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                Department of Mathematical Sciences                       
                   The Johns Hopkins University                           
                                                                        
                              SEMINAR                                
                                                                        
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Professor M. Ali Khan                             March 2, 2000
Department of Economics                           304 Whitehead Hall
The Johns Hopkins University                      Preseminar: 3:00 p.m.
                                                  Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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         ASSET PRICING MODELS AND THE LAW OF LARGE NUMBERS
               WITH A CONTINUUM OF RANDOM VARIABLES

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                             ABSTRACT

This talk draws on joint work with Yeneng Sun. In it, I present a model of a
financial market which captures the main ingredients of the Sharpe-Lintner
capital-asset-pricing model (CAPM) and of the arbitrage pricing theory (APT)
of Ross.  In the model, an asset's unexpected return can be decomposed into
a _systematic_ part and an _unsystematic_ part, as in the APT,
and the systematic part can be further decomposed into an _essential_
part and an _inessential_ part, as in the CAPM.  This tri-partite
decomposition leads to a pricing formula expressed in terms of a beta that
is based on a specific index portfolio identifying essential risk, and
constructed from factors and factor loadings that are endogenously extracted
from the process of asset returns by a procedure analogous to the
Karhunen-Loeve expansion of continuous time stochastic processes.  The 
idealized limit model is based on a continuum of assets indexed by a
hyperfinite Loeb measure space, and it is asymptotically implementable in a
setting with a large but finite number of assets.

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