On some topics of financial theory

Abstract

Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, 1999.Includes bibliographical references (p. [126]-133).Thesis consists of three unrelated Chapters, three Financial Economics research topics: (I) Approximate Factor Structure: Concept of approximate factor structure is equivalent to assumption of Arbitrage Pricing Theory (APT). Novel estimation procedure and tests for approximate factor structure of series of sample covariance matrices with increasing order are developed from APT research. Time/crosssection double-limit asymptotics is addressed by proposed random aggregation. It is shown that resulting small-order sample covariance matrix of the portfolios is informative about approximate factor structure even for time samples size and portfolio set size growing slower than cross-section. Procedure is applied to weekly NYSE/AMEX 1988-92 stock returns panel. Empirical results are ambiguous and vary across asymptotically equivalent tests and number of aggregated portfolios. Simulations show significant bias of sample statistic from asymptotic counterparts. Bias reduction and related corrections resembling bootstrap are considered. Besides small-sample deviation from asymptotic model, weak results might result from non-existence of approximate factor structure in considered sample. Possible inconsequentiality of APT assumption for portfolio investment is discussed briefly: that approximate factor structure is not preserved under change of asset base is known but underappreciated. (II) Rebundling in Mean-Variance Portfolio Theory: Concept of "rebundling", economically irrelevant change of full set of base investment assets, is studied within context of mean/variance portfolio theory. Complete set of rebundling invariants is found, characterized, discussed; results applied to CAPM. Alternative approaches of CAPM arc also illustrated. Further, invariants for time scale and stochastic numeraire indeterminacy and their relationships are studied. Empirical research project on associated issues is proposed. (III) Trading Volume and MiniCRSP Database: Description of MiniCRSP database is provided together with first results of trading volume empirical analysis based on it. MiniCRSP is database of daily and weekly prices, returns and turnovers data derived from CRSP Stocks daily file, with superior storage, convenience, portability, and speed parameters. Analysis includes advantages of of weekly over daily data financial research. Errors in input volume data are investigated and important class of them characterized and remedied. Exploratory analysis of turnover behavior in interaction with return behavior is studied.by Petr Adamek.Approximate factor strucutre -- Rebundling in mean-variance portfolio theory -- Trading volume and miniCRSP database.Ph.D