Discussion of ‘Portfolio Optimisation for the
Anxious’ presented by Greg Davies
Behavioural Finance Working Group Conference
Fairness, Trust and Emotions in Finance
1–2 July 2010
Behavioural Finance Working Group
Cass Business School
London
Martin Sewell
[email protected]
The Cambridge Centre for Climate Change Mitigation Research (4CMR)
Introduction
• The problem of how to maximize growth of wealth has been solved:
maximize the expected value of the logarithm of wealth after each period
(Kelly 1956, Breiman 1961)
• Most investors are unwilling to endure the volatility of wealth that such a
strategy entails
• Risk preferences are a personal thing
Normative vs descriptive
• Normative — economists, expected utility hypothesis (Bernoulli 1738, von
Neumann and Morgenstern 1944)
problem: risk preferences undefined
• Descriptive — psychologists, prospect theory (Kahneman and Tversky
1979, Tversky and Kahneman 1992)
problem: people will pay for risk (e.g. lottery), detrimental to wealth
Note that there are two fundamental reasons why prospect theory (which
calculates value) is inconsistent with the expected utility hypothesis:
• Whilst utility is necessarily linear in the probabilities, value is not.
• Whereas utility is dependent on final wealth, value is defined in terms
of gains and losses (deviations from current wealth).
Loss aversion
• The idea of loss aversion is that losses and disadvantages have a greater
impact on preferences than gains and advantages.
The figure is descriptive,
based on empirical data
Risk aversion
The figure is descriptive,
based on empirical data
• When wealth is generated by a multiplicative process such as a financial
market, it is loge(wealth) that is additive.
• If one is risk neutral in terms of loge(wealth), because the log utility
function is concave, it follows that one must exhibit a small degree of risk
aversion regarding wealth.
Endowment effect
• The evolution of private property gave rise to the endowment effect
(Gintis 2007).
• The endowment effect is the phenomenon in which people value a good
or service more once their property right to it has been established
(Thaler 1980).
Are we really just conservative?
• Endowment effect leads to loss aversion
• Endowment effect leads to risk aversion
• Endowment effect is an example of the status quo bias
Time horizon and risk
• No one takes the future quite as seriously as the present.
• People generally prefer to have benefits today rather than in the future.
• This is quite rational.
• The academics Samuelson (1969) and Merton (1969) have shown that,
for investors with utility functions characterized by constant relative risk
aversion, the optimal asset-allocation strategy is independent of the
investment horizon.
• The above is counter-intuitive, and investment managers generally
subscribe to the principle of time diversification.
Normative + descriptive = prescriptive?
• Normative — economists, e.g. expected utility hypothesis
• Descriptive — psychologists, e.g. prospect theory
• Prescriptive — investment managers, e.g. Portfolio optimization for the
anxious