Derivation and Modelling of Risk–Return Time Profiles

Paolo Sironi

Time is money.

Benjamin Franklin (1706–90)

In this chapter we present the risk–return profile as a function of time, discuss investors’ styles and personalities, derive the risk and return profiles of risk aversion, and summarise risk mitigation, risk tolerance and other elements of goal-based investing.

INTRODUCTION

The representation of real investors’ preferences and constraints is a key element in making investment decision-making more transparent and intuitive. Modern Portfolio Theory does not allow us to model real investors’ risk–return profiles consistently. The Markowitz approach combines the investors’ utility function and the efficient frontier with reference to a defined single point in time after the optimal market mix of investment opportunities has been indicated, whereas the Black–Litterman approach allows for information asymmetry by introducing investors’ views on excess return (not on risk appetite or on consumption) as a posterior modification of the vector of expected excess returns implied by market equilibrium portfolios. Yet, investors are economic individuals who, rationally or irrationally, express ambitions and fears over time. With this in