# Financial economics

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Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade".[1] Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: Asset pricing (or "Investment theory") and corporate finance; the first being the perspective of providers of capital and the second of users of capital.

The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment".[2] It therefore centers on decision making under uncertainty in the context of the financial markets, and the resultant economic and financial models and principles, and is concerned with deriving testable or policy implications from acceptable assumptions. It is built on the foundations of microeconomics and decision theory.

Financial econometrics is the branch of financial economics that uses econometric techniques to parameterise these relationships. Mathematical finance is related in that it will derive and extend the mathematical or numerical models suggested by financial economics. Note though that the emphasis there is mathematical consistency, as opposed to compatibility with economic theory.

Financial economics is usually taught at the postgraduate level; see Master of Financial Economics. Recently, specialist undergraduate degrees are offered in the discipline.[3]

## Underlying economics

 JEL classification codes In the Journal of Economic Literature classification codes, Financial Economics is one of the 19 primary classifications, at JEL: G. It follows Monetary and International Economics and precedes Public Economics. Detailed subclassifications are linked in the following footnote.[4] The New Palgrave Dictionary of Economics (2008, 2nd ed.) also uses the JEL codes to classify its entries in v. 8, Subject Index, including Financial Economics at pp. 863–64. The corresponding footnotes below have links to entry abstracts of The New Palgrave Online for each primary or secondary JEL category (10 or fewer per page, similar to Google searches): JEL: G – Financial Economics[5] JEL: G0 – General[6] JEL: G1 – General Financial Markets[7] JEL: G2 – Financial institutions and Services[8] JEL: G3 – Corporate finance and Governance[9] Tertiary category entries can be also be searched.[10]

As above, the discipline essentially explores how rational investors would apply decision theory to the problem of investment. The subject is thus built on the foundations of microeconomics and decision theory, and derives several key results for the application of decision making under uncertainty to the financial markets.

### Present value, expectation and utility

Underlying all of financial economics are the concepts of present value and expectation. Present value is developed in an early book on compound interest by Richard Witt ("Arithmeticall Questions" (1613)). These ideas were further developed by Johan de Witt and Edmond Halley. Combining probabilities with present value leads to the expected value criterion which sets asset value as a function of the sizes of the expected payouts and the probabilities of their occurrence. These ideas originate with Blaise Pascal and Pierre de Fermat. Various inconsistencies observed, such as the St. Petersburg paradox, suggested that valuation is instead subjective and must incorporate Utility. Here, the Expected utility hypothesis states that, if certain axioms are satisfied, the subjective value associated with a gamble by an individual is that individual's statistical expectation of the valuations of the outcomes of that gamble. See also: Ellsberg paradox; Risk aversion; Risk premium.

### Arbitrage-free pricing and equilibrium

The concepts of arbitrage-free “Rational” pricing and equilibrium are then coupled with these to derive "classical" financial economics. Rational pricing is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset, as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

Where market prices do not allow for profitable arbitrage, i.e. comprise an arbitrage-free market, so these prices are also said to constitute an arbitrage equilibrium. Intuitively, this may be seen by considering that where an arbitrage opportunity does exist, then prices can be expected to change, and are, therefore, not in equilibrium. An arbitrage equilibrium is thus a precondition for a general economic equilibrium. See Fundamental theorem of asset pricing.

General equilibrium deals with the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium (this is in contrast to partial equilibrium, which only analyzes single markets.) Further specialized is the Arrow–Debreu model which suggests that, under certain economic conditions, there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy. The analysis here is often undertaken assuming a Representative agent.

