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# Linear Regression

This tutorial written and reproduced with permission from Peter Ponzo We assume that some set of variables, y1, y2, … yK, is dependent upon variables xk1, xk2, … xkn (for k = 1 to K). We assume the relationship betwen the ys and xs is “almost” linear, like so: [1] y1 = ß0 + ß1×11 + ß2×12 + … +ßnx1n + e1 y2 = ß0 + ß1×21 + ß2×22 + … +ßnx2n + e2 …….. yK = ß0 + ß1xK1 + ß2xK2 + … […]

# Kurtosis

This tutorial written and reproduced with permission from Peter Ponzo I want to talk about a total Portfolio gain, over N years (or days or months), and how it depends upon the MEAN return and the distribution of returns and … Like Normal of Lognormal stuff? Yes. Suppose that the […]

# Johnson Curves

This tutorial written and reproduced with permission from Peter Ponzo I’ve never been enthusiastic about the common assumptions that stock returns are distributed normally or lognormally or … whatever. For example, the normal and lognormal distributions look like Figure 1a. The normal density distribution is described by:   [1]   […]

# Statistical Distribution

This tutorial written and reproduced with permission from Peter Ponzo You stare raptly at a collection of stock returns and ask: Are they distributed Normally or maybe Lognormally or may something else? Or, you’ve found some strange formula which generates random returns and you ask: Are they distributed Normally or […]

# Correlations

This tutorial written and reproduced with permission from Peter Ponzo We’re talking about generating joint distributions for two variables, say x and y, with prescribed properties. Just two? Pay attention! Before we run, we walk. For example, we introduced the 1-parameter family of Frank’s Copulas:   [F1]   where (for […]