# Arbitrage Pricing Model APT - Novel Approaches and Tools

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The Arbitrage Pricing Model APT – A New Approach to Explaining Asset Prices

Financial Risk Manager (FRM®), Part 1 of the FRM Exam covers the fundamental tools and techniques used in risk management and the theories that underlie their use. Arbitrage Pricing Theory.

Welcome to the 7th lecture in the preparation of FRM Part 1 exam. In this lecture, we will study a relatively new pricing model based on arbitrage. APT, or the Arbitrage Pricing Theory or the Arbitrage Pricing Model, is a pricing model based on the concept of arbitrage. Arbitrage is used to define a situation where one can earn riskless profit by entering into two reverse trades at one time. Such an opportunity does not exist for long, as investors will act to quickly drive away such opportunity. As such, at equilibrium, arbitrage opportunity does not exist. This model also overcomes some shortcomings of the CAPM as it is a multifactor model and does not need to depend on the market return. Here we can use multiple risk factors that drive asset prices to arrive at the arbitrage-free price of the asset.

AGENDA

We will begin our discussion with the assumptions underlying the Arbitrage Pricing Theory. Based on these assumptions, we will derive the mathematical expression for the model and then we will see how it compares to the CAPM. Finally, we will see the applications of APT in passive and active investment management.

ASSUMPTIONS

Let us begin with the first assumption of APT: There is no opportunity for arbitrage, and equivalent assets that give the same return and have similar risk cannot be sold at different prices, as investors will quickly act to generate the riskless profit and drive away the opportunity. For example, if the same security is selling at \$20 and \$25 at two different places, then immediately investors will purchase at \$20 and sell at \$25 at the same time, thus earning a riskless profit of \$5. In the second assumption, the returns are dependent on multiple risk factors, and dependence on just market risk as in CAPM is not necessary. Also, as in CAPM, the unsystematic risk can be diversified away and the investor is rewarded only for bearing the systematic risk.

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