Two Essays on General Equilibrium Foundation of Finance

Abstract

thesis consists of two essays: The CAPM -- A General Equilibrium Foundation and The Foreign Exchange Rate in Financial Markets. The Capital Asset Pricing Model (CAPM) is one of the most successful models for portfolio selection. utility functions are assumed to depend positively on mean and negatively on variance of returns. Therewith explicit solutions of equilibria are possible only in the harmonic mean of investors' absolute risk aversions. Actually, the practical advantages are the simple risk measure and the quite applicable properties of CAPM-equilibria: Mutual Fund Theorem, the Beta-pricing Formula, and the Efficient Frontier. Those nice results come just into effect at the expense of an ad-hoc assumption: the strict fulfillment of investors' budget identities. However, for mean/variance-utility functions monotonicity is not at all guaranteed. It is indeed possible that an investor values a positively paying asset negatively due to an increased variance of portfolio returns. Non-monotonicity can even lead to equilibrium prices permitting simple arbitrage opportunities. In the two-period consumption based CAPM with homogeneous expectations, without a riskless asset, and with non-marketed endowments non-monotonicity is analysed. Known conditions ruling out this problem are more restrictive and given in a less general setup than those derived here. This issue is embedded in an extensive review of the theoretical literature about the CAPM. Different aspects, like the relationship between expected and mean/variance-utility, existence and uniqueness of equilibria, etc. are also addressed. The prognosis of foreign exchange rates is still an econometric challenge. empirical literature has shown that fundamental factors do contribute little to the forecast. Especially in the '80s empirical investigations about the information efficiency of foreign exchange markets came up. hypothesis had been formulated that efficiency implies the forward being an unbiased predictor for the spot exchange rate. To avoid Siegel's paradox the logarithms of the forward and the spot exchange rate are usually employed. This is better known as the uncovered interest parity. It will be shown that the uncovered interest parity can generally not be regarded as a no-arbitrage condition and can be considered as an equilibrium condition only non-generically. true arbitrage-free correlation between the exchange rate, interest rates, and security prices is theoretically derived in a Black/Scholes-model with complete asset markets. Reduced form equations of this relationship will be estimated with real data for the USD/DEM-exchange rate. Arbitrage pricing may only explain relationships between market prices. To determine the influence of fundamental factors on the exchange rate the equilibrium of a quite general example economy is considered. In this economy each country's representative consumer provides labor as the only production factor to the domestic industry. relative price between both consumption goods (the respective numeraires) serves as the real exchange rate. It will turn out that the exchange rate is equal to the ratio of the present values of all future net imports and exports.