Linear Factor Models in Finance
Combining actual quantitative finance experience with analytical research, this book covers the science of asset pricing by concentrating on the most widely used modelling technique called linear factor modelling.
TABLE OF CONTENTS Linear Factor Models in Finance
Chapter 7: The Small Noise Arbitrage Pricing Theory and Its Welfare Implications
Stephen E. Satchell [ ]
Abstract
This chapter presents a small-noise version of the Arbitrage Pricing Theory (APT) which allows us to interpret the approximate linearity of the risk premia in terms of factor exposures for a fixed number of assets. The approximation becomes more accurate as the noise of the system decreases, even though the number of assets stays fixed. The Pareto optimality of such noise reduction is proven for a particular economy.
[*] This chapter was written when the author was visiting the University of Technology, Sydney. He would like to thank A. D. Hall, J. Knight, S. J. Lin and L. Middleton for their helpful advice and comments.
[ ] Trinity College, University of Cambridge, Cambridge, UK.
7.1 Introduction
Arbitrage Pricing Theory (APT) stresses the approximate linearity of the risk premia of assets in terms of the factor loadings. The basic assumption is that returns are generated by a linear factor model and the theory shows that the above linear approximation becomes increasingly accurate as N, the number of assets, increases to infinity.
The original paper by Ross (1976) has been generalized in many directions. The linear factor model has been dispensed with by Bansal and Viswanathan (1993). The problem has been put in an equilibrium setting by Connor (1984) and has been given a very general factor structure by Chamberlain and Rothschild (1983) and Reisman (1992). Many other important papers have been put forward but they all stress the approximate linearity of the risk premia...
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