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| Mensuel : | Edition de juin 2010 |
| Rubrique : | Economie/Conseil |
| Titre : | Recherche en Finance
Of the impact of fundamental uncertainty on “fair values” |
| Article : | Probably some readers of our last column might have thought the critical analysis of financial market efficiency quite theoretical without any applicability. That this is not so, is actually indicated by some post-crisis research. In that respect, the recent financial crisis has led to some puzzling situations as far as financial economics is concerned. Indeed, quite many markets exhibited a lack of volume. Even though dealers continued to post bid and ask prices, in some markets no trade actually materialized at those prices. This occurrence is at variance with standard asset pricing and microstructure models. Actually, the fact that no trade occurs at differing bid-ask spreads seems to indicate the existence of price indeterminacy.
Thus, a recent paper by Easley and O’Hara (2010) discusses liquidity and valuation when there exists indeterminacy. They use a representation of incomplete preferences where traders have difficulties to completely rank all portfolios. As they point out, “representations that reflect complete preferences in finance and economics are typically driven more by convenience than by economic reality”. The authors have recourse to Bewley’s (2002) framework with so-called Knightian uncertainty. The latter term, also known as ambiguity refers to the fact that probabilities of future payoffs are not known. We thus distinguish risky situations, where probability distributions are known, from uncertain situations, where the probability distributions are not known. As the distributions are not known, different traders can have heterogeneous beliefs concerning the future values of assets. It is important to realize that those different beliefs do not necessarily stem from differential information as in standard microstructure models. In that regard, recent papers on learning argue that it is quite impossible that all traders would converge to the same beliefs (Al-Najjar (2009)). It turns out that the existence of heterogeneous beliefs is a fundamental assumption to legitimate trade. Indeed, Milgrom and Stokey’s no-trade theorem indicates that if traders have common beliefs, no trade actually occurs. The only trade would take place when optimal allocations are not yet reached, but information flows would not impact trade, provided, however, that markets are complete (Blume et al. (2006)). In order to analyze the impact of uncertainty, two scenarios are considered. In the first scenario, a future shock occurs but there is no ambiguity about it’s impact on the future asset value. In the second scenario, there is ambiguity about the amplitude of the shock. In order to focus on the impact of ambiguity, traders are supposed to maximize expected utility of wealth and have common constant absolute risk aversion of 1. Concerning scenario 2, in Bewley’s (2002) framework, traders have a set of beliefs concerning the future values of the assets and trade away from their current portfolio only if the trade is beneficial according to every belief they consider. Actually, Bewley shows that under standard assumptions, incomplete preferences can be represented with a single utility function and a set of probability measures. An act is thus preferred to another act if and only if it yields greater expected utility for every probability in the set. In both scenarios, a shock which negatively impacts the Sharpe ratio will change the asset demand. In case the new value of the asset is unambiguous, traders decrease the riskiness of portfolios and this leads to an increased volume of trade. In case the new asset value is ambiguous, there is a region of prices for which the traders do not trade. The shock thus does not necessarily lead to increased volume. The region of indeterminacy is given by a price interval which is determined by the traders beliefs and in which there is no trade. The highest point of this no trade region is determined by the trader who has the smallest price at which it would begin to sell the asset. The lowest point is determined by the trader who has the highest price at which he would begin to buy the asset. Hence, the more ambiguous, in the sense of fundamental uncertainty, the market movements, the larger the region of indeterminacy in which no trades occur. If such a situation of large fundamental uncertainty occurs, there is no simple price for the asset. The equilibrium is thus characterized by: 1) A range of prices at which nobody trades 2) For prices outside the indeterminacy region, supply and demand do not equalize The problem is that now we have many potential candidates for the valuation. In that respect, the extreme points of the region of indeterminacy have interesting characteristics. The maximum price in the range is the lowest price at which any trader is willing to sell the risky asset. For a higher price, some traders would sell the asset but nobody would buy it. It is the ask price. Conversely, the minimum price in the indeterminacy region is the highest price at which any trader would buy the asset. It is thus the bid price of the asset. The ask price