Arbitrage Pricing Theory Definition

APT is notably used to form a pricing model for the stocks. Compared to the CAPM, the arbitrage pricing model takes into account multiple factors of risk. The elements of risk can be hard to determine in some cases but will often give the investor a more accurate rate of return.

Key Takeaways

  • The APT is an economic model for estimating the expected return of a particular asset, offering an efficient alternative to the capital asset pricing model (CAPM).The concept considers multiple factors of macro-economic risk such as inflation, gross domestic product (GDP), yield curve changes, and changes in interest rates. It estimates the price of an asset by holding a linear function between expected return and these factors.The APT offers more accurate, reliable, and complicated asset pricing results than CAPM.

Arbitrage Pricing Theory Explained

The arbitrage pricing theory model help exploit the short-term profit opportunities presented by the misaligned prices of securities. Individual investors and institutions alike can use the APT to determine the fair value of a particular financial assetFinancial AssetFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more, including:

  • StocksBondsDerivativesDerivativesDerivatives in finance are financial instruments that derive their value from the value of the underlying asset. The underlying asset can be bonds, stocks, currency, commodities, etc. The four types of derivatives are - Option contracts, Future derivatives contracts, Swaps, Forward derivative contracts.
  • read moreCommoditiesCommoditiesA commodity refers to a good convertible into another product or service of more value through trade and commerce activities. It serves as an input or raw material for the manufacturing and production units.read more

To understand APT, let us first take a look at the term arbitrageArbitrageArbitrage in finance means simultaneous purchasing and selling a security in different markets or other exchanges to generate risk-free profit from the security’s price difference. It involves exploiting market inefficiency to generate profits resulting in different prices to the point where no arbitrage opportunities are left.read more. In finance, arbitrage refers to the act of finding discrepancies in the value of an asset through two different markets and taking advantage of the price difference. For example, say an investor found out that Apple’s stock is trading for $120 on the NASDAQ stock exchange and is trading on the Frankfurt stock exchange for $120.50. It offers investors an arbitrage opportunity of $0.50 profit for buying on the Frankfurt stock exchange and selling on the NASDAQ.

You are free to use this image on you website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be HyperlinkedFor eg:Source: Arbitrage Pricing Theory (wallstreetmojo.com)

The APT was first developed in 1976 by former Wharton School of Business professor and economist Stephen Ross. He developed the concept as an alternative to the Capital Asset Pricing Model.

Ross built upon his predecessors’ ideas and knowledge to build a model that considers multiple components of risk that can be used to explain the co-movements among stocks. According to the theory, risk components generate all the co-movements among the assets. Any slight differences can be attributed to the individual securities and not the system as a whole.

Elements of risk

For investors, the more critical risk factor will be the asset’s sensitivity or exposure to risk components. The elements of risk can include:

  • Changes in inflationGross Domestic Product (GDP)Changes in interest ratesYield curveYield CurveA yield curve is a plot of bond yields of a particular issuer on the vertical axis (Y-axis) against various tenors/maturities on the horizontal axis (X-axis). The slope of the yield curve provides an estimate of expected interest rate fluctuations in the future and the level of economic activity.
  • read more changesMarket sentimentsExchange rates

The model was designed to calculate the fair value of an asset, and if the actual value is different, it can be considered either overvalued or undervalued. For example, suppose the arbitrage pricing model estimates the value of Apple’s stock to be $200. But the actual price is $210, and therefore, the stock would be considered overvalued. According to the APT theory, it should correct itself, presenting an arbitrage opportunity.

Arbitrage Pricing Theory Formula

The formula for APT is as follows.

E(x) = Rf + β1 *(factor 1) + β2 *(factor 2) + …+ βn *(factor n)

where,

  • E(x) = the expected return of an assetRf = the expected return assuming zero systematic riskSystematic RiskSystematic Risk is defined as the risk that is inherent to the entire market or the whole market segment as it affects the economy as a whole and cannot be diversified away and thus is also known as an “undiversifiable risk” or “market risk” or even “volatility risk”.read more, or market riskMarket RiskMarket risk is the risk that an investor faces due to the decrease in the market value of a financial product that affects the whole market and is not limited to a particular economic commodity. It is often called systematic risk.read moreβ = the sensitivity the asset has to the risk factor (betaBetaBeta is a financial metric that determines how sensitive a stock’s price is to changes in the market price (index). It’s used to analyze the systematic risks associated with a specific investment. In statistics, beta is the slope of a line that can be calculated by regressing stock returns against market returns.read more)n factor = risk premiumRisk PremiumEquity Risk Premium is the expectation of an investor other than the risk-free rate of return. This additional return is over and above the risk free return.read more

Example

Let us take a look at an arbitrage pricing theory example. For this example, let’s consider our asset as a commodity stock called GOLD 123. The stock has two risk factors associated with it – inflation and the price of the U.S Dollar currency.

