Constructing behavioral portfolios

Constructing behavioral portfolios

Meir StatmanLeavey School of Business

Santa Clara University

Question

If you could increase your chances of having a more comfortable retirement by taking more risk, would you:

a. Be wiling to take a little more riskwith all your money?

b. Be willing to take a lot more risk with some of your money?

If you could increase you chances of improving your returns by taking more risk, would you:

=xA lot more risk

Some of your money

Addition to portfolio risk

Risk Money

=x All of your money

A little more risk

Addition to portfolio risk

a.

b.

The plan for this session

Compare

Mean-variance portfolio theory to

Behavioral portfolio theory

Provide tools to implement behavioral portfolio theory

Standard Finance and Behavioral Finance

Standard Finance – Investors are rational.

Behavioral Finance – Investors are normal.

Behavioral Finance

First Lesson

Know YourselfMake yourself your ally

Know your goals

Know your emotions

Know your cognitive biases

Behavioral Finance

Second Lesson

Protect YourselfMake science your ally

Know the science of financial markets.

Know the science of human behavior.

Use the tools of science to overcome cognitive biases and emotions

Mean-variance portfolio theory

Investors consider portfolios as a whole.

Investors care only about expected returns and risk (standard deviation)

of the overall portfolio.

Investors are always averse to risk.

9

Mean-Variance Portfolio Theory

Individual investors care about reaching ultimate goals (retirement, education, travel, charity)

Institutional investors care about reaching ultimate goals. (Pensions, health care, surplus)

(Expected returns and standard deviations are only intermediate goals)

Investors consider their portfolios not as a whole but as a pyramid of distinct mental accounting layers, arranged by

goals

Investors are not always averse to risk

(Investors buy both insurance policies and lottery tickets)

Behavioral Portfolio Theory

11


Behavioral Portfolio TheoryPyramids of mental accounts

arranged by goal

Pensions

Health Care

Surplus

Behavioral portfolio theoryCore and Satellite

A LOT more risk with SOMEof your money

Satellite

Core


Low risk vs. high risk? (Risk budget)

Diversified vs. concentrated?

Passive vs. active?

Downside protection vs. Upside potential?

Satellite

Core

Mean-Variance Portfolio TheoryIt all mixes in the stomach

Investors want highly nourishing and low cost meals.

Behavioral Portfolios TheoryPortfolios from the perspective of the palate as well as the perspective of the stomach. Investors want highly

nourishing and low cost meals. But they also want palatable meals.

Palatable meals are more nutritiousExperiment with Thai and Swedish

women

Mean-variance portfolio theoryEfficient frontier and optimal choice

The one and only question to investors.

What is your utility function?

Or, more intelligibly, which of the combinations of

expected return and standard deviation for

your overall portfolio is optimal for you?

Expected Return

Standard Deviation

5% 3%

6% 5%

7% 10%

12% 18%

14% 20%

Have you ever seen a question like this in any investor questionnaire?

Generally, I prefer investments with little or no fluctuations in value, and I’m willing to accept the

lower return associated with these investments

o Strongly disagreeo Disagreeo Somewhat agreeo Agreeo Strongly agree

Insights from investment questionnairesWhat you are likely to see is a question like this in the

Vanguard questionnaire:

Does the question guide you to the right portfolios on the efficient frontier?

Is it about the portfolio as a whole?Unintelligible questions lead to unintelligble

Behavioral portfolio theoryHow much of your portfolio would you

allocate to each goal

Downside protection

Full Funding

Upside potential 10%

90%

Surplus

Behavioral portfolio theory What is the probability of reaching this

goal?

Different probabilities for different goals

Risk is the probability of not

reaching a goal

I’m virtually sure that my downside is protected

(Almost 100% chance to reach the goal)

I have some chance of upside potential

(20% chance to reach the goal)

Efficient frontier in behavioral portfolio theory

Link between behavioral portfolio theory and value-at-risk (VaR)

Expected return (Aspiration level)

Risk (Probability of failing to achieve this expected return)

When your aspiration level (expected

return) is high, the probability of failing

to reach it is high. This is a version of Value-at-Risk (VaR)

Behavioral portfolio theory Goals are liabilities

Full funding Surplus

Proportion allocated to the goal

90% 10%

Desired probability of reaching the goal

100% 20%

1

2

Outflows minus inflows in each period

3


Use Monte Carlo Simulation to find the best sub-portfolio for each goal.

The overall portfolio is the sum of the sub-portfolios

Is that overall portfolio on the mean-variance efficient frontier?

Committee Work Analysis of 13 Investment Committees

Size of committee: 3-12 with 6 as a median

Managing $20 million to $15 billion

Decisions include:• Investment policy• Asset allocation

• Hiring and managing money managers• Market discussion

• Specific investment options

Payne and Wood

Committee Work

Intellectual tasksThere is a demonstrably correct answer

Judgmental tasksNo clear correct answer

Preferences matterStrength in numbers is often used as the

decision rule

Committee WorkHow committees reach good decisions.

