# 11_Oheads - Lecture Notes 11 The Arbitrage Pricing Theory...

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1 Lecture Notes 11 The Arbitrage Pricing Theory The basic idea • The APT aims to explain correlations between returns by devel- oping a model of where those correlations come from. • This is most useful when one is attempting to make out of sam- ple predictions. • Since CAPM is based on historical data it is most appropriate when conditions are relatively stable. If conditions change, the beta coefficient estimated from the sample may not correspond to the likely future value. • APT focuses on a small number of sources of systematic risk. • Each source of risk has an implicit “market price” reflected in a “beta coefficient” analogous to the CAPM beta coefficient. • The two models can both be valid. If they are, the APT betas can be thought of as components of the overall CAPM beta.

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2 • APT claims that the required R i on a risky asset i depends on: i. the extent to which each risk affects R i , measured by a set of beta coefficients analogous to the beta coefficient of CAPM; and ii. the risk premiums for bearing the different systematic risks. • To derive a risk premium, we determine the systematic risks af- fecting a cash flow and use the implicit “market prices” to get R . • The idea of arbitrage underlies the APT. Arbitrage ensures that the same “bundle” of systematic risks sells for the same price. Expected and unexpected returns • The expected return R i on an asset i in any given period is not a random variable and is not a source of risk . • The ex-post actual return R i will generally differ from R i as a re- sult of unanticipated or unexpected shocks u i : (1) • Although u i is separate from the expected return R i , risk arises from u i , so the characteristics of u i influence expected return R i . R i R i u i + =
3 Systematic and unsystematic risk • Unexpected returns u i can be further split into: i. a systematic or market risk, which affects u i for many assets and cannot be eliminated by holding a diversified portfolio; and ii. an unsystematic or idiosyncratic risk which can be eliminated by diversification: (2) where, for N assets in the market portfolio with proportion x i in- vested in stock i , the idiosyncratic shocks ε i satisfy . (3) • Also, m i and ε i are uncorrelated and have zero means, since any constant would be included in R i . • Unsystematic risk reflects mainly microeconomic shocks affect- ing relative prices, outputs, and employments. • Systematic risk reflects mainly macroeconomic shocks that af- R i R i u i + R i m i ε i ++ == var x i ε i i 1 = N    0 =

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4 fect the aggregate behavior of the economy. • But the correspondence is not perfect: i. most macroeconomic shocks have microeconomic compo- nents, with risks that may be reduced through diversification.
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## This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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11_Oheads - Lecture Notes 11 The Arbitrage Pricing Theory...

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