### State prices

Originating from the Arrow–Debreu model is the concept of a state price security (also called an Arrow-Debreu security), a contract that agrees to pay one unit of a numeraire (a currency or a commodity) if a particular state occurs at a particular time in the future and pays zero numeraire in all the other states. The price of this security is the state price of this particular state of the world, which may be represented by a vector. The state price vector is the vector of state prices for all states. As such, any derivatives contract whose settlement value is a function of an underlying whose value is uncertain at contract date can be decomposed as a linear combination of its Arrow-Debreu securities, and thus as a weighted sum of its state prices. Analogously, for a continuous random variable indicating a continuum of possible states, the value is found by integrating over the state price density; see Stochastic discount factor. These concepts are extended to Martingale pricing and the related Risk-neutral measure.

## Resultant models

Modigliani–Miller Proposition II with risky debt. As leverage (D/E) increases, the WACC (k0) stays constant.
Efficient Frontier. The hyperbola is sometimes referred to as the 'Markowitz Bullet', and its upward sloped portion is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight line is the efficient frontier.
Security market line: the representation of the CAPM displaying the expected rate of return of an individual security as a function of its systematic, non-diversifiable risk.
Simulated geometric Brownian motions with parameters from market data.
 The Black–Scholes equation $\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} - rV = 0$
Binomial Lattice with CRR formulae

Applying the above economic concepts, we may then derive various economic and financial models and principles. As above, the two usual areas of focus are Asset pricing and corporate finance, the first being the perspective of providers of capital, the second of users of capital. Here, and for (almost) all other financial economics models, the questions addressed are typically framed in terms of "time, uncertainty, options, and information",[1] as will be seen below.

• Time: money now is traded for money in the future.
• Uncertainty (or risk): The amount of money to be transferred in the future is uncertain.
• Options: one party to the transaction can make a decision at a later time that will affect subsequent transfers of money.
• Information: knowledge of the future can reduce, or possibly eliminate, the uncertainty associated with future monetary value (FMV).

Applying this framework, with the above concepts, leads to the required models. This derivation begins with the assumption of "no uncertainty" and is then expanded to incorporate the other considerations.

### Certainty

A starting point here is “Investment under certainty". The Fisher separation theorem, asserts that the objective of a corporation will be the maximization of its present value, regardless of the preferences of its shareholders. The Theory of Investment Value (John Burr Williams) proposes that the value of an asset should be calculated using “evaluation by the rule of present worth”. Thus, for a common stock, the intrinsic, long-term worth is the present value of its future net cash flows, in the form of dividends. The Modigliani-Miller theorem describes conditions under which corporate financing decisions are irrelevant for value, and acts as a benchmark for evaluating the effects of factors outside the model that do affect value.

It will be noted that these "certainty" theorems are all commonly employed under corporate finance (see comments under Corporate finance#Quantifying uncertainty and Financial modeling#Accounting); uncertainty is the focus of "asset pricing models", as follows.

### Uncertainty

For "choice under uncertainty", the twin assumptions of rationality and market efficiency lead to modern portfolio theory and the Capital asset pricing model (CAPM) — an equilibrium-based result — and to the Black–Scholes–Merton theory (BSM; often, simply Black-Scholes) for option pricing — an arbitrage-free result.

Portfolio theory studies how investors should balance risk and return when investing in many assets or securities. The CAPM describes how — in equilibrium — markets set the prices of assets in relation to how risky they are. The theory demonstrates that if one can construct an efficient frontier, introduced by Harry Markowitz, then mean-variance efficient portfolios can be formed simply as a combination of holdings of the risk-free asset and the Market portfolio, a particular efficient fund; this principle being the Mutual fund separation theorem. Combining these, any asset may then be priced independent of the investor's utility function. See also: Security characteristic line; Security market line; Capital allocation line; Capital market line; Sharpe ratio; Jensen's alpha; Portfolio optimization.

Black-Scholes provides a mathematical model of a financial market containing derivative instruments, and the resultant formula for the price of European-styled options. The Black–Scholes equation is a partial differential equation describing the price of the option over time. The key financial insight behind the equation is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk". This hedge, in turn, implies that there is only one right price — in an arbitrage-free sense — for the option: then, assuming log-normal, geometric Brownian motion, we may derive the Black–Scholes option pricing formula, which will return the correct option price, and here without reference to the share's expected return, and with justifiably assumed risk neutrality. Note that the pricing formula may also be derived directly via risk neutral expectation.

