1 Tibor Neugebauer Prepared for Foundations of Utility and Risk Rome June 23 – 26, 2006 An Experiment on Portfolio-Choice Tibor Neugebauer, University Hannover

2 1Experiment 2Motivation & Theoretical Prediction 3Experimental Results 4Conclusion Tibor Neugebauer, University Hannover Road Map

3 Tibor Neugebauer, University Hannover 1 Experiment Division of €1 0  a, b, a+b  1 Alternativestate X 50% state Y 50% a:A3 b:B-36 1-a-b:C11 Payoff 3a -a -3b 6b (1-a-b) 3a-3b+(1-a-b) -a+6b+(1-a-b)

4 Tibor Neugebauer, University Hannover Motivation & Theoretical Prediction Perfect Negative Correlation  Motivation 2.2 Portfolio Possibility Set in  -  -space 2.3 Safety First Portfolio in  -  -space 2.4Prospective Portfolio Choice

5 Tibor Neugebauer, University Hannover Perfect Negative Correlation 2.1 f(A) = B, C A (3, -3) (-1, 6)  Motivation 1.Kroll et al (1988): Experimental subjects disregard correlations. 2.Siebenmorgen & Weber (2002): Fundmanager disregard correlations. 3.A student (Hannover 2005): “I do not understand how risk can be eliminated in the case of perfect negative correlation.“ 4.Experimental evidence shows that probability weighting is flat for intermediary risks and discontinuous at extremes.

6 Tibor Neugebauer, University Hannover Portfolio Possibility Set in  -  -space 2.2 pp pp efficient frontier B C A 15/13 3a-3b+(1-a-b) -a+6b+(1-a-b) = Payoff in XPayoff in Y 3a-3b -a+6b = 4a 9b = a/b 9/4 = a = 9/13 b = 4/13  r x = 3a - 3b + (1-a-b) = 27/ /13 = 15/13 Riskless Portfolio  p = 15/13 + 1/9  p

7 Tibor Neugebauer, University Hannover Safety First Portfolio (Roy 1952) 2.3 pp pp B C A r* downside-risk SFP  p = r* + z  max z  Foundation of Behavioral Portfolio Theory

8 Tibor Neugebauer, University Hannover Prospective Portfolio 2.4 B Efficient Frontier r(Y) r(X) C A 45° sure outcomes locally convex locally concav Direction of stronger preference PP indifference curves

9 Tibor Neugebauer, University Hannover Experimental Results 3 3.1Original Experiment 3.2High-Stake Experiment (tenfold payoff) 3.3Control Experiment (controls for errors) 3.4Credit-Experiment 3.5High-Stake Credit-Experiment

10 Tibor Neugebauer, University Hannover Choices in Original Experiment 3.1 r(Y)r(X) r(Y) r(X) B C A Efficient Frontier Efficient Allocation  = 1  = 1.5  = 1  = 0  = 1 95% efficiency 100

11 Tibor Neugebauer, University Hannover Comments in Original Experiment A ist less risky than B, I prefer the riskless asset Assets A and B are very risky, I do not want to take any risk B‘s variance is huge perfect negative correlation, I try to estimate the optimal portfolio Diversification Payoffs always positive I always have a positive payoff My payoff is always positive No loss, but relatively high gain possible Diversification with a tendency towards the more risky asset I take the risk, because there is little at stake. In the case of higher stakes I would decide differently.      r(Y)r(X)abc  NO NEGATIVE PAYOFF

12 Tibor Neugebauer, University Hannover Choices in High-Stake Original Experiment r(Y) r(X) B C A Efficient frontier Efficient allocation  (Y)  (X) % efficiency 1000

13 Tibor Neugebauer, University Hannover Comments in High-Stake Original Experiment YXabc            r(Y) > r(X) No deposit payment. I am very risk averse. Don‘t invest in A, since  =10 = r(C). For B  > 10, but  is too high. Risk relatively neutralized. In any case, I receive more than C. I am risk averse. I do not want to lose any, but I want a chance to earn some money. It is difficult to decide between A and B. I am risk neutral. No Loss. Would C be greater, I would invest more in C. Because: C is riskless. B, A involve a possibilty of loss or gain No loss possible, asset A insures loss of B in X No negative payoff, because budget = 0. 50% chance of having a „high" payoff All or nothing, but incur no losses. No risk of loss, but prospect of positive gain! I do not feel like losing money 50% chance to receive something. Since one-shot gamble, I do not want to make a loss. If repeated I‘d always choose B. In all states there is no loss. All or nothing.    NO NEGATIVE PAYOFF

14 Tibor Neugebauer, University Hannover Control Experiment on Errors (Within-Subjects) 3.3 B Efficient frontier r(Y) r(X) C A assets offered in control question r(Y)r(X) r(X)r(Y) Original question Control question Result: risk level in control question remains unchanged. No subject chooses any share in C, all decisions are efficient.

