Measuring Financial Investors Risk Aversion Guillaume Cousin, Be-Partner Philippe Delqui, INSEAD...
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Informs NovemberCousin(Be-Partner) – Delquié (INSEAD)3 Our context Asset managers describe portfolio with annual expected returns and standard deviation For one investor, identify the best point on the efficient frontier Expected returns Volatility Most Risky Least Risky Efficient Frontier Best Portfolio for the investor Investor’s iso-utility curve
Transcript of Measuring Financial Investors Risk Aversion Guillaume Cousin, Be-Partner Philippe Delqui, INSEAD...
Measuring Financial Investor’s Risk Aversion
Guillaume Cousin, Be-PartnerPhilippe Delquié, INSEAD
INFORMS San Antonio, November 2000
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 2
Risk aversion and other criteria
• Objectives • Time Horizon • Age• Available income• Market products• Taxes, fees
Yes
Deterministic
Consumption planning Is there any
investment possible for
you ?
No
Reconsider criteria
Consider Risk Aversion
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 3
Our context• Asset managers describe portfolio with annual
expected returns and standard deviation
• For one investor, identify the best point on the efficient frontier
Expected returns
Volatility
Most Risky
Least Risky
Efficient Frontier
Best Portfolio for the investor
Investor’s iso-utility curve
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 4
General Framework
• Psychology
• Economics
• Finance
Return
Risk
U(W)
W
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 5
Basic Elements
• Investment amount, time horizon
• Efficient frontier
• Family of lognormal distributions of final wealth
$ 5000 for 5 years
Return
Risk
=
+
Outcomes
Probability of outcomes
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 6
Approaches to capturing Preferences• Optimization • Indifference
Return
Risk
Best Portfolio
? ?
Return
Risk
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 7
Optimization MethodAdjustable Lottery
Return
Risk
$ -3000 $ -1700 $ 0 $ 1000 $ 2500
Investor modifies both
return and volatility to
find best distribution
These are two extreme references
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 8
Indifference MethodInvestor adjusts gains or
probabilities to create indifferenceProbabilities
Gains
Return
Risk
Reference lottery
Adjustable Lottery
We confront Investor with risk increase or return decrease
Gains
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 9
Outcomes Adjustment
• Investor uses scroll-bar to shift Gains. Probabilities are constant.
50%
40%
$ -3337 $ -2354 $ 0 $ 3495 $ 6990
2% 6%
Gains
These values depend on lognormal distribution
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 10
Probabilities Adjustment• Outcomes are fixed. Probabilities adjusted so as to keep a
lognormal distribution. Both expected returns and volatility are affected.
2% 6%
50%
40%
Maximum loss
(Market)
Maximum loss acceptable by
investor
$ -5000 $ -1000 $ 0
No gain, no loss
Investor’s goal
$ 5000 $ 7000
Maximum gain
(Market)
Investor
Informs 2000 - November Cousin(Be-Partner) – Delquié (INSEAD) 11
Challenges
• Consistency between different approaches ?• Validation of the link between observed Portfolios
and ”true” risk preferences ?
Risk W
U(W)Return
?
• What is the right link between Psychology and Financial Engineering ?
Extreme concavity
