Greg B Davies PhD Head of Behavioural Finance gregdavies2barclayswealthcom June 2010 2 The market can stay irrational longer than you can stay solvent John Maynard Keynes Harry Markowitz Nobel Prize 1990 ID: 262492
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Slide1
Portfolio Optimisation for the Anxious
Greg B Davies, PhD
Head of Behavioural Finance
greg.davies2@barclayswealth.com
June 2010Slide2
2
“The market can stay irrational, longer than you can stay solvent”
John Maynard Keynes
Harry Markowitz – Nobel Prize 1990
Daniel Kahneman – Nobel Prize 2002Slide3
Value function in descriptive theories: CPT
Losses (£)
Utility
Loss aversion: Steeper for losses
Reference Point
Gains (£)Slide4
4
And with risk=variance, expected utility theory is equivalent to mean-variance optimisation
Portfolio Efficient Frontier
Risk free rate
Market Portfolio
Optimal Portfolio
Risk/Return Trade-off
(Indifference Curve)Slide5
5
Only works under specific, and largely incorrect assumptions
Only true if one of two assumptions holds:
Log Returns are normally distributed (no fat tails; no black swans; no skewness)
OR
Individuals have a rational utility function that is quadratic
Neither assumption is valid
Example Quadratic Utility Function
Return
UtilitySlide6
6
This means both the risk measure and the risk-return trade-off are flawed
Risk free rateSlide7
The exponential function shows aversion to left tail events and preference for positive skewness in log returns
Low Risk Tolerance
Medium Risk Tolerance
High Risk Tolerance
Utility
Log returns
All display CRRA throughout domainSlide8
8
These result in a remarkably simple rational trade-off between adjusted risk and expected returns
Desirability
Expected Excess Returns
Total return – risk-free return
Compensation for risk
Risk / Risk Tolerance Slide9
9
Illustrating in risk-return space
Risk free return
All components measured in % log returns
Reject
Accept
Risk compensation
Desirability
Maximum Desirability
DesirabilitySlide10
10
Because risk is mis-specified, the mean-variance ‘efficient’ frontier is not truly risk-return efficient
Desirability
(In)efficient Frontier
True Efficient FrontierSlide11
11
Traditional portfolio theory trades off risk and return of the portfolio in the long run
Portfolio Risk
Expected Portfolio Return
Efficient Frontier
Low risk tolerance, low portfolio risk, low return
High risk tolerance, high portfolio risk, high returnSlide12
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12
The emotional experience with the investment journey has potentially greater influence on the final result
Which investor is happier?
(Green, black or red)
Portfolio Value
Time
Danger of selling low
Danger of buying highSlide13
Ulysses
Self-control
Dual self model
Two systems of reasoningMethods for self-controlDifferences in short-term and long-term distributions
13Slide14
The short term investor has a further emotional transformation of returns
Composure value function
Rational linear functionSlide15
Investors with short-term reactions will attribute utility to returns differently to long-term rational investors
Loss aversionSlide16
Investors with short-term reactions will attribute utility to returns differently to long-term rational investors
Loss aversionSlide17
17
These result in a remarkably simple rational trade-off between adjusted risk and expected returns
Desirability
Expected Excess Returns
Total return – risk-free return
Compensation for risk
Risk / Risk Tolerance Slide18
18
Effect can be completely reflected through a separate Anxiety score for any investment
Compensation for risk
Compensation for Anxiety
(
relative to risk free)
Excess Returns
DesirabilitySlide19
19
Introducing the Anxiety measure
Total psychological compensation for returns variability
Compensation for rational risk
Reduction in anxiety from existence of risk free investmentSlide20
20
Illustrating in risk-return space
Risk free return
All components measured in % log returns
Reject
Accept
Risk compensation
Desirability
Maximum Desirability
DesirabilitySlide21
21
Representing Anxiety graphically
Risk free return
Reject
Accept
Risk compensation
Maximum Desirability
Desirability
ANXIETYSlide22
22
Portfolio optimisation for the anxious
Desirability
True Efficient Frontier
Maximum DesirabilitySlide23
23
Portfolio optimisation for the anxious
Desirability
True Efficient FrontierSlide24
24
Portfolio optimisation for the anxious
Desirability
True Efficient Frontier
AnxietySlide25
25
Portfolio optimisation for the anxious
True Efficient Frontier
Anxiety Efficient FrontierSlide26
26
Portfolio optimisation for the anxious
True Efficient Frontier
Anxiety Efficient Frontier
DesirabilitySlide27
Why would we use this?
Pander to short term self
Understand costs of Anxiety
Bargaining between planner and doerUse small degree of short-term preferences to ‘take off the edge’Use different time horizons to overcome myopia
27Slide28
28
The effect of time horizon on risk and desirabilitySlide29
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The effect of time horizon on anxietySlide30
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The effect of time horizon on anxietySlide31
31
Desirability for the rational and the anxious