CHAPTER 30

Portfolio Optimization and Risk Parity

This chapter discusses portfolio selection techniques, including portfolio optimization methodologies, risk budgeting, and a portfolio construction approach titled risk parity. The primary perspective of this chapter is that of an asset allocator selecting a portfolio from assets including both traditional assets and alternative assets.

30.1 MEAN-VARIANCE PORTFOLIO OPTIMIZATION

The mathematics underlying risk and return were discussed in Chapters 3 and 5. Knowing how to estimate risk and return is useful, but it is even more important to be able to use those estimates to determine the portfolio allocations that can be invested in various assets or asset classes to form a portfolio that meets specific targets for risk and return. The type of question that investors ask is this: Which asset allocation can generate an expected portfolio return of at least 8.4% with a standard deviation of returns of no more than 7.5%? This is a challenging exercise, as the analyst needs to estimate the future returns and risks of each asset class, as well as the correlations between the returns of all asset classes that will be considered for the allocation. Further, the analyst needs to understand how to compute the statistics for the returns of a portfolio based on the statistics of the portfolio's constituent assets and to prioritize among competing goals.

30.1.1 Calculating a Portfolio's Expected Return and Standard Deviation

Consider a three-asset ...

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