Narrow Results

Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the Black-Scholes setting with time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization. We review the results from our previous work in unconstrained portfolio optimization, and then investigate and solve the corresponding problems with the additional constraint of no-short-selling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.

The main purpose of this paper is to explore a high-frequency tactical asset allocation strategy. In particular, we investigate the profitability of momentum trading and contrarian investment strategies for equities listed on the Australian Stock Exchange (ASX). In these two strategies we take into consideration the short-selling restrictions imposed by the ASX on the stocks used. Within our sample portfolios we look at the relationship between stock returns and past trading volume for these equities. This research also investigates the seasonal aspects of contrarian portfolios and observes weekly, monthly and yearly effects. We report significant contrarian profits for the period investigated (from 2001 to 2006) and show that contrarian profit is a persistent feature for the strategies examined. We also document that contrarian portfolios earn returns as high as 6.54% per day for portfolios with no short-selling restrictions, and 4.71% in the restricted model. The results also support the view that volume traded affects stock returns, and show that market imperfections such as short-selling restrictions affect investors' returns.

Consider a stochastic securities market model with a finite state space and a finite number of trading dates. We study how arbitrage price theory is modified by a no short-selling constraint. The principle of No Arbitrage is characterized by the existence of an equivalent supermartingale measure. If we measure present value as conditional expectations after an equivalent change of measure, then the fundamental value of a security might fall below its market value, leading to the possibility of a price bubble. We show that the Law of One Price holds for marketed claims if and only if there exists an equivalent martingale measure. The latter condition indicates that price bubbles are fragile. Given that the Law of One Price prevails, then a contingent claim has a unique fundamental value if and only if it is the difference of two marketed claims. The main tool for arbitrage analysis in this essay is finite-dimensional LP duality theory.

We formulate a short-selling strategy of a stock and seek the optimal timing of short covering in the presence of a random recall and a loan fee rate in an illiquid stock loan market. The aim is to study how the optimal trading strategy of the short-seller is influenced by the relevant features of the stock loan market. We consider a regime-switching stock price model that captures the transition in between the bull and the bear markets. The solution to the optimal stopping problem is obtained in closed-form based on the techniques in Guo and Zhang (2005). We provide the numerical example to illustrate of importance of a regime-dependent stopping rule for the short-seller's problem.