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The Actuary The magazine of the Institute & Faculty of Actuaries
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On the catallactic actuary

IN ANY CASE SO IMPORTANT AS THAT OF SHAKESPEARE, it is goodthat we should from time to time change our minds… it isprobable that we can never be right; and if we can never beright, it is better that we should from time to time changeour way of being wrong. Whether Truth ultimately prevails isdoubtful and has never been proved; but it is certain that nothingis more effective in driving out error than a new error.So wrote TS Eliot in his essay ‘Shakespeare and the stoicismof Seneca’; it is interesting to find that fair value andShakespeare have so much in common.Little is of more interest to the actuarialogist than to followfads and fashions in the world of valuation methods,and to watch good errors – as they will undoubtedly beregarded in 50 years – driving out the bad. To the distantobserver, the fair value debate reduces to one question:whether an object, be it an asset or a liability, should bevalued according to the owner’s criteria or according tothe rude criteria of the market. This is hardly a new questionand, as with many questions facing us, it is interestingto consider what has been written about it over thecourse of recorded history.Aristotle touches on the question in The Politics:… a shoe may be used either to put on your foot or to offer inexchange. Both are uses of the shoe; for even he that gives ashoe to someone who requires a shoe, and receives in exchangecoins or food, is making use of the shoe as a shoe, but not theuse proper to it…but the distinction between value and price is notaddressed directly.Moving on in great temporal leaps and bounds, we findthat Saint Thomas Aquinas addressed the problem in the13th century in his comprehensive Summa theologica.After opining on areas of theological uncertainty such as‘Can angels know many things simultaneously?’ and ‘Canthe same act be good and bad?’, St Aquinas moves on tousury and commerce. He devotes four articles to ‘Sinscommitted in buying and selling’, including a considerationof whether it is lawful to sell a thing for more than itsworth.In his discussion, St Aquinas recognises the differencebetween an article’s intrinsic value to the owner and thevalue that a buyer might place on it, and comes out generallyin favour of intrinsic worth:If either the price exceed the quantity of the thing’s worth, or,conversely, the thing exceed the price, there is no longer theequality of justice: and consequently, to sell a thing for morethan its worth, or to buy it for less than its worth, is in itselfunjust and unlawful.We find little more said about the question until the19th century, when the field of ‘political economy’ grewfrom nowhere with the contributions of Smith, Ricardo,Whately, and various others (Whately proposed thecharming name of ‘catallactics’ – the theory of exchanges– for the subject, but it never took hold). Debates of thetime revolved around the problems associated with measuringthe value of goods: what currency to use (corn,hours of labour, or money?), and what value to measure,the article’s ‘natural’ value or what the market might payfor it?Surprisingly, political economy became a great interestof Thomas de Quincey, and was a field about which hewrote much when not busy with his Confessions of an EnglishOpium-eater, On Murder Considered as One of the FineArts, and other such works. He summarises the thinkingof the time in an article written in 1827:What is called natural price, is price governed by the singleconsideration of cost; and it takes place undisturbed when thesupply happens to be just equal to the demand, neither morenor less. What is called market price, is price governed by thecost complicated with the quantity, and never takes place…except when the quantity in the market is above or below thedemand.It is interesting that for over 2,000 years the idea of fairvalue has generally corresponded to an object’s intrinsicworth, not to its market price; only recently have wechanged allegiance. The two measures are obviously connected:for frequently traded objects, market price represents,in theory, the aggregate of individual valuations ofintrinsic worth conducted by marginal buyers and sellers,and so can be regarded as a reasonable valuation. However,for an infrequently traded object, that no longerholds; the market price provides at best an expedient referencepoint, at worst an unstable and meaningless number.Furthermore, we may find a curious problem ofcircularity: an insurance company’s market value will bedetermined on the basis of published accounts, which arethemselves formulated on the basis of the market valuesof… Where large amounts of infrequently traded objectsare involved, how much external input will be necessaryto ensure stable and meaningful results?A final observation: it is a shame that, since the suggestionof ‘catallactic’ around 1830, no one has suggested aname for this field more suitable – and less emotionallyloaded – than ‘fair value’ (after all, who would want toargue the case for ‘unfair value’?). I look forward to nextyear’s Catallactic Convention.

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