Quantitive Analysis

Intro

There are two kinds of investment processes. The first one is fundamental process which is mainly based on human decisions using information and judgement. Secondly is quantitative process in which decisions are computer –driven following fixed rules. The combination of fundamental and quantitative processes is called hybrid .For instance, when a fundamental manager uses a computer-driven stock screening system to narrow his or her portfolio choices. (..)

Main

The history price developments of S&P 500 represent a specific type of simple discrete stochastic process, the so called random-walk. Firstly introduced by Louis Bachelier in 1900, the random walk model proved to be successfully useful to describe the behavior of various financial markets like the equity, commodity and fixed-income markets. The term random walk is based on time-series analyses of past price values. Its increments construct a white-noise process. Changes in returns can be expressed as arithmetic random walks when the increments form a Gaussian white noise and the log return changes are representable by geometric random walks with drift representing long-term returns of equity-investments. Random walks are considered to magnitale processes for all t and all . The value today equals all expected future values. In most of the financial markets random walks are not stationary and fulfill not the conditions of a white-noise process. Due to the positive drift in most of the markets price development, we speak of submagnitale random walk processes, notated as EXt+∆tXt=xt≥ xt. Cuthbertson and Nitzsche (2004) define a random walk with a drift (δ) as an individual stochastic series Xt that behaves as:

Xt= ∂+Xt-1+e(t) where ∂ represents a weighted average of the probabilities of each price the stock price could possibly move to in the next period, called a drift and e(t) is the individual and identically distributed error term with expected value of 0 and a constant, finite variance. The...