Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Home > Modern portfolio theory

First Prev [ 1 2 3 4 ] Next Last

Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how an asset should be priced given its risk relative to the market as a whole. The basic concepts of the theory are the efficient frontier, Capital Asset Pricing Model and beta coefficient, the Capital Market Line and the Securities Market Line.

MPT models the return of an asset as a random variable and a portfolio as a weighted combination of assets; the return of a portfolio is thus also a random variable and consequently has an expected value and a variance. Risk in this model is identified with the standard deviation of portfolio return. Rationality is modeled by supposing that an investor choosing between several portfolios with identical expected returns, will prefer that portfolio which minimizes risk.

1 Risk and reward

The model assumes that investors are risk averse. This means that given two assets that offer the same return, investors will prefer the less risky one. Thus, an investor will take on increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher returns must accept more risk. The exact trade-off will differ by investor. The implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more favourable risk-return profile - i.e. if for that level of risk an alternative portfolio exists which has better expected returns.

1.1 Mean and variance

It is further assumed that investor's risk / reward preference can be described via a quadratic utility function. The effect of this assumption is that only the expected return, i.e. mean return, and the volatility, i.e. the standard deviation, matter to the investor. The investor is indifferent to other characteristics of the distribution of returns, such as its skew. Note that the theory uses an historical parameter, volatility, as a proxy for risk while return is an expectation on the future.

Under the model:

Portfolio return is the component-weighted return (the mean) of the constituent assets. Return changes linearly with component weightings, .
Portfolio volatility is a function of the correlationIn probability theory and statistics, the correlation also called correlation coefficient between two random variables is found by dividing their covariance by the product of their standard deviations. It is defined only if these standard deviations are f of the component assets. The Change in volatility is non-linear as the weighting of the component assets changes.

Mathematically:

In general:

Expected return:

Portfolio variance:

The variance of the portfolio will be the sum of the product of every asset pair's weights and covarianceIn probability theory and statistics, the covariance between two real-valued random variables X and Y with expected values and is defined as: : where E is the expectation operator. This is equivalent to the following formula which is commonly used in actu, - this sum includes the squared weight and variance (or ) for each individual asset. Covariance is often expressed in terms of the correlationIn probability theory and statistics, the correlation also called correlation coefficient between two random variables is found by dividing their covariance by the product of their standard deviations. It is defined only if these standard deviations are f in returns between two assets where

Portfolio volatility:

For a two asset portfolio:

Portfolio return:

Portfolio variance:

For a three asset portfolio, the variance is:

(As can be seen, as the number of assets (n) in the portfolio increases, the calculation becomes “computationally intensive” - the number of covariance terms = n (n-1) /2. For this reason, portfolio computations usually require specialized software. These values can also be modeled using matricesAbstract algebra Algebra Linear algebra In mathematics, a matrix (plural matrices is a rectangular table of numbers or, more generally, of elements of a fixed ring. In this article, if unspecified, the entries of a matrix are always real or complex number; for a manageable number of assets, these statistics can be calculated using a spreadsheetA spreadsheet is a rectangular table (or grid) of information, often financial information. It is, therefore, a kind of matrix. The word came from "spread" in its sense of a newspaper or magazine item (text and/or graphics) that covers two facing pages, e.)

Politics	Business	Finance

Topics: Modern Portfolio Theory Risk Asset Return Market Assets...

ModernismThis article focuses on the cultural movement labeled 'modernism' or 'the modern movement'. See also: Modernism (Roman Catholicism) or Modernist Christianity; Modernismo for specific art movement(s) in Spain and Catalonia. Just as the ancients drew the in	Modern danceModern dance is a dance form developed in the early 20th century. Although the term Modern dances has also been applied to a category of 20th Century ballroom dances, Modern dance as a term usually refers to 20th century concert dance. In the early 1900s	Modern naval tacticsModern Naval Tactics It is tempting to regard modern naval combat as the purest expression of tactics. There is no cover, there are no civilians and the area of combat is level and flat. It is a pity that this isn't true. The presence of land, changing wa
Modern pentathlonGoudi Sports Complex on August 26, 2004. The modern pentathlon is a sports contest consisting of 5 events, hence the name pentathlon''. The events are epee fencing, pistol shooting, 200 m freestyle swimming, a show jumping course on horseback, and a cross	Modern TimesModern Times Overview Release Date 1936 Video Release July 10, 2003 MPAA Rating G Runtime 89 minutes Academy Awards ''None Cast Charlie Chaplin Paulette Goddard Henry Bergman Chester Conklin Tiny Sandford Hank Mann Stanley Blystone Allan GarciaCrew Direct	Modern discovery of Babylonia and AssyriaFor many centuries knowledge of Babylonia and Assyria was largely confined to the often dubious classical sources. See also Classical authorities of Babylonia and Assyria The Nineteenth Century The excavations of P. Botta and Austen H. Layard at Nineveh a
Modern evolutionary synthesis	Modern animation of the United States	Modern Orthodox Judaism
Modern art	Modern world	Modernity
Modern Dances	Modern English	Modern Islamic philosophy

Non User