increases total losses, yet decreases averagelosses.a Of the 21 subjects who chose to make the investment andwere presented the data as total profits, 14 explicitly showedthat they calculated average profit (i.e., ROI) before making thenonprofit-maximizing decision.

single-decision experiment first in the packet, oth-ers the multidecision experiment. Due to the natureof data collection, participation in each cell of eachdesign is not equal. However, it is relatively bal-anced, which reinforces the randomization under-lying the distribution of the instrument.

Single-decision experiment

Of the 218 subjects, 216 responded to this ques-tion. Table 1 summarizes their responses. Here,subjects evaluated whether or not to make aninvestment that would decrease total profit to−$1.08M from −$1.00M. Clearly, the profit-maximizing decision is to forgo this invest-ment. However, this investment increases ROI to−9 percent from −10 percent.

Our hypothesis is that subjects who were pre-sented with investment performance as averages(i.e., ROI data) would be more likely to recom-mend the investment than those who were pre-sented with the profit data. The results in Table 1confirm our expectation. When presented with dataon total profits 93 of the 114 subjects [81.6%]forgo the investment; whereas 71 of 102 [69.6%]forgo the investment when presented with ROIdata. This difference is statistically significant[Fisher exact test, p < 0.02].

Two points regarding the magnitudes in eachexperimental condition are noteworthy. First,



although 31 subjects [30.4%] in the ROI conditionmade the nonprofit-maximizing choice, the major-ity of subjects did make the profit-maximizingchoice. What we want to emphasize is that sub-jects in this condition were about twice as likely tomake the nonprofit-maximizing decision comparedto those presented the profit data.

Second, 21 of the 114 subjects [18.4%] whowere presented with the profit data made thenonprofit-maximizing decision. To understandwhy they would have made an investment thatclearly decreased profits, we examined these sub-jects’ written responses. We found that 14 of the 21subjects calculated the average return on the pageand subsequently decided to make the investmentbecause it increased average profit! In essence, weobserved that calculating averages and using themas the decision criteria was an important sourceof nonprofit-maximizing answers in the conditionwhere we did not present the ROI data. It appearsthat the subjects introduced the experimentalmechanism upon themselves and subsequentlymade the nonprofit-maximizing decision.

In summary, when we presented subjects withdata in the form of average profit (i.e., ROI)versus total profits, they were more likely tomake an investment that decreased total profits,yet increased average profits. This is consistentwith subjects evaluating changes in average profitsrather than marginal effects and anchoring on pastaverage performance.

Multidecision experiment

Of the 218 subjects, 217 responded to this ques-tion. Again, our expectation for the multidecisionexperiment was that multiple comparisons wouldinvoke the calculation of averages, because it aidscomparability of the two investments. This, in turn,would enhance the bias and strengthen reliance onthe anchor of past average performance.

Recall that in the multidecision experimentsubjects were presented with two investments. Inall conditions, both investments increased firmprofits. Moreover, in all conditions one of theinvestments had the same average return as thefirm’s existing investments. However, one of theexperimental manipulations was that the otherinvestment had (1) lower average profits (i.e., ROI)than the firm’s existing investments or (2) higheraverage profits (i.e., ROI) than the firm’s existinginvestments.

In this experiment, the profit-maximizing deci-sion is to make both investments. Our hypothesiswas that subjects with one investment that hadlower average profits would be less inclined tomake both investments than subjects presentedwith one investment that had higher average prof-its. Panel A of Table 2 presents the results.

As expected, we found that 52 of the 105 sub-jects [49.5%] in the condition where one of theinvestments had lower ROI than existing invest-ments made both investments. In contrast, 79 of112 subjects [70.5%] recommended both invest-ments in the condition where one of the invest-ments had higher ROI than existing investments.This difference is statistically significant [Fisherexact test, p < 0.001].

It is also noteworthy that in the multidecisionexperiment—in which comparisons were likely toinvoke the use of averages—the degree to whichsubjects focused on changes in averages appearsmore pronounced than in the single-decisionexperiment. In the single-decision experiment, inthe condition in which we expected the bias,31 of 102 subjects [30.4%] made a nonprofit-maximizing choice (Table 1, second column). Inthe multidecision experiment, in the conditionin which we expected the bias, 53 of 105subjects [50.5%] made a nonprofit-maximizingchoice (Table 2, Panel A, first column).