Rf (risk free rate) = 2%

Inflation – Risk premium = 2%, Beta = 0.2

U.S Dollar – Risk Premium =10%, Beta = 0.5

E(x) = 0.02 + 0.2 * (0.02) + 0.5 * (0.10)

    = 0.02 + 0.004 + 0.05

    = 0.074, or 7.4%

In this arbitrage pricing theory example, the expected return of GOLD 123 is equivalent to 7.4%.

Assumptions of APT

The arbitrage pricing theory model is based on the following three assumptions.

  • First, participants in a capital marketCapital MarketA capital market is a place where buyers and sellers interact and trade financial securities such as debentures, stocks, debt instruments, bonds, and derivative instruments such as futures, options, swaps, and exchange-traded funds (ETFs). There are two kinds of markets: primary markets and secondary markets.read more execute trades to maximize profit.Second, the capital market is perfectly competitive and frictionless (free access to the markets, freely available information, and abundant traders.)Third, there are no arbitrage cases, and if one presents itself, investors will take advantage of it.

Arbitrage Pricing Theory vs. Capital Asset Pricing Model (CAPM)

Both APT and CAPM modelsCAPM ModelsThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more produce the theoretical rate of return of an asset. Since market risk premium is the only factor considered in the case of CAPM, it is easier to calculate and takes up less time to produce results.

The formula for CAPM is: E(x) = Rf + βn *(E(r)- Rf)

Where:

  • E(x)- expected return of an assetRf- the risk-free rate of returnβ – beta coefficient related to the benchmark indexE(r) – expected return of benchmark index

The two theories are very different in their approaches and assumptions regarding capital markets. Here is how they differ from one another.

  • Factors Considered – The APT considers multiple macroeconomic risk factors. In contrast, the CAPM uses only one factor, i.e., expected market return (based on federal funds rate or the ten-year bond yield.) Accuracy – Since the APT is based on multiple factors, it is typically considered a more accurate model. However, the APT doesn’t specify which factors are used, and hence one will have to establish which element should be used for a particular asset. This can determine how accurate the model is. Asset Relationship – Both the APT and CAPM models assume assets have a linear relationship or that assets move in relation to one another.Assumptions – Both the models assume that assets have unlimited demand and that investors have the same access to information, which may not always be true.Market portfolio- CAPM requires an efficient market portfolio and assumes that the returns are normally distributedNormally DistributedNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more. But APT makes no such assumption and does not require an efficient portfolio.

Which is better – APT vs CAPM?

The APT model provides better efficiency and more reliability. It gives an accurate estimation of long-term asset pricing. But in many cases, one can observe similar results with CAPM, which uses a much simpler means of risk assessment. APT is recommended for single assets while CAPM can be used on an asset portfolio to avoid complicated calculations. In most instances, one can ultimately go with either model determined by the risk factors they choose to involve with an asset.  

This has been a guide to Arbitrage Pricing Theory (APT) and its definition. Here we explain how APT works along with its formula, examples, and assumptions. You can learn more from the following articles –

The arbitrage pricing theory model holds the expected return of a financial asset as a linear relationship with various macroeconomic indices to estimate the asset price. A beta coefficient represents the change in sensitivity of the price to each factor. One can then leverage the arbitrage to make short-term profits that are free of risks.

The APT was first modeled by Stephen Ross in 1976 as an alternative to the capital asset pricing model(CAPM).

APT provides a better risk assessment model than its counterpart, the Capital asset pricing model. The APT uses lesser assumptions than CAPM and makes use of multiple factors instead of taking into account a single risk factor like CAPM. Therefore, the APT provides a more accurate model for long-term asset pricing than CAPM. While APT is more suited for single assets, CAPM can be useful for a portfolio of assets. It is best to choose a risk assessment model depending on the risks one chooses to involve with an asset.

  • ArbitrageArbitrageArbitrage in finance means simultaneous purchasing and selling a security in different markets or other exchanges to generate risk-free profit from the security’s price difference. It involves exploiting market inefficiency to generate profits resulting in different prices to the point where no arbitrage opportunities are left.read moreConvertible ArbitrageConvertible ArbitrageConvertible Arbitrage refers to the trading strategy used in order to capitalize on the pricing inefficiencies present between the stock and the convertible. The person using the strategy takes the long position in the convertible security and the short position in underlying common stock.read moreMerger ArbitrageMerger ArbitrageMerger Arbitrage, also known as risk arbitrage, is an event-driven investment strategy that aims to exploit uncertainties that exist between the period when the M&A is announced and when it is successfully completed. This strategy, mainly undertaken by hedge funds, involves buying and selling stocks of two merging companies to create risk-free profit.read more