is determined by the highest possible valuation as expected by the least optimistic trader, whereas the bid price is determined by the lowest possible valuation as expected by the most optimistic trader. The prices are thus determined by the least and most optimistic traders. The bid-ask spread is a so-called ambiguity spread as compared to the standard asymmetric information spread from the microstructure literature. In the latter framework, the spread arises due to asymmetry of information between traders. Buying and selling orders thus signal good or bad information and thus revisions of the asset which leads to adjustments of the bid and ask prices. The bid and ask prices are thus asset values conditional on sell and buy orders. In that case, the bid-ask mid-point is a good approximation of the conditional expected value of the asset. In our case, we focus on ambiguity where spreads stem from heterogeneous beliefs concerning asset valuations. It should be highlighted that this heterogeneity in beliefs is not related to differences in information sets. The size of the spread is positively related to ambiguity and there is a range of prices at which nobody trades as described in Rigotti and Shannon (2005). This leads to equilibria with high illiquidity. This, however, leads to a fundamental problem as it is rather difficult to determine the so-called “fair value” of the asset. The Financial Accounting Standards Board (FASB, henceforth) through the FAS 157 section on “Fair Value Measurements” requires firms to determine “the price that would be received to sell an asset or transfer a liability in an orderly transaction between market participants at the measurement date”. Ryan (2008) critically analyses the definition of “fair value”. He notes that the definition refers to an optimal “exit value” notion of fair value, namely, the highest values of assets and the lowest values of liabilities currently held by the firm. A fundamental challenge to the determination of “fair values” is how to value when markets are illiquid or incapable of providing transaction prices. “At the measurement date” indicates that fair values should reflect the conditions that exist at the balance sheet date. “An orderly” transaction is supposed unforced and unhurried. The problem is that when markets are illiquid and no transactions occur it might be quite impossible to find an orderly transaction at the measurement date. Here, FAS 157 distinguishes different levels of inputs into fair value measurements that move from the least to the most reliable. At level 1, inputs are unadjusted quoted market prices in active markets for identical items. In case level 1 cannot be implemented, level 2 inputs which are other directly or indirectly observable market data can be used. Typically, quoted prices in active markets for similar items or in inactive markets for identical items are used. Finally, at level 3 so-called mark-to-model valuations can be used. As far as a model is based on historical data, mark-to-model valuations are heavily depend on the past, which under ambiguity may be prove a bad guide. We thus stay with the fundamental problem that we do not know what the fair value is in ambiguously illiquid markets. Even worse, Easley and O’Hara (2010) show that in some cases the so-called notional value of the asset can even be outside the bid-ask spreads. Basically, in general we don’t really know what the fair value is? Easley and O’Hara come up with, in our opinion, a disappointing solution, namely that as we do not have information on what the fair value is in a range of indeterminacy, the value that presupposes the less is given by the mid-point of bid-ask spreads. It should be highlighted that this approach is also somewhat inconsistent with the fact that the notional value could be outside the bid-ask range. Anyway, as the reader will have noticed, fundamental uncertainty is a serious problem to be addressed while discussing fair value measurement. We would also suggest that regulatory changes be analyzed through the lens of fundamental uncertainty. Dr. Michel Verlaine Associate Professor of Finance ICN Business School Expert for IFB Advisory Services Michel.verlaine@icn-groupe.fr ICN Business School jointly with IFB Advisory offer Executive Education programs on the subjects treated in this page. IFB Fund Due Diligence Expert team also provides consulting activities on these topics. For further details the author can be contacted via the contact details above. www.icn-groupe.fr www.ifb-group.com References Al-Najjar, N. (2009) “Decision Makers as Statisticians: Diversity, Ambiguity and Learning”, Econometrica, Vol. 77. 1371-1401. Bewley, T.F. (2002) “Knightian decision theory: Part I”, Decisions in Economics and Finance, 91, 59-82. Blume, L., Coury, T. and Easley, D. (2006) “Information, Trade and Incomplete Markets”, Economic Theory, 29, 379-394. Easley, D. and O’Hara, M. (2010) “Liquidity and Valuation in an uncertain World”, forthcoming Journal of Financial Economics Rigotti, L. and Shannon, C. (2005) “Uncertainty and Risk in Financial Markets”, Econometrica, Vol. 73, 203-243. Ryan, S. (2008) “Accounting in and for the Subprime Crisis”, Stern School of Business Working Paper. |
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