It can be shown that the two models are consistent, and that, as is to be expected, classical financial economics is thus unified. Here, the Black Scholes equation may be derived from the CAPM, and the price obtained from the Black-Scholes model is thus consistent with the expected return from the CAPM.[11] The Black-Scholes theory, although built on Arbitrage-free pricing, is therefore consistent with the equilibrium based capital asset pricing. Both models, in turn, are ultimately consistent with the Arrow-Debreu theory, and may be derived via state-pricing,[12] further explaining, and if required demonstrating, this unity.

### Extensions

More recent work further generalizes and / or extends these models. Multi-factor models such as the Fama-French three-factor model and the Carhart four-factor model, propose factors other than market return as relevant in pricing. The Intertemporal CAPM, Black–Litterman model, and arbitrage pricing theory similarly extend modern portfolio theory. See also: Post-modern portfolio theory; Mathematical finance#Risk and portfolio management: the P world.

As regards derivative pricing, the Binomial options pricing model provides a discretized version of Black-Scholes, useful for the valuation of American styled options; discretized models of this type are built using state-prices (as above), while exotic derivatives although modeled in continuous time via Monte Carlo methods for option pricing are also priced using risk neutral expected value. Various other numeric techniques have also been developed. The theoretical framework too has been extended such that Martingale pricing is now the standard approach. Since the work of Breeden and Litzenberger in 1978,[13] a large number of researchers have used options to extract Arrow–Debreu prices for a variety of applications in financial economics. See also Mathematical finance#Derivatives pricing: the Q world.

Derivative models for various other underlyings and applications have also been developed, all departing from the same logic. Beginning with Oldrich Vasicek, various Short rate models, as well as the HJM and BGM forward rate-based techniques, allow for an extension to fixed income- and interest rate derivatives. (The Vasicek and CIR models are equilibrium-based, while Ho–Lee and subsequent models are based on arbitrage-free pricing.) Real options valuation allows that option holders can influence the option's underlying; Models for Employee stock option valuation explicitly assume non-rationality on the part of option holders; Credit derivatives allow that payment obligations / delivery requirements might not be honored.

Note that Real Options theory is also an extension of corporate finance theory: asset-valuation and decisioning here no longer need assume "certainty". Relatedly, as discussed above, Monte Carlo methods in finance, introduced by David B. Hertz in 1964, allow financial analysts to construct "stochastic" or probabilistic corporate finance models, as opposed to the traditional static and deterministic models; see Corporate finance#Quantifying uncertainty. Other extensions here include Agency theory, which analyses the difficulties in motivating corporate management (the "agent") to act in the best interests of shareholders (the "principal"), rather than in their own interests. Clean surplus accounting and the related Residual income valuation provide a model that returns price as a function of earnings, expected returns, and change in book value, as opposed to dividends. This approach, to some extent, arises due to the implicit contradiction of seeing value as a function of dividends, while also holding that dividend policy cannot influence value per Modigliani and Miller’s “Irrelevance principle”; see Dividend policy#Irrelevance of dividend policy.

## Challenges and criticism

Implied volatility surface. The Z-axis represents implied volatility in percent, and X and Y axes represent the option delta, and the days to maturity.
See also: Capital asset pricing model#Problems of CAPM; Modern portfolio theory#Criticisms; Black–Scholes model#Criticism; Financial mathematics#Criticism; List of unsolved problems in economics#Financial economics.

As seen, a common assumption is that financial decision makers act rationally; see Homo economicus. However, recently, researchers in experimental economics and experimental finance have challenged this assumption empirically. These assumptions are also challenged, theoretically, by behavioral finance, a discipline primarily concerned with the limits to rationality of economic agents.