Returning to the results in panel A of Table 2,we examined the justifications provided by the53 subjects who did not make both investmentsin the condition where one investment decreasedaverage profits and the other equaled averageprofits [Panel A—lower left cell]. Of the 53subjects, 47 chose to make only the investmentwith the same ROI as existing operations.3 Ofthese 47 subjects, 8 explicitly stated that only thisinvestment hit the company’s average return; 37stated that they choose the highest return but didnot expand further; and 2 gave no justification.We also examined the justifications of the 33subjects who did not make both investments inthe maximizing decision in the condition whereone investment increased average profits and theother equaled average profits [Panel A—lower

3 Of the other six subjects, five choose to make no investmentstating they wanted higher returns. The other subject choosethe investment that decreased average profits, yet provided theexplanation of why the investment that equaled average profitswould have been chosen.



Table 2. Multidecision experiment

A. Comparison of the condition where the investments equal and increase average profits versusequal and decrease average profitsa

One investment decreasedaverage profits, the otherequaled average profits

One investment increasedaverage profits, the otherequaled average profits

Recommend making both investments [percentage] 52 [49.5] 79 [70.5]Recommend not to make both investments [percentage] 53 [50.5] 33 [29.5]

B. Of the investments where one investment decreased average profits and the other equaled averageprofits—analysis based on whether the investments were of equal sizeb

Presented as total profitsPresented as average

profit (i.e. ROI)Recommend making both investments [percentage] 28 [52.8] 24 [46.2]Recommend not to make both investments [percentage] 25 [47.2] 28 [53.9]

C. Of the investments where one investment decreased average profits and the other equaled averageprofits—analysis based on whether the investments were of equal sizec

Investment sizes the sameacross investments

Investment sizes differedacross investments

Recommend making both investments [percentage] 26 [48.2] 26 [51.0]Recommend not to make both investments [percentage] 28 [51.8] 25 [49.0]

a n = 217, p < 0.001, one-tailed Fisher exact test.b n = 105, p < 0.46, one-tailed Fisher exact test.c n = 105, p < 0.32, one-tailed Fisher exact test.The profit-maximizing decision under all conditions is to make both investments because every investment increases total profits.

right cell].4 Twenty eight of the 33 subjects choseonly the investment with ROI greater than currentinvestments. Of these 28 subjects, 8 explicitlystated that they chose the higher ROI investmentbecause it exceeded the company’s average return;18 stated that they choose the highest return butdid not provide further explanation; and 2 gaveno justification. Again, we saw many instanceswhere the subjects made explicit comparisons tothe current ROI when making their decisions.

Our reasoning for employing the other manip-ulations in the multidecision experiment was totry to invoke stronger inducements for subjectsto assess changes in averages versus marginaleffects. Because we find the effects in the mul-tidecision structure overall, we do not necessarilyexpect to find further effects based on the other

4 Of the other five subjects, two choose to make no investmentstating they wanted higher returns. The other three subjects chosethe investment that equaled past ROI (two stating that they didso because it equaled past ROI, the other proving an explanationof why the investment that exceeded average profits would havebeen chosen).

manipulations. Panel B of Table 2 breaks downthe investments where we expect the bias [one ofthe investments has a lower ROI] by whether ornot the data are presented as averages (i.e., ROI)or profits.

The data show a slightly higher incidence ofbias among subjects who had the data presentedas averages. Here 28 of 52 subjects [53.9%] didnot make both investments. This is in contrastto 25 of 53 subjects [47.2%] not making bothinvestments when having the data presented asprofits. This slight difference is not statisticallysignificant [Fisher exact test, p < 0.32].

Panel C of Table 2 breaks down the investmentswhere we expect the bias [one of the investmentshas a lower ROI] by whether or not the investmentmagnitudes were equal versus different. Herewe find no discernable difference in whether thesubjects made both investments. Of 54 subjects,28 [51.8%] did not make both investments whenthe investment magnitudes were the same, and25 of 51 subjects [49.0%] did not make both



Table 3. Within-subject accuracy across experiments: frequencies of profit-maximizing decisions across bothexperiments [conditioned on the multidecision experiment being in the condition subject to bias]

Made profit-maximizing

decision in thesingle-decision

experiment

Did not makeprofit-maximizing

decision in thesingle-decision

experiment Total

Made profit-maximizing decision in the multidecision experiment 42 [40.4]a 10 [9.6] 52Did not make profit-maximizing decision in the multidecision experiment 36 [34.6] 16 [15.4] 52Total 78 26 104

p < 0.001, of the test that subjects made either (1) both profit maximizing decisions or (2) did not make either profit-maximizingdecision [i.e., that the count in the off-diagonal cells equals 0].a Number in brackets is the percentage of all 104 observations.

investments the investment magnitudes differed[Fisher exact test, p < 0.46].

