Two-Period Model: Mean-Variance Approach

Indeed we will start our journey to financial markets with only one step: the step from one time period (in which we invest into assets) to another time period (in which the assets pay off). To make this two-period model even simpler, we assume in this chapter mean-variance preferences mean-variance preferences. We will see later that this model is a special case of two-period models with more general preferences (Chap. 4 ) and that we can extend the model to arbitrarily many time-periods (Chap. 5 ). Finally we generalize to continuous model continuous models, where the time does not any longer consists of discrete steps (Chap. 8 ). For now, the assumptions of two periods and mean-variance preferences allow us to get some intuition on financial markets without being overwhelmed by an overdose of mathematical formalism. Nevertheless, we want to point out that this simplicity comes at a price: we need to impose strong and not very natural assumptions. In Sect. 2.3 , we have seen some of the potential problems of the mean-variance approach. In practical applications, however, this approach is still standard. We will use it to develop a first model of asset pricing, the so-called “Capital Asset Pricing Model” ( capital asset pricing model CAPM see capital asset pricing model CAPM). This model has been praised by many researchers in finance, and in 1990 Markowitz and Sharpe were awarded the Nobel Prize in economics for its development.