Matching and portfolio selection: Part 1

Abstract

1.1 My paper entitled ‘The Matching of Assets to Liabilities’ described a new study of the subject of matching. The paper outlined the mathematical framework, showed some calculations, and suggested various applications in the field of actuarial valuation.1.2 Subsequently A. D. Wilkie published a note entitled ‘Portfolio Selection in the Presence of Fixed Liabilities: a Comment on “The Matching of Assets to Liabilities”’. Wilkie's note appears to represent a new extension of portfolio selection theory which enables him to encompass the conventional portfolio theory and to show where my approach to matching fits into the picture.1.3 This paper is in the nature of a reply to that of Wilkie. My objective at the stage of the first draft was to re-examine the matching portfolio, as defined in relation to specified liabilities, in view of the wide range of alternative portfolios which Wilkie has described. The scope of this work progressed well beyond my original plans when I found a most interesting mathematical relationship between the ‘matching portfolios’ described in my earlier paper and the ‘efficient portfolios’ described in Wilkie's.