The Arbitrage Pricing Theory APT

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Lecture 11

• The Arbitrage Pricing Theory (APT)

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Basic Idea
APT aims to explain correlation between returns.
Whereas CAPM focuses on market risk, the APT
argues that each source of systematic risk will
have an implicit market price.
Arbitrage ensures that the same bundle of
systematic risks has to sell for the same price.
To derive an appropriate risk premium
for an asset, we attempt to forecast the
systematic risks affecting that asset and then
use the implicit market prices of the factors.
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Expected and Unexpected Returns
The ex-post actual return will generally be
different from as a result of
unanticipated or unexpected shocks
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Systematic and Unsystematic Risk
Decompose as
systematic or market risk can not be eliminated
by holding a diversified portfolio
unsystematic or idiosyncratic risk can be
eliminated by diversification
The market portfolio with N assets, and
proportion invested in asset i, the
idiosyncratic risk satisfy
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Systematic and Unsystematic Risk (continued)
Unsystematic risk reflects mainly microeconomic
shocks affecting relative prices, outputs and
employments.
Systematic risk reflects mainly macroeconomic
shocks that affect aggregate behavior of the
economy.
The correspondence is not, however, perfect
some microeconomic shocks such as changes in
technology or the supply of oil, can have
pervasive effects on many firms.
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Example Problem 11.2
Suppose a three factor model describes the
returns on a stock.
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Example Problem 11.2 (continued)
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As with CAPM, the beta coefficients are obtained
in practice from performing a regression analysis
using historical returns data.
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Expected Returns
In a well-diversified portfolio, only systematic
risk is relevant for determining expected returns.
A stock with no risk (I.e. not affected by any
risk factors) will have expected return r.
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Expected Returns (continued)
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Actual Returns under APT
Unexpected movements in each factor affect
unexpected returns in proportion
to the beta coefficient for the factor.

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Actual Returns under APT (continued)
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The APT and CAPM
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The APT and CAPM (continued)
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Problem 11.6
You can invest in only one of two stock markets,
each driven by the same common force F (mean 0,
standard deviation 10). The expected return on
every stock in either market is 10.
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Problem 11.6 (continued)
If the correlation between surprises in returns
on any two stocks is zero in each market, in
which market would a risk-averse person prefer to
invest? (Market 2)
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Problem 11.6 (continued)
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Problem 11.6 (continued)