Capital asset pricing modelIn finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.
Asset pricingIn financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.
Efficient-market hypothesisThe efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. Because the EMH is formulated in terms of risk adjustment, it only makes testable predictions when coupled with a particular model of risk.
Fundamental theorem of asset pricingThe fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitrage-free, and for a market to be complete. An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss. Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit.
Arbitrage pricing theoryIn finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, it is widely believed to be an improved alternative to its predecessor, the Capital Asset Pricing Model (CAPM). APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually realised.
Financial modelingFinancial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project, or any other investment. Typically, then, financial modeling is understood to mean an exercise in either asset pricing or corporate finance, of a quantitative nature. It is about translating a set of hypotheses about the behavior of markets or agents into numerical predictions.
Rational pricingRational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.
Financial economicsFinancial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
ArbitrageIn economics and finance, arbitrage (ˈɑːrbᵻtrɑːʒ, -trɪdʒ) is the practice of taking advantage of a difference in prices in two or more markets; striking a combination of matching deals to capitalise on the difference, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs.
Financial engineeringFinancial engineering is a multidisciplinary field involving financial theory, methods of engineering, tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance. Financial engineering plays a key role in a bank's customer-driven derivatives business — delivering bespoke OTC-contracts and "exotics", and implementing various structured products — which encompasses quantitative modelling, quantitative programming and risk managing financial products in compliance with the regulations and Basel capital/liquidity requirements.
Brownian model of financial marketsThe Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F. Sharpe, and are concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic processes. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes.
Algorithmic tradingAlgorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price, and volume. This type of trading attempts to leverage the speed and computational resources of computers relative to human traders. In the twenty-first century, algorithmic trading has been gaining traction with both retail and institutional traders. A study in 2019 showed that around 92% of trading in the Forex market was performed by trading algorithms rather than humans.
Filtration (mathematics)In mathematics, a filtration is an indexed family of subobjects of a given algebraic structure , with the index running over some totally ordered index set , subject to the condition that if in , then . If the index is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic structure gaining in complexity with time.
Covered interest arbitrageCovered interest arbitrage is an arbitrage trading strategy whereby an investor capitalizes on the interest rate differential between two countries by using a forward contract to cover (eliminate exposure to) exchange rate risk. Using forward contracts enables arbitrageurs such as individual investors or banks to make use of the forward premium (or discount) to earn a riskless profit from discrepancies between two countries' interest rates. The opportunity to earn riskless profits arises from the reality that the interest rate parity condition does not constantly hold.
Statistical arbitrageIn finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days). These strategies are supported by substantial mathematical, computational, and trading platforms. Broadly speaking, StatArb is actually any strategy that is bottom-up, beta-neutral in approach and uses statistical/econometric techniques in order to provide signals for execution.
Automated trading systemAn automated trading system (ATS), a subset of algorithmic trading, uses a computer program to create buy and sell orders and automatically submits the orders to a market center or exchange. The computer program will automatically generate orders based on predefined set of rules using a trading strategy which is based on technical analysis, advanced statistical and mathematical computations or input from other electronic sources. These automated trading systems are mostly employed by investment banks or hedge funds, but are also available to private investors using simple online tools.
Day tradingDay trading is a form of speculation in securities in which a trader buys and sells a financial instrument within the same trading day, so that all positions are closed before the market closes for the trading day to avoid unmanageable risks and negative price gaps between one day's close and the next day's price at the open. Traders who trade in this capacity are generally classified as speculators. Day trading contrasts with the long-term trades underlying buy-and-hold and value investing strategies.
Martingale (probability theory)In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Originally, martingale referred to a class of betting strategies that was popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins their stake if a coin comes up heads and loses it if the coin comes up tails.
Valuation using discounted cash flowsValuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money. The cash flows are made up of those within the “explicit” forecast period, together with a continuing or terminal value that represents the cash flow stream after the forecast period. In several contexts, DCF valuation is referred to as the "income approach".