Within-subject analyses

A possible concern about interpreting our results isthat subjects might differ in their ability to assessinvestments or in their susceptibility to focus onchanges in averages versus marginal effects [e.g.,they believe that they should maximize ROI ver-sus profits]. Although the experimental conditionswere randomized among subjects, there exists thepossibility that less adept subjects fall into the con-ditions where we expect the bias to be invoked andmore adept subjects fall into the other conditions.

An advantage of our design is that most subjects[215 of 218] completed both the single-decisionexperiment and the multidecision experiment.Therefore, it is possible to assess if the results wepreviously report hold within subjects across thetwo experiments.

The data presented in Table 3 do not sup-port the interpretation that subject differencesdrive the results because there appears to be sig-nificant within-subject variation in showing thebias. Columns of the table reflect whether anindividual made the profit-maximizing decisionin the single-decision experiment. The rows ofthe table reflect whether an individual made theprofit-maximizing decision in the multidecisionexperiment—provided the subject was in a con-dition that would subject to the bias.5

If the results were driven by subject differ-ences and not anchoring [e.g., subjects did not

5 Assessing if a subject that was not in the condition assumedto be affected by the bias did not exhibit that the bias does notadd to the analysis.

maximize profit because they thought they shouldmaximize ROI], then we would expect subjectseither to provide the profit-maximizing or thenonprofit-maximizing answer to both questions.We would not expect a subject to profit max-imize in one instance and not in the other. Inother words, we would expect no observations inthe off-diagonal [top-right and lower-left cells]. Abinomial test that the count in the off-diagonal cellsis zero rejects this null-hypothesis [p < 0.001].

A further examination of the within subjecteffect is to assess if subjects are sensitive to theexperimental manipulations designed to invoke thebias regardless of how they answered the otherquestion. Table 4 presents data that are consistentwith the conclusion that subjects remain sensi-tive to the manipulation regardless of how theyanswered the other question. In all four instances[2 questions × profit-maximizing or nonprofitmaximizing answers], the pattern of results is con-sistent with what we presented previously—thereis a greater likelihood of nonprofit-maximizinganswers in the condition subject to the bias. Inthree of the four cases, the difference is statisticallysignificant at p < 0.10 level.

More specifically, in panel A of Table 4 wesee that subjects who did not profit maximize inthe single-decision experiment were subject to themanipulation of the multidecision experiment. Tenof 26 subjects [38.5%] made both investments inthe condition where we expected the anchor to bestronger, and 16 of 26 subjects [61.5%] made bothinvestments in the condition where we expectedthe anchor to be weaker [p < 0.10, Fisher exacttest].

Likewise, in panel B of Table 4 we see that sub-jects who profit maximized in the single-decisionexperiment were also subject to the manipulation



Table 4. Within-subject accuracy across experiments

A. Responses to the multidecision experiment of the subjects who made the profit-maximizing decision forthe single-decision experimenta



Made profit-maximizing decision for multidecisionexperiment [percentage]

10 [38.5] 16 [61.5]

Did not make profit-maximizing decision for multidecisionexperiment [percentage]

16 [61.5] 10 [38.5]

B. Responses to the multidecision experiment of the subjects who did not make the profit-maximizingdecision for the single-decision experimentb



Made profit-maximizing decision for multidecisionexperiment [percentage]

42 [53.9] 62 [72.9]

Did not make profit-maximizing decision for multidecisionexperiment [percentage]

36 [46.2] 23 [27.1]

C. Responses to the single-decision experiment of the subjects who made the profit-maximizing decisionfor the multidecision experimentc

Presented astotal profits

Presented as averageprofit (i.e., ROI)

Made profit-maximizing decision for single-decision experiment [percentage] 33 [78.6] 26 [60.5]Did not make profit-maximizing decision for single-decision experiment

[percentage]9 [21.4] 17 [39.5]

D. Responses to the single-decision experiment of the subjects who did not make the profit-maximizingdecision for the multidecision experimentd

Presented astotal profits

Presented as averageprofit (i.e. ROI)

Made profit-maximizing decision for single-decision experiment [percentage] 59 [83.1] 45 [76.3]Did not make profit-maximizing decision for single-decision experiment

