1 tibor neugebauer prepared for foundations of utility and risk rome june 23 – 26, 2006 an...

1

Tibor Neugebauer

Prepared for Foundations of Utility and Risk

RomeJune 23 – 26, 2006

An Experiment on Portfolio-Choice

http://www.wiwi.uni-hannover.de/finanzmarkt/dnpubl/portfolio.pdf

Tibor Neugebauer, University Hannover

2

1 Experiment

2 Motivation & Theoretical Prediction

3 Experimental Results

4 Conclusion


Road Map

3


1 Experiment

Division of €10 a, b, a+b 1

Alternative state X50%

state Y50%

a: A 3 -1

b: B -3 6

1-a-b: C 1 1

Payoff

3a -a

-3b 6b

(1-a-b) (1-a-b)

3a-3b+(1-a-b) -a+6b+(1-a-b)

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Motivation & Theoretical Prediction2

2.1 Perfect Negative Correlation Motivation

2.2 Portfolio Possibility Set in --space

2.3 Safety First Portfolio in --space

2.4 Prospective Portfolio Choice

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Perfect Negative Correlation2.1

f(A) = B, C

A

(3, -3)

(-1, 6) Motivation

1AB

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.

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Portfolio Possibility Set in --space2.2

p

p

efficient frontierB

CA

15/13

3a-3b+(1-a-b) -a+6b+(1-a-b)=

Payoff in X Payoff in Y

3a-3b -a+6b=

4a 9b=

a/b 9/4=

a = 9/13 b = 4/13

rx = 3a - 3b + (1-a-b)

= 27/13 - 12/13 = 15/13Riskless Portfolio

p = 15/13 + 1/9 p

1AB

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Safety First Portfolio (Roy 1952)2.3

p

p

B

CA

r*

downside-risk

SFP

p = r* + z

max z

Foundation of Behavioral Portfolio Theory

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Prospective Portfolio2.4

B

Efficient Frontier

r(Y)

r(X)

C

A

45° sure outcomes

locally convex

locally concav

Direction of stronger preference

PP

indifference curves

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Experimental Results3

3.1 Original Experiment

3.2 High-Stake Experiment (tenfold payoff)

3.3 Control Experiment (controls for errors)

3.4 Credit-Experiment

3.5 High-Stake Credit-Experiment

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Choices in Original Experiment3.1

r(Y) r(X)

90 120

100 100

105 110

133 100

175 50

175 50

190 40

200 33

210 20

210 20

220 20

250 0

250 0

300 -50

600 -300

-100 100

-300

600

300

r(Y)

r(X)

B

C

A

Efficient Frontier

Efficient Allocation

1 2 3 4# observations

= 1

= 1.5

= 1

= 0

= 1

95% efficiency

100

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Comments in Original Experiment3.1.1

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

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) a b c

90 120 30 10 60

100 100 0 0 100

105 110 35 15 50

133 100 67 33 0

175 50 25 25 50

175 50 25 25 50

190 40 30 30 40

200 33 33 33 33

210 20 20 30 50

210 20 20 30 50

220 20 40 40 20

250 0 50 50 0

250 0 50 50 0

300 -50 25 50 25

600 -300 0 100 0

NO NEGATIVE PAYOFF

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Choices in High-Stake Original Experiment3.2

-1000 1000

-3000

6000

3000

r(Y)

r(X)

B

C

A

Efficient frontier

Efficient allocation

(Y) (X)

600 1600

700 1400

1000 1000

1000 1200

1400 800

1750 500

1800 400

1900 400

1900 400

2000 333

2100 200

2400 0

2400 0

2500 0

2500 0

2500 0

2500 0

2500 0

1 2 5# observations

95% efficiency

1000

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Comments in High-Stake Original Experiment3.2.1

Y X a b c

600 1600 70 20 10

700 1400 40 10 50

1000 1000 0 0 100

1000 1200 50 20 30

1400 800 30 20 50

1750 500 25 25 50

1800 400 10 20 70

1900 400 30 30 40

1900 400 30 30 40

2000 333 33 33 33

2100 200 20 30 50

2400 0 30 40 30

2400 0 30 40 30

2500 0 50 50 0

2500 0 50 50 0

2500 0 50 50 0

2500 0 50 50 0

2500 0 50 50 0

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

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Control Experiment on Errors (Within-Subjects)3.3

BEfficient frontier

r(Y)

r(X)

C

A

assets offered in control question

r(Y) r(X)

0.0 2.5

0.0 2.5

0.0 2.5

0.0 2.5

0.0 2.5

-0.5 3.5

0.3 2.0

0.6 1.8

1.0 1.0

1.0 1.0

1.0 1.0

1.0 1.0

1.6 0.4

r(X) r(Y)

2.5 0

2.5 0

2.5 0

2.5 0

2.5 0

2.5 0

2.23 0.23

2.23 0.23

1.88 0.58

1.15 1.15

1.15 1.15

1.15 1.15

1.15 1.15

Original question Control question

Result: risk level in control question remains unchanged. No subject chooses any share in C, all decisions are efficient.

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Small-Stake Credit Experiment3.4

B‘

C

A‘

B

A

Efficient frontier

r(Y)

r(X)

Subjects can sell asset C short (once).

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Choices in Small-Stake Credit Experiment3.4.1

r(Y) r(X)

50 200

50 200

110 110

120 120

125 100

130 120

150 80

167 100

167 100

169 98

180 50

200 33

230 0

250 0

250 0

250 0

400 -100

-100 100

-300

600

300

r(Y)

r(X)

B

C

A

Efficient frontier



Erroneous Computation 91% efficiency

100

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Choices High-Stake Credit Experiment3.5

r(Y) r(X)

800 1400

800 1400

1100 1200

1400 1000

2000 333

2100 400

2100 400

2280 50

2300 0

2500 0

2500 0

3100 -600

-1000 1000

-3000

6000

3000

r(Y)

r(X)

B

C

A

Efficient frontier



88% efficiency

1000

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Comments in High-Stake Credit Experiment3.5.1

r(Y) r(X) a b c

800 1400 60 20 20

800 1400 60 20 20

1100 1200 70 30 0

1400 1000 80 40 -20

2000 333 33 33 33

2100 400 70 50 -20

2100 400 70 50 -20

2275 50 17.5 32.5 50

2300 0 10 30 60

2500 0 50 50 0

2500 0 50 50 0

3100 -600 20 50 30

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

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No High-Stake Effect3.6

Original Experiment Credit Experiment

H0: aOR = aHS 0.272 0.107

H0: bOR = bHS 0.864 0.388

H0: cOR = cHS 0.695 0.144

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.

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Risky Portfolio Share in Original Experiment3.7.1

b

a

100%

100%

Results:

(a/b) = 1, symmetry

c = 34%

45°

# observations1 2 3 7


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Risky Portfolio Share in Credit Experiment3.7.2

1 2 5# observations

Results (no credit):

(a/b) = 1, symmetry

c = 35%

# observations


b

a

100%

100%

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.

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Summary of Results5.1

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).

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Conclusion5.2

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.

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THE END

The first rule of investing is not to lose money. The second rule is not to forget the fist rule!

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