• More information – What are the likely inflows and outflows?– What are likely returns?

• Checking errors in facts and reasoning• Incorporation all preferences• Generating feelings of participation and

acceptance of decisions

Committee WorkHow committees reach poor decisions

Poor information sharingAmplification of cognitive biases and emotions

Social loafingConformity pressures

Polarization of attitudes

The tools of science– The science of financial markets– The science of human behavior

Game

1. I have just given you $20. We will play 20 rounds of a game.

2. You have to choose if you play each round. If you play you have a 50-50 chance to lose $1 or win $1.5.

Do we have stable expectations of returns and attitudes toward risk?

What were our expectations of returns and risk tolerance in late 1999?

What were our expectations of returns and risk tolerance in early 2003?

The role of fear and exuberance (lack of fear) in expectations of returns and risk

tolerance.

Fear decreases our expectations of returns

Fear increases our aversion to risk

Do we have stable expectations of returns and attitudes toward risk?

Do you think that now is a good time to invest in the financial markets?

Percent of investors who said Yes

0

10

20

30

40

50

60

70

80

90

Jun-98 Jun-02 Jun-06

July 07 - 63%

March 03 - 41%

Feb 00 - 78%

Percent

Source: UBS Index of Investor Optimism

From August 31, 2000, through March 31, 2001, stocks lost more than 25%. If I

owned a stock investment that fell more than 35% in 7 months, I would

o Sell all of the remaining investmento Sell a portion of the remaining investmento Hold on to the investment and sell nothingo Buy more of the investment

Insights from investment questionnaires

From the Vanguard questionnaire

Question

Please rate your level of agreement with the following statement on a scale

ranging from “Strongly Disagree” to “Strongly Agree”

“Now is a good time to invest in stocks”

1 2 7 8 9 1063 4 5Strongly Disagree

Strongly Agree

We need to calibrate our level of fear (or exuberance) when we estimate expected returns,

inflows, and outflows.

QuestionnaireReturn

Please circle the number that reflects your perception of the expected return of a broad index of stocks of each country in the following 12 months, from 1 for a low expected return to 10 for a high expected return.

Low Return High Return

Albania 1 2 3 4 5 6 7 8 9 10

Canada 1 2 3 4 5 6 7 8 9 10

Iraq 1 2 3 4 5 6 7 8 9 10

United States 1 2 3 4 5 6 7 8 9 10

QuestionnaireRisk

Please circle the number that reflects your perception of the risk of a broad index of stocks of each country in the following 12 months, from 1 for a low risk to 10 for a high risk.

Low Risk High Risk

Albania 1 2 3 4 5 6 7 8 9 10

Canada 1 2 3 4 5 6 7 8 9 10

Iraq 1 2 3 4 5 6 7 8 9 10

United States 1 2 3 4 5 6 7 8 9 10

Affect

High returns (thrills) and low risk?

Affect

Positive affect, like exuberance, increases risk tolerance.

The relationship between assessments of expected returns and assessment of risk of

210 companies

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Risk score

Exp

ecte

d re

turn

sco

re

Expected return score = 8.6 - 0.5 Risk score (24.4) (-7.2)

R2 = 0.2n = 210

Expectations about future returns and realized past returns

UBS Index of Investor OptimismWhat overall rate of return do you expect to get on your portfolio in the NEXT twelve

months?

02468

101214161820

-40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0

Realized stock return in the past 12-months

Expe

cted

retu

rn in

the

next

12-

mon

ths

Expected future return = 10.6 + 0.1 Realized past return (49.9) (8.4)

r2 = 41.2n = 102

Returns are of the CRSP 1-10 Index

Expectations about future returns and realized future returns

UBS Index of Investor Optimism What overall rate of return do you expect to get on your portfolio in the

NEXT twelve months?

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

0 2 4 6 8 10 12 14 16 18 20

Expected return in the next 12 months

Real

ized

sto

ck re

turn

in th

e ne

xt 1

2 m

onth

s

Realized future return = 21.4 - 1.5 Expected future return (2.9) (-2.3)

r2 = 5.7n = 90

Revising portfoliosRebalancing

After the market has gone up we are tempted to transfer funds to the

“surplus” mental account.

After a particular asset has gone up we are tempted to increase its proportion in

the portfolio (Private equity? Hedge funds? REITs?

Use the tools of science

Conclusion

Behavioral portfolios

Compare

Mean-variance portfolio theory to

Behavioral portfolio theory

Provide tools to implement behavioral portfolio theory

Behavioral portfolios

Behavioral portfolios have a natural fit with liability driven investing

Documents

Constructing behavioral portfolios