[percentage]12 [16.9] 14 [23.7]

a n = 52, p = 0.082, one-tailed Fisher exact test.b n = 163, p = 0.009, one-tailed Fisher exact test.c n = 85, p = 0.057, one-tailed Fisher exact test.d n = 130, p = 0.227, one-tailed Fisher exact test.

of the multidecision experiment. Forty-two of 78subjects [53.9%] made both investments in thecondition where we expected the anchor to bestronger and 62 of 85 subjects [72.9%] made bothinvestments in the condition where we expectedthe anchor to be weaker [p < 0.01, Fisher exacttest].6

6 The difference in the proportion of subjects sensitive to themanipulation in the multidecision experiment across panels Aand B (38.5% versus 53.9%) does not test different.

In panel C of Table 4, we find that subjectswho did not profit maximize in the multidecisionexperiment were subject to the manipulation inthe single-decision experiment. Of 41 subjects, 33[78.6%] forwent the investment when presentedthe investment data as profits and 26 of 43 subjects[60.5%] forwent the investment when presentedthe investment data as averages (ROI) [p < 0.06,Fisher exact test].

Finally, in panel D of Table 4, we find thatsubjects who profit maximized in the multidecision



experiment were subject to the manipulation inthe single-decision experiment. Of 71 subjects 59[83.1%] forwent the investment when presentedthe investment data as profits, and 45 of 59 subjects[76.3%] forwent the investment when presentedthe investment data as averages (ROI). Althoughthe difference is in the predicted direction and ofmeaningful magnitude, it does not test significant[p < 0.227, Fisher exact test].

Summary

With two paper and pencil decision-making exper-iments, we find supportive evidence that manysubjects anchor investment decisions on the pastaverage performance of investments. In a singledecision experiment, as expected, we find that thebias is pronounced when subjects are presentedwith performance data as averages (ROI) versustotals [profits]. We also find that the bias appearswhen subjects are presented with two investmentdecisions. This is consistent with our expectationthat subjects use averages to make comparisons,and this invokes the anchor.

An advantage of our research design is thatwe can assess within-subject effects. We find thatour results are not driven by astute/naı̈ve subjectsbecause there is sensitivity to the experimentalmanipulations within individuals. Moreover,it appears that individuals were sensitive tothe manipulations that invoked the bias in oneexperiment, regardless of how they answered theother experiment.

DISCUSSION

We set out to analyze the possible reasons forthe tendency of managers to make decisions oninvestment in new projects based on changes inROI [i.e., change in average performance] ratherthan on NPV [i.e., marginal profits]. Severalearlier studies documented the tendency to focuson ROI or internal rate of return (IRR) ratherthan on NPV without providing a mechanism toexplain it [see, e.g., Aggarwal and Gibson, 1989;Ferraro and Taylor, 2005; Hermes, Smid andYao, 2007; Mao, 1970; and Petty, Scott and Bird,1975). We argue that the anchoring heuristic is atwork here. Practicing managers are anchored ontheir firms’ average profits so strongly that they

tend to ignore the fact that positive NPV projectscan increase total profits.

Support for this argument comes from ourconversations with the Chairman and CEO of aStandard and Poor’s (S&P) midcap company. Hementioned that “no-brainer” decisions were thehigh-return investments. However, they were oftensmall investments that would only marginallyaffect his firm’s overall profits. The difficult invest-ment decisions were large-dollar investments thatreturned close to the cost of capital. These invest-ments had the ability to have large profit impacts.However, they had to be managed carefully.

Finally, an example of the prevalence of theeffect we demonstrate was reflected in the com-ments of two Executive MBA students who par-ticipated in the pilot study. In that study, we alsoasked subjects, to describe further if there wouldbe other considerations in selling their decisionto the board of directors or their senior manage-ment. Interestingly, two subjects mentioned that,although they would want to make the investmentthat increased total profits yet decreased averageprofits, they would not recommend the project tosenior management because they didn’t think theycould convince senior management that this wasthe correct thing to do. Apparently, they had expe-riences similar to the Coke example, brought inthe introduction, where there was a focus on onlyconsidering projects that enhanced average profits.

Alternative explanations

Before concluding, we wish to highlight two alter-native explanations for why managers would avoidmaking investments that increased profits, yetdecreased average profits. Although these reasonsare valid and consistent with profit maximization,we also discuss why we do not expect them to holdin our experimental setting.

