Abstract
Diversification is the strategy of investing small fractions of wealth in each of a large number of securities and thereby reducing risk. The basic argument in support of diversification is an appeal to the Law of Large Numbers. A portfolio in which an investor's wealth is invested in equal fractions in each ofNsecurities with i.i.d. returns, has a return that converges to a riskless return asNincreases indefinitely. Any risk averse investor would prefer the limit riskless return to the return of any portfolio. In this paper we use the space ba of all finitely additive signed measures on the set of natural numbers (the index set for securities) to model the set of portfolios from which an investor may choose. This portfolio space contains arbitrary finite portfolios and a nontrivial portfolio which is the limit of the sequence of portfolios having the fraction of wealth 1/Ninvested in each ofNsecurities. We identify a class of portfolios which we call perfectly diversified. These portfolios are described by purely finite additive measures. In a perfectly diversified portfolio, wealth invested in each individual security is a negligible fraction of the total wealth of the portfolio. We show that the return of every perfectly diversified portfolio of securities with uncorrelated returns is riskless. It is shown that modeling of the portfolio space as the space ba makes possible a rigorous derivation of a general equilibrium version of the Arbitrage Pricing Theorem (APT). The APT provides a good illustration of the implications of diversification for equilibrium prices of securities.Journal of Economic LiteratureClassification Numbers: D52, G20.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 89-103 |
| Number of pages | 15 |
| Journal | Journal of Economic Theory |
| Volume | 75 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 1997 |
Bibliographical note
Funding Information:* Financial support from the Deutsche Forschungsgemainschaft, SFB 303, and from the Graduate School Fellowship, Univrsity of Minnesota is gratefully acknowledged. I am indebted to Harald Uhlig, Don Brown, John Kareken, and Steve LeRoy for very helpful conversations.