The Cambridge Centre for Climate Change Mitigation Research (4CMR) 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

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 log e (wealth) that is additive. If one is risk neutral in terms of log e (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