First, managers might face investment con-straints, such as limited capital or managerialresources to oversee projects. Here, optimizingmanagers would rank investments on their contri-bution to profitability and forgo profitable invest-ments once constraints became binding. We do notbelieve this effect drives our results for the follow-ing reasons: (1) We are explicit in the instructionsthat such a constraint is not binding. (2) To theextent that subjects did not read or believe thatconstraints were not binding, we find that subjectsequate the constraint with current average profits.



This reflects the anchoring mechanism central toour arguments; however, there is no reason tobelieve that this would necessarily be the pointwhere the constraint binds.7 (3) Experiment 1reflects a loss condition where the investment con-straint would not be an alternative mechanism.With the loss-making investment in Experiment 1,it would not make sense to make this investmentwhether the firm was constrained or not.

Second, firms might have better noninvestmentalternatives than low-profit investments. Here,firms would forgo profitable investments to findother uses for the capital. We do not believe thiseffect drives our results because we were explicitin the noninvestment alternatives. Moreover, tothe extent this trade-off occurred, it again wouldappear to occur at the level of current averageprofits. There is no reason to believe that thiswould necessarily be the point where the alterna-tive becomes more attractive and is consistent withthe anchor of using changes in average profits.

Another alternative explanation is that subjectsmight believe that maximizing average profits iswhat the company assesses or rewards. As wepreviously noted, if a subject holds this belief thenwe should not observe the within-subject effectsthat we find. Nevertheless, there is the possibilitythat our experimental manipulations might suggestthat average profits are assessed in some casesand not in others. For example, when we presentaverage profits in the single-decision experiment,this could prime subjects into thinking that averageprofits are what the company assesses or rewards.Therefore, making investments based on averageprofits reflects that decision makers believe theywould be assessed on this metric. There are tworeasons why we do not believe this is the primarydeterminant for the results that we find. First, inthe multidecision experiment, subjects were notmore likely to make the nonprofit-maximizingassessment when presented with average versustotal profit figures (Table 2B). Here it appeared thetask advantages to using averages drove the result.If presenting averages lead subjects to believe that

7 Average profits would reflect the cutoff for current investmentsonly if all investments have the same average return. Considera situation where the average payoff was 11 percent. Unless allinvestments pay 11 percent return, then at least some investmentshave a return less than 11 percent. For example, if the firm hasthree investments with an average 11 percent return and onereturns 12 percent; then at least one of the other investmentsmust return less than 11 percent.

average profits are the performance metric theyshould assess, then we would expect to see thisacross experiments—and we do not. Second, inthe single-decision experiment we observed thatsome subjects calculated averages when presentedtotal profit figures and subsequently make thenonprofit-maximizing decision. Apparently it wasthe use of averages—but not being primed to useaverages—that drove the outcome.

CONCLUSION

“Average” profitability measures such as ROIplay an important and legitimate role in man-agerial decision making because they facilitatethe comparison of investment alternatives. How-ever, changes in average profit measures are notmarginal effects, and attention to changes in aver-ages can lead to systematic deviations from profitmaximization. We demonstrate how focusing onchanges in averages causes managers to anchorinvestment decisions on current performance.

We provide experimental evidence that MBAstudents—many of whom were practicingmanagers—were susceptible to this anchoringheuristic when asked to make a strategic invest-ment decision. In the case of making an isolateddecision, we find the bias more pronouncedwhen decision makers have average performancemetrics presented to them. We also find that thebias is pronounced when decision makers have tocompare investment alternatives. Moreover, wefind evidence that our experimental manipulationsshowed within-subject effects. This aids in rulingout alternative explanations based on subject skillas the driver of the results that we find.

Our findings suggest that the ways in whichmanagers process investment decisions can lead tosystematic biases in the outcomes. Anchoring hasbeen demonstrated in many studies of managerialdecision making. For example, Lant and Shapira(2008) show that the term expectation is a majororganizing concept for professional economists;whereas, managers tend to focus on targets andaspirations. Targets are often set in a relative man-ner where a company’s performance is evaluatedin relation to historical profitability (Baum et al.,2005; Greve, 2002). Recognizing that random fluc-tuations in the environment can lead to variationsin performance over time, average performanceis perceived as a much more stable and validindicator of performance. Indeed, many companies



advertize their average performance over differ-ent periods of time to help investors evaluate theirvalue. This information is very accessible to man-agers and potentially enhances its role as an anchorwhen evaluating future projects.

