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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 […]

# Ito Calculus

This tutorial written and reproduced with permission from Peter Ponzo   Kiyosi Ito studied mathematics in the Faculty of Science of the Imperial University of Tokyo, graduating in 1938. In the 1940s he wrote several papers on Stochastic Processes and, in particular, developed what is now called Ito Calculus. I haven’t […]

# Interest Rates

Overview Interest rates play a key role in the general business cycle and the financial markets. When interest rates change, or interest rate expectations change, the effects are far-reaching. When rates rise, consumers spend less which causes retail sales to slow, which leads to reduced corporate profits, a declining stock […]

# Implied Volatility

This tutorial written and reproduced with permission from Peter Ponzo Historical Volatility (HV) is calculated by looking at historical returns and calculating some kind of average deviation from their mean value using the magic formula for Standard Deviation … also called Volatility. But aren’t their several magic formulas for Standard […]