15 Tibor Neugebauer, University Hannover Small-Stake Credit Experiment 3.4 B‘ C A‘ B A Efficient frontier r(Y) r(X) Subjects can sell asset C short (once).

16 Tibor Neugebauer, University Hannover Choices in Small-Stake Credit Experiment r(Y)r(X) r(Y) r(X) B C A Efficient frontier Efficient allocation Erroneous Computation91% efficiency 100

17 Tibor Neugebauer, University Hannover Choices High-Stake Credit Experiment 3.5 r(Y)r(X) r(Y) r(X) B C A Efficient frontier Efficient allocation 88% efficiency 1000

18 Tibor Neugebauer, University Hannover Comments in High-Stake Credit Experiment r(Y)r(X)abc Asset B features a high  and a high . Riskless asset helps to reduce risk. Make the expected value positive, minimize risk Negatively correlated, but I have no calculator handy. Zero correlation. Short sale would risk high loss. Negative payoff should be avoided. Intuitive decision. At least, I want to pay my coffee Since c is certain (no negative payoff), high weight. No loss possible Since I am risk averse, I choose a sure gain or nothing. I am a risk lover! But I want to diversify too. Weighing  low,  high.       NO NEGATIVE PAYOFF

19 Tibor Neugebauer, University Hannover No High-Stake Effect 3.6 Original ExperimentCredit Experiment H 0 : a OR = a HS H 0 : b OR = b HS H 0 : c OR = c HS Mann-Whitney-Test significance levels  POOL LOW- UND HIGH-STAKE DATA Result: In the low-stake credit experiment, a is greater and c is smaller than in the high- stake credit experiment. The differences are insignificant, though.

20 Tibor Neugebauer, University Hannover Risky Portfolio Share in Original Experiment b a 100% Results:  (a/b) = 1, symmetry  c = 34% 45° # observations Efficient allocation

21 Tibor Neugebauer, University Hannover Risky Portfolio Share in Credit Experiment Results (no credit):  (a/b) = 1, symmetry  c = 35% # observations Efficient allocation Results (credit):  (a/b) = 64/36  c = -68% Result: If no credit is taken, decisions seem identical to those made in the Original Experi- ment. Credit takers hold a higher share in asset A.

22 Tibor Neugebauer, University Hannover Summary of Results 5.1  Experiment on portfolio choice with perfect negative correlation.  Only a few subjects recognized correlation, although most of them heard of modern portfolio theory and CAPM in their lectures.  The data in the control experiment suggest that errors cause efficiency losses. Efficiency levels are 95% in the Original and 89% in the Credit Experiment.  The data suggest that subjects hold a share of the riskless asset C and a 50:50 lottery of the risky assets. The 50:50 risky component corresponds to the maximization of the expected value conditional on non-negative payoffs.  Subjects who borrow money choose a 64:36 ratio of the risky assets. (almost in line with the predictions of Safety First Portfolio Theory or Cumulative Prospekt Theory).

23 Tibor Neugebauer, University Hannover Conclusion 5.2  Two criteria (according to subjects‘ comments): Don‘t want to lose anything, and want to achieve a high expected return.  Comments suggest that subjects do not want to risk a negative payoff (pricing the participation in the experiment at zero cost).  Portfolio Choice seems to follow two criteria which are consistent with behavioral portfolio theory of Shefrin/Statman ; SP/A Theory Lopes. 1.Choice of a sure portfolio share (aspiration level to be reached in most states). 2.Choice of a risky share, which avoids negative payoffs and maximizes expected value. (Maximization of payoff in one state through purchase of a lottery ticket).  Problem: Naive diversification of risky assets leads to the same result.

24 Tibor Neugebauer, University Hannover THE END The first rule of investing is not to lose money. The second rule is not to forget the fist rule! Jokes for Economists