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# CHAPTER 3Quantitative Foundations

Quantitative tools and quantitative analysis are foundational concepts in alternative assets. This chapter provides details regarding return computation and analysis.

## 3.1 Return and Rate Mathematics

Returns can be computed with different compounding assumptions and, over time, with intervals of different lengths. These choices have implications for the mathematics and statistics of the returns. This section demonstrates, among other things, the usefulness of basing return computations on continuous compounding, which is tantamount to saying that the returns should be expressed as log returns.

### 3.1.1 The Compounding Assumption

Compounding is the recognition of interest on interest or, more generally, earnings on earnings. Simple interest is an interest rate computation approach that does not incorporate compounding. But returns are often compounded. For example, earning 10% over one year is equivalent to earning 9.64% per year compounded quarterly: [1 + (.0964/4)]4 = 1.10.

Continuous compounding assumes that earnings can be instantaneously reinvested to generate additional earnings. Discrete compounding includes any compounding interval other than continuous compounding such as daily, monthly, or annual.

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