Chapter 9Some Basic Concepts of Portfolio Theory
Portfolio theory studies two related problems: (1) how to construct a portfolio with desirable properties and (2) how to evaluate the performance of a portfolio. In this chapter, we concentrate on the concepts related to the construction of portfolios. A portfolio is constructed by allocating the available wealth among some basic assets. The return of a portfolio is a weighted average of the returns of the basic assets, the weights expressing the proportion of wealth allocated to each basic assets. There exist also portfolios that require zero initial wealth. Such portfolios are constructed using borrowing or option writing.
A main topic of the chapter is to introduce concepts related to the comparison of return and wealth distributions, and this topic is addressed in Section 9.2. In order to study portfolio construction we need to define what it means that a wealth distribution or a return distribution is better than another such distribution. (Here wealth distribution means the probability distribution of wealth, when wealth is considered as a random variable, and we do not mean the distribution of wealth in the sense of allocation of wealth among different people.) In portfolio selection we try to select the weights of basic assets so that the distribution of the return of the portfolio is in some sense optimal.
The optimal distribution of the return is such that the expected return is high but the risk of negative returns ...
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