Abstract
An arbitrage portfolio provides a cash flow that can never be negative at zero cost. We define the weaker concept of a “desirable portfolio” delivering cash flows with negative risk at zero cost. Although these are not completely risk-free investments and subject to the risk measure used, they can provide attractive investment opportunities for investors. We investigate in detail the theoretical aspects of this portfolio selection procedure and the existence of such opportunities in fixed income markets. Then, we present two applications of the theory: one in analyzing market integration problem and the other in gauging the credit quality of defaultable bonds in a portfolio. We also discuss the model calibration and provide some numerical illustrations.
Highlights
We introduce a methodology by using risk measures that can detect more general risk–return tradeoff opportunities than classical arbitrage ones
A type of risk statistics is created in order to numerically implement the model in bond markets
The randomness in the bond market is described by an interest rate model
Summary
We introduce a methodology by using risk measures that can detect more general risk–return tradeoff opportunities than classical arbitrage ones. We apply the theory to analyze market integration and to study the credit quality of bonds issued in defaultable markets. We use convex risk measures and ignore transaction costs, which implies a linear pricing functional to formulate and detect the desirable opportunities in markets by forming a static optimal portfolio in a sense to be precisely defined. We maximize the profit and minimize risk simultaneously, subject to some sequential arbitrage constraints introduced in Balbás and López (2008) These optimization problems are applied to quantify and detect the desirable portfolios in markets. The second, and main, application of this work is to introduce a numerically implementable procedure to gauge the credit quality of bonds in a defaultable market assumed not to provide any desirable opportunities.
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