##
**A unified beta pricing theory.**
*(English)*
Zbl 0545.90009

The paper considers an economy where asset payoffs are generated by linear functions of expected payoffs, common random influences (market factors), and idiosyncratic risk variates. Total portfolio return is then the sum of three components: expected payoff, factor risk, and idiosyncratic risk. A Pareto-efficiency argument shows that any competitive allocation of the economy consists entirely of well- diversified portfolios (with no idiosyncratic risk), provided that it is always possible for all investors to diversify. Under the same assumption, it is shown that the competitive equilibrium prices are linear in the expected asset returns and market factor prices.

The author then considers a limiting case of such an economy, where the number of assets tends to infinity, certain other characteristics of the economy remaining constant. It is shown that the equilibrium prices in the limit economy are given by the same linear functions of expected payoffs and market factor prices as in the finite economy, and furthermore that the portfolio payoffs are the same in each economy.

The author then considers a limiting case of such an economy, where the number of assets tends to infinity, certain other characteristics of the economy remaining constant. It is shown that the equilibrium prices in the limit economy are given by the same linear functions of expected payoffs and market factor prices as in the finite economy, and furthermore that the portfolio payoffs are the same in each economy.

Reviewer: P.J.Deschamps

### MSC:

91B50 | General equilibrium theory |

91B28 | Finance etc. (MSC2000) |

91B24 | Microeconomic theory (price theory and economic markets) |

### Keywords:

beta pricing theory; mutual fund separation theory; arbitrage pricing; portfolio choice; Asset pricing; competitive equilibrium; idiosyncratic risk### References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.