58 Frequently Asked Questions In Quantitative Finance
What is Arbitrage Pricing Theory?
Short Answer
The Arbitrage Pricing Theory (APT) of Stephen Ross
(1976) represents the returns on individual assets as
a linear combination of multiple random factors. These
random factors can be fundamental factors or statistical.
For there to be no arbitrage opportunities there must
be restrictions on the investment processes.
Example
Suppose that there are five dominant causes of ran-
domness across investments. These five factors might
be market as a whole, inflation, oil prices, etc. If you
are asked to invest in six different, well diversified
portfolios then either one of these portfolios will have
approximately the same risk and return as a suitable
combination of the other five, or there will be an arbi-
trage opportunity.
Long Answer
Modern Portfolio Theoryrepresents each asset by its
own random return and then links the returns on dif-
ferent assets via a correlation matrix. In theCapital
Asset Pricing Modelreturns on individual assets are
related to returns on the market as a whole together
with an uncorrelated stock-specific random component.
In Arbitrage Pricing Theory returns on investments
are represented by a linear combination of multiple
random factors, with as associated factor weighting.
Portfolios of assets can also be decomposed in this
way. Provided the portfolio contains a sufficiently large
number of assets then the stock-specific component can
be ignored. Being able to ignore the stock-specific risk
is the key to the ‘‘A’’ in ‘‘APT.’’
