Differential information, arbitrage, and subjective value

de Bruin et al. (in: Zalta (ed) The Stanford encyclopedia of philosophy, Stanford University, Stanford, 2018) write that it is a philosophically interesting question “whether there is such a thing as an “intrinsic” value of financial assets” noting that the calculation of any intrinsic price will depend, in part, on subjective elements. McCauley suggest that there are at least five different notions of the ‘true value’ of an asset in finance theory, and argues, consistent with de Bruin et al. that in many cases the calculation of such values “makes impossible information demands on our knowledge of future dividends and returns” (McCauley (Dynamics of markets-econophysics and finance, Cambridge University Press, Cambridge, 2004). This paper explores some of the subjective elements involved in calculating the intrinsic value of an asset, and their implications for the Law of One Price. The Law of One Price states that investors should not pay different prices for the same investment. Consequently, the existence, and persistence, of arbitrage opportunities is often attributed to investor irrationality. However, if subjectivity is involved in the calculation of intrinsic value then two investors can, rationally, disagree about the value of a security. This implies that arbitrage opportunities may not always be instances of irrationality, or genuine mispricing, but reflect different investor’s perceptions of the security. In economics, value is taken to be subjective, and Postigo (Axiomathes 27:591–576, 2017) describes how goods have value because of the role they play in the satisfaction of our needs. By applying this to finance, this paper will argue that a security can play a number of roles in a portfolio, depending on an investors’ strategy. Given these different roles, different investors will be working with different data in their assessment of intrinsic value. In order to establish that an arbitrage opportunity exists it is therefore necessary to understand what information is relevant to pricing the investment in different locations, or markets. It may, in fact, be the case that the same security can trade at different prices because different investors do not see it as the ‘same thing’ at all. This analysis can also be used to throw doubt on the emphasis that fundamental analysis receives in discussions of rationality.