In parallel to these developements, various (and persistent) market anomalies have been documented, these being price and/or rate of return distortions which appear to contradict the efficient-market hypothesis. Areas of research attempting to address (or at least model) these phenomena include noise trading, market microstructure, and Heterogeneous agent models. The latter is extended to Agent-based computational economics, where price is treated as an emergent phenomenon, resulting from the interaction of the various market participants (agents). See also: Equity premium puzzle; A Random Walk Down Wall Street.

Other common assumptions include market prices following a random walk and / or asset returns being normally distributed. Empirical evidence suggests that these assumptions may not hold and that in practice, traders, analysts and particularly risk managers frequently modify the "standard models". Benoît Mandelbrot discovered in the 1960s that changes in financial prices do not follow a Gaussian distribution, the basis for much option pricing theory, although this observation was slow to find its way into mainstream financial economics. See also: Financial models with long-tailed distributions and volatility clustering; volatility smile; Local volatility; Stochastic volatility; Implied binomial tree; Implied trinomial tree.

Particularly following the financial crisis of 2007–2010, financial economics and mathematical finance have been subjected to criticism; notable here is Nassim Nicholas Taleb, who claims that the prices of financial assets cannot be characterized by the simple models currently in use, rendering much of current practice at best irrelevant, and, at worst, dangerously misleading. A topic of general interest studied in recent years has thus been financial crises.[14] See also, Financial Modelers' Manifesto.

## References

1. ^ a b "Financial Economics". Stanford.edu. Retrieved 2009-08-06.
2. ^ "Robert C. Merton - Nobel Lecture" (PDF). Retrieved 2009-08-06.
3. ^
4. ^ JEL classification codes — Financial economics JEL: G Subcategories
5. ^ All entries under JEL: G: http://www.dictionaryofeconomics.com/search_results?,q=&field=content&edition=all&topicid=G
6. ^ http://www.dictionaryofeconomics.com/search_results?q=&field=content&edition=all&topicid=G0
7. ^ http://www.dictionaryofeconomics.com/search_results?q=&field=content&edition=all&topicid=G1
8. ^ http://www.dictionaryofeconomics.com/search_results?q=&field=content&edition=all&topicid=G2
9. ^ http://www.dictionaryofeconomics.com/search_results?q=&field=content&edition=all&topicid=G3
10. ^ In particular by clicking to Advanced searches from http://www.dictionaryofeconomics.com/, which brings up http://www.dictionaryofeconomics.com/advanced_search, drilling to the secondary category, then to the tertiary category, followed by clicking the Search button at the bottom. For example, from secondary code JEL: G0, http://www.dictionaryofeconomics.com/search_results?,q=&field=content&edition=all&topicid=G0, then to the JEL: G00, then pressing the Search button to bring up the entry links at http://www.dictionaryofeconomics.com/search_results?q=&field=content&edition=all&topicid=G00.
11. ^ Don M. Chance. Option Prices and Expected Returns
12. ^ See Rubinstein parts IVa and IVb, under "External links".
13. ^ Breeden, Douglas T.; Litzenberger, Robert H. (1978). "Prices of State-Contingent Claims Implicit in Option Prices". Journal of Business 51 (4): 621–651. doi:10.1086/296025. JSTOR 2352653.
14. ^ From The New Palgrave Dictionary of Economics, Online Editions, 2011, 2012, with abstract links:
• "regulatory responses to the financial crisis: an interim assessment" by Howard Davies
• "Credit Crunch Chronology: April 2007–September 2009" by The Statesman's Yearbook team
• "Minsky crisis" by L. Randall Wray
• "euro zone crisis 2010" by Daniel Gros and Cinzia Alcidi.
• Carmen M. Reinhart and Kenneth S. Rogoff, 2009. This Time Is Different: Eight Centuries of Financial Folly, Princeton. Description, ch. 1 ("Varieties of Crises and their Dates," pp. 3-20), and chapter-preview links.