Essays in financial economics

These essays cover two areas of financial economics. Chapters 1 and 2 deal with portfolio choice, and chapter 3 deals with a novel problem of price search and inventory control in a world where futures markets play an important role. In chapter 1, an equation for the mean-variance-skewness portfolio frontier in portfolio space is derived, extending the well-known mean-variance theory. No closed form solution to this equation can be found. This precludes a general description of the frontier in moment space. The frontier is completely derived for two special cases with three and four assets whose returns have no coskewnesses. With four assets, three-fund separation obtains if individuals choose mean-variance-skewness efficient portfolios. This result depends on the existence of a basis of mutual funds and no coskewnesses, so casts doubt on the realism of the much-used two-fund separation result of mean-variance theory. The derivation of the frontier is essentially a search for a hedge portfolio in the direction of the maximal rate of change of skewness with respect to variance. The main purpose of chapter 2 is to show why the elegant connection between two-moment preferences and two-fund separation does not carry over to higher moments. Various theorems giving conditions on investor preferences and asset return distributions for k-fund or k-moment results are discussed. In chapter 3, the optimal strategy of a customer carrying out a costly search among dealers for the best spot price (while also participating in a futures market) is shown to have a reservation margin property. This solution is consistent with optimal dealer behaviour, to the extent that the latter can be analysed. Dealers\u27 optimal price quotes depend on inventory and on cash reserves. One conclusion is that the principal usefulness of the futures price is not, as conventionally assumed, in predicting future spot price movements, but in signalling the range of concurrent, unobservable, spot prices. The dealer\u27s optimisation problem is only partially solved, but the relevant Bellman equation is derived and its solution discussed, providing ideas for future research