As we show, anchoring on average performanceis very powerful due to its accessibility andrelevance. Anchoring has been recently shownto affect the way consumers pay their creditcard debt (Stewart, 2009) and the way consumersand professional insurance agents evaluate thevalue of alternative insurance policies (Shapira andVenezia, 2008). Our study suggests that anchoringaffects strategic decision investments as well.

One could argue that within corporations, ifsome decision makers are prone to the anchoringbias yet others are not, then we would notobserve the effect central to our study. Whilethis is possible, we believe it can still manifestor be organizationally important for the followingreasons. The aggregate decision of a group ofmanagers, where part of them are inclined toanchor on ROI and other are not, does notguarantee that in the aggregate the anchoring onROI disappears. Not all decision makers haveequal influence or power. Likewise, other biaseshave been shown to affect investor behavior andthe market as a whole (e.g., De Bondt and Thaler,1985). Thus, firms might have external pressure toanchor on average performance lending power todecision makers that anchor on ROI. Finally, evenif these factors do not prevail, if some decisionmakers are subject to the bias, we expect thatit prolongs the decision-making process and thisis costly to organization—especially in terms ofoccupying managerial resources.

To conclude, we believe that better understand-ing the psychological processes underlying theways managers make decisions within their jobcontext can help explain strategy choices. This hasbenefits beyond enhancing our understanding ofthe strategic decision-making process. Understand-ing systematic determinants of strategy choice isalso important to discern accurately how firmstrategies affect performance (e.g., Shaver, 1998).

ACKNOWLEDGMENTS

We appreciate helpful comments from theanonymous reviewers, the editor Rich Bettis,David Souder, and seminar participants atLondon Business School, National University of

Singapore, New York University, NorthwesternUniversity, University of Illinois, Universityof Minnesota, University of North Carolina,University of Southern California, University ofWestern Ontario, and Washington University. Wethank Benjamin Ilhardt for research assistance.

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APPENDIX 1

Single-decision

Two conditions: (A) Data presented as totals, (B)Data presented as averages.

The following is a decision that we would likeyou to assess:

You work for a company that currently, afteraccounting for the cost of capital, has ([A] totallosses of $1 million/[B] a return of −10%) on$10 million of invested capital.

You are asked for your opinion about thefollowing project that is being considered.

The project will require $2 million of capitalinvestment. After making this investment andaccounting for the cost of capital, the expectedperformance of the firm will be ([A] losses of$1.08 million/[B] a return of − 9%) on $12 millionof invested capital.

Please recommend if the company should investin this project.

The following information might aid yourassessment.

• The risk profile of this project does not materi-ally differ from the risk profile of your existingbusiness.

• This is the only project that you have to considerat this time.

• Any decision that you make is not expectedto aid or hinder your ability to make furtherinvestments should the opportunity arise.

• Any cash that the company does not use to makeinvestments will be invested in liquid assets thathave returns of about one percent [and expertsdo not think that the return for such instrumentswill materially change in the future].

Explain your decision [feel free to add anyqualifications to your answer].

APPENDIX 2

Multidecision experiment

For presentational clarity, we present only onecondition of the 2 × 2 × 2 design. The condition is(a) one investment equals current ROI, one invest-ment is greater than current ROI, (b) data presentedas totals, (c) investments are of different size. Thecomplete instrument is available upon request.

The following is a strategic investment decisionthat we would like you to assess:

You work for a company that currently, afteraccounting for the cost of capital, has total profitsof $1 million on $10 million of invested capital.

You are asked for your opinion about thefollowing two projects that are being considered.

Project A, which after accounting for the costof capital, has an expected discounted return of$150,000 on a $1 million investment.

Project B, which after accounting for the costof capital, has an expected discounted return of$100,000 on a $1 million investment.

Please recommend if the company should doProject A, Project B, both, or neither.

The following information might aid yourassessment.

• Making either of these investments does notaffect your ability to make the other.

• The risk profiles of these projects do notmaterially differ from each other or from therisk profile of your existing business.

• These are the only projects that you have toconsider at this time.

• Any decision that you make is not expectedto aid or hinder your ability to make furtherinvestments should the opportunity arise.

• Making either of these investments is notexpected to affect the profitability of yourexisting operations.

• Any cash that the company does not use to makeinvestments will be invested in liquid assets thathave returns of about one percent [and expertsdo not think that the return for such instrumentswill materially change in the future].Explain your decision [feel free to add any

qualifications to your answer].


confounding changes in averages with marginal effects: how anchoring...

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