Modern Portfolio Theory

Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced. The basic concepts of the theory are Markowitz diversification, the efficient frontier, capital asset pricing model, the alpha and beta coefficients, the Capital Market Line and the Securities Market Line.
MPT models an asset's return as a random variable, and models a portfolio as a weighted combination of assets so that the return of a portfolio is the weighted combination of the assets' returns. Moreover, a portfolio's return is a random variable, and consequently has an expected value and a variance. Risk, in this model, is the standard deviation of return.

Mosaic theory

In finance is the method used in security analysis to gather information about a corporation. Mosaic theory involves collecting information from different sources, public and private, to calculate the value of security. Applying the mosaic theory is as much art as it is science. An analyst gleans as many pieces of information as possible, see if they tell a story that makes sense, and decide whether to do a trade.

Using mosaic theory requires substantial experience and logic to put together the various pieces of information, for some of them may be pure speculation.

Technical Analysis

Technical analysis is a security analysis technique that claims the ability to forecast the future direction of prices through the study of past market data, primarily price and volume. In its purest form, technical analysis considers only the actual price and volume behavior of the market or instrument. Technical analysts, sometimes called "chartists", may employ models and trading rules based on price and volume transformations, such as the relative strength index, moving averages, regressions, inter-market and intra-market price correlations, cycles or, classically, through recognition of chart patterns.

Technical analysis stands in distinction to fundamental analysis. Technical analysis "ignores" the actual nature of the company, market, currency or commodity and is based solely on "the charts," that is to say price and volume information, whereas fundamental analysis does look at the actual facts of the company, market, currency or commodity. For example, any large brokerage, trading group, or financial institution will typically have both a technical analysis and fundamental analysis team.

Technical analysis is widely used among traders and financial professionals, and is very often used by active day traders, market makers, and pit traders. In the 1960s and 1970s it was widely discredited by academic mathematics. In a recent review, Irwin and Park reported that 56 of 95 modern studies found it produces positive results, but noted that many of the positive results were rendered dubious by issues such as data snooping so that the evidence in support of technical analysis was inconclusive; it is still considered by many academics to be pseudoscience.

Academics such as Eugene Fama say the evidence for technical analysis is sparse and is inconsistent with the weak form of the efficient market hypothesis. Users hold that even if technical analysis cannot predict the future, it helps to identify trading opportunities.

Fundamental Analysis

Fundamental analysis of a business involves analyzing its financial statements and health, its management and competitive advantages, and its competitors and markets. The term is used to distinguish such analysis from other types of investment analysis, such as quantitative analysis and technical analysis.

Fundamental analysis is performed on historical and present data, but with the goal of making financial forecasts.

There are several possible objectives:
a. to conduct a company stock valuation and predict its probable price evolution,
b. to make a projection on its business performance,
c. to evaluate its management and make internal business decisions,
d. to calculate its credit risk.

Efficient-market hypothesis

In finance, the efficient-market hypothesis (EMH) asserts that financial markets are "informationally efficient", or that prices on traded assets, e.g., stocks, bonds, or property, already reflect all known information. The efficient-market hypothesis states that it is impossible to consistently outperform the market by using any information that the market already knows, except through luck.

Information or news in the EMH is defined as anything that may affect prices that is unknowable in the present and thus appears randomly in the future.
The EMH was developed by Professor Eugene Fama at the University of Chicago Booth School of Business as an academic concept of study through his published Ph.D. thesis in the early 1960s at the same school.

It was widely accepted up until the 1990s, when behavioral finance economists, who were a fringe element, became mainstream. Empirical analyses have consistently found problems with the efficient markets hypothesis, the most consistent being that stocks with low price to earnings (and similarly, low price to cash-flow or book value) outperform other stocks.

Alternative theories have proposed that cognitive biases cause these inefficiencies, leading investors to purchase overpriced growth stocks rather than value stocks. Although the efficient markets hypothesis has become controversial because substantial and lasting inefficiencies are observed, it remains a worthwhile starting point.

Signal Processing

The MACD is a filtered measure of the velocity. The velocity has been passed through two first order linear low pass filters. The "signal line" is that resulting velocity, filtered again. The difference between those two, the histogram, is a measure of the acceleration, with all three filters applied. The "MACD crossing the signal line" suggests that the direction of the acceleration is changing. "MACD line crossing zero" suggests that the average velocity is changing direction.

Trading Signals

MACD, which stands for Moving Average Convergence / Divergence, is a technical analysis indicator created by Gerald Appel in the 1960s. It shows the difference between a fast and slow exponential moving average (EMA) of closing prices. During the 1980s MACD proved to be a valuable tool for any trader. The standard periods recommended back in the 1960s by Gerald Appel are 12 and 26 days:

A signal line (or trigger line) is then formed by smoothing this with a further EMA. The standard period for this is 9 days,

The difference between the MACD and the signal line is often calculated and shown not as a line, but a solid block histogram style. This construction was made by Thomas Aspray in 1986. The calculation is simply
histogram = MACD − signal

The example graph above shows all three of these together. The upper graph is the prices. The lower graph has the MACD line in blue and the signal line in red. The solid white histogram style is the difference between them.

The set of periods for the averages, often written as say 12,26,9, can be varied. Appel and others have experimented with various