National open university of nigeria introduction to econometrics I eco 355

3.4.1. Relationship with the capital asset pricing model 
The APT along with the capital asset pricing model (CAPM) is one of two influential 
theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in 
its assumptions. It allows for an explanatory (as opposed to statistical) model of asset 
returns. It assumes that each investor will hold a unique portfolio with its own particular 
array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM 
can be considered a "special case" of the APT in that the securities market line represents 
a single-factor model of the asset price, where beta is exposed to changes in value of the 
market. 
Additionally, the APT can be seen as a "supply-side" model, since its beta coefficients 
reflect the sensitivity of the underlying asset to economic factors. Thus, factor shocks 
would cause structural changes in assets' expected returns, or in the case of stocks, in 
firms' profitabilities. 
On the other side, the capital asset pricing model is considered a "demand side" model. 
Its results, although similar to those of the APT, arise from a maximization problem of 
each investor's utility function, and from the resulting market equilibrium (investors are 
considered to be the "consumers" of the assets). 
3.4.2. Co integration 
Co integration is a statistical property of a collection (X
1
,X
2
,...,X
k
) of time series 
variables. First, all of the series must be integrated of order 1 (see Order of Integration). 
Next, if a linear combination of this collection is integrated of order zero, then the 
collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order 1, 
and there exist coefficients a,b,c such that aX+bY+cZ is integrated of order 0, then X,Y, 
and Z are co integrated. Co integration has become an important property in 
contemporary time series analysis. Time series often have trends — either deterministic 
or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided 
statistical evidence that many US macroeconomic time series (like GNP, wages, 
employment, etc.) have stochastic trends — these are also called unit root processes, or 
processes integrated of order 1 — I(1). They also showed that unit root processes have 
non-standard statistical properties, so that conventional econometric theory methods do 
not apply to them. 
If two or more series are individually integrated (in the time series sense) but some linear 
combination of them has a lower order of integration, then the series are said to be 
cointegrated. A common example is where the individual series are first-order integrated 
(I(1)) but some (co integrating) vector of coefficients exists to form a stationary linear 
combination of them. For instance, a stock market index and the price of its associated 
futures contract move through time, each roughly following a random walk. Testing the 

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hypothesis that there is a statistically significant connection between the futures price and 
the spot price could now be done by testing for the existence of a co integrated 
combination of the two series.