Investigating Risk: Rational Gluttony and Market Corrections
"Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models."
-The Lucas Critique (1976)
The revision of macroeconomic policies from Keynesian intervention to Monetarist theories of purported voluntary hires and layoffs in the 1970s also prompted the onset of using micro-foundations in conventional macro decision making. The usage of deep parameters in probabilistic econometric models inspired by Lucas’ critique of Keynesian models incorporated micro level utility maximization along with neoclassical rational expectations with perfect information. However, behavior and heuristics coupled with empirical evidence point out significant departures from standard normality assumptions of noise in expectation rules. The value attached to noise is crucial to comprehend the existence of arbitrage, free riding in capital markets, and asset price bubbles.
The Rational Expectations Hypothesis (REH) explains agent behavior who “knows the model” and has perfect insight about the “one truth”. Adopted by virtually all economists and modern schools of thought, REH is also now a key assumption of New Keynesian schools and the neoclassical synthesis. It also finds a footing in explaining how money illusions and surprises in government policymaking impact stability paths, coined as the Policy Ineffectiveness Proposition. Foundations of behavioral finance courses have the Efficient Market Hypothesis (EMH) at their core. EMH propounds the supply of accurate market signals for resource allocation. Asset prices reflect all information and there is also the standard assumption of normal and stochastic noise. From EMH, it is implied that asset prices must reflect the present discounted value of all future income streams that it intends to generate, i.e. its fundamental value. Furthermore, under such conditions of information and flexible capital constraints, present values of consumption must equal the present value of all assets in the economy, removing the existence of price bubbles which are in clear contradiction of the theory (Fama, 1970).
Taking these two theories together (REH+EMH), it is clear that agents must be indifferent between holding assets and selling them for capital gains. Any short term deviations in said price prompts arbitrage opportunities where any market participant can earn risk-less profit until prices return back to fundamentals. Thus, Efficient Markets imply no profits out of trading above the average market profit. Normality tests and output gaps of GDP in various countries often reflect autocorrelation marked with strong kurtosis and clusters of booms and recessions. This also opens a discussion about the cognitive strength of individuals to know the true model. The existence of such cognitive limitations, imperfect information, and market inefficiencies are markers of constrained, or bounded rationality (Simon, 1957). This does not imply that agents are irrational. It means that there exists a gradual adjustment mechanism, or a diverse range of iterated learning within agents that reflect such deviations. This is where heuristics chime in to aid in the development of adjustment mechanisms. One may argue about the existence of strict statistical and trial/error methods of adaptive learning. This also implies that agents have heterogeneous decision making methods which drives REH+EMH away from everyone having the same information set.
Two prominent heuristic rules  are of the Fundamentalist, who expects any deviation of asset value from fundamentals to be zero, and the extrapolative Chartist, who relies on past values of the asset in question. The Chartist do not necessarily assume the existence of Fundamentalists and do not require knowledge of the entire model due to which they are departures from REH. Cognitive limitations and bounded rationality also explain the magnitude of reliance on a certain inexplicable animal spirit and instinct. Unpredictable psychological components become related to waves of optimism and pessimism. The limits of arbitrage and risk can be shown primarily by the influence and power held by a few professional investors in the market that either pool in resources of other smaller investors or highly distort market equilibrium results. Asymmetric information and monopolistic arbitrageurs constantly misquotes markets with capital constraints (Shleifer and Vishny, 1997).
Short-term CIP Deviations, measured by 10-day moving averages of
three-month Libor cross-currency basis (Source: Du, Tepper and Verdelhan, The
Journal of Finance 2018)
The international forex market is an important example of decentralized trading with arbitrage. It is an over-the-counter affair without any central or physical exchange agency. Transactions are undertaken completely online. Market participants include brokers who primarily play the role of financial intermediaries and dealers who are commercial and investment banks. The bulk of trading is conducted by banks, often lending the term interbank market to the trading platform. Profit making in forex trading can be explained using bid-ask spreads. Ask (offer/sell) is the rate at which the trader wants to sell currency. Bid (purchase/buy) is the rate at which the trader is willing to buy currency. A liquid market would usually imply a low spread (difference), whereas illiquid or rigid markets imply relatively higher spreads. At least till 2008, interbank dealings among large players dominated the trading stage and stabilized exchange rates. The backdrop of the Lehman Brothers fiasco has fashioned a demand for derivative instruments and has also led to stricter regulations such as restrictions on uncollateralized lending (Basel 3 norms), which played a key role in arbitrage.
The illustrated image describes deviations from covered interest rate parity  of the London Interbank Offered Rate (LIBOR), a benchmark interest rate for borrowing. Post-2008, large and consistent deviations indicate multiple opportunities of arbitrage. However, the recent popularity of macroprudential regulation and financial responsibility indicates a safety net of supervision against greedy and distortionary speculation. There seems to be a completely different world of trading marked by significant departure from fundamentals and greater risk aversion. The availability of high frequency data shall soon reveal new improvements in extant models of expectations and is a promising venture for research.
"The value attached to noise is crucial to comprehend the existence of arbitrage, free riding in capital markets, and asset price bubbles."
The Fundamentalist approach to expectation formation takes the form
Etf yt+1 = 0
Where current period (t) expectations deviations of future values (t+1) from fundamental is zero.
The Chartist extrapolates future values by past values, i.e.
Ete yt+1 = yt-1
Together, the market forecast under a heterogeneous heuristic rule is given by
Et yt+1 = αf, t (Etf yt+1) + αe, t (Ete yt+1)
Where the two expectation rules are given a weightage that all sum to unity.
Covered interest rate parity describes domestic and international interest rates covered or insured against exchange rate volatility, originally formulated under conditions of flexible capital mobility (The Mundel-Fleming Model). Simply stated, it represents a situation of no-arbitrage and indifference. Further disposition of the parity condition would become far too complex to comprehend.