Financial economics

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".

Its concern is thus the interrelation of financial variables, such as share prices, interest rates and exchange rates, as opposed to those concerning the real economy.

It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.

It thus provides the theoretical underpinning for much of finance.

The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment". 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 thus also includes a formal study of the financial markets themselves, especially market microstructure and market regulation.

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 the relationships identified.

Mathematical finance is related in that it will derive and extend the mathematical or numerical models suggested by financial economics.

Whereas financial economics has a primarily microeconomic focus, monetary economics is primarily macroeconomic in nature.

Underlying economics

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|Fundamental valuation equation and was further developed by Johan de Witt in 1671 and by Edmond Halley in 1705.

(Note that here, "<math>r</math>" represents a generic (or arbitrary) discount rate applied to the cash flows, whereas in the valuation formulae, the risk-free rate is applied once these have been "adjusted" for their riskiness; see below.)

An immediate extension is to combine probabilities with present value, leading 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, <math>X_{s}</math> and <math>p_{s}</math> respectively.

This decision method, however, fails to consider risk aversion. In other words, since individuals receive greater utility from an extra dollar when they are poor and less utility when comparatively rich, the approach is therefore to "adjust" the weight assigned to the various outcomes, i.e. "states", correspondingly: <math>Y_{s}</math>. See indifference price. (Some investors may in fact be risk seeking as opposed to risk averse, but the same logic would apply.)

Choice under uncertainty here may then be defined as the maximization of expected utility. More formally, the resulting expected utility hypothesis states that, if certain axioms are satisfied, the subjective value associated with a gamble by an individual is that individuals statistical expectation of the valuations of the outcomes of that gamble.

The impetus for these ideas arises from various inconsistencies observed under the expected value framework, such as the St. Petersburg paradox and the Ellsberg paradox.

Arbitrage-free pricing and equilibrium

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|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. The New Palgrave Dictionary of Economics also uses the JEL codes to classify its entries. The primary and secondary JEL categories are:

:JEL: G – Financial Economics (archived link)

:JEL: G0 – General

:JEL: G1 – General Financial Markets

:JEL: G2 – Financial institutions and Services

:JEL: G3 – Corporate finance and Governance

Each is further divided into its tertiary categories.

The concepts of arbitrage-free, "rational", pricing and equilibrium are then coupled

with the above to derive various of the "classical" (or "neo-classical"

The formal derivation will proceed by arbitrage arguments.

Lionel W. McKenzie is also cited for his independent proof of equilibrium existence in 1954.

Breeden and Litzenberger's work in 1978 established the use of state prices in financial economics.

This result 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 Arrow–Debreu model applies to economies with maximally complete markets, in which there exists a market for every time period and forward prices for every commodity at all time periods.

A direct extension, then, 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 ("up" and "down" in the simplified example above) 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 <math>\pi_{s}</math> of this particular state of the world; the collection of these is also referred to as a "Risk Neutral Density". Given the pricing mechanism described, one can decompose the derivative value – true in fact for "every security"

These recovered state-prices can then be used for valuation of other instruments with exposure to the underlyer, or for other decision making relating to the underlyer itself.

Stochastic discount factor

The stochastic discount factor (SDF) — also called the pricing kernel — provides an alternative but closely related approach to valuation.

the third equation above.

In equilibrium models, this factor corresponds to the intertemporal marginal rate of substitution in consumption,

and 1963.

The mechanism for determining (corporate) value is provided by

John Burr Williams' The Theory of Investment Value, which 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 cashflows, in the form of dividends; in the corporate context, "free cash flow" as aside. What remains to be determined is the appropriate discount rate. Later developments show that, "rationally", i.e. in the formal sense, the appropriate discount rate here will (should) depend on the asset's riskiness relative to the overall market, as opposed to its owners' preferences; see below. Net present value (NPV), the result of this discounted cashflow valuation, is the direct extension of these ideas typically applied to Corporate Finance decisioning. For other results, as well as specific models developed here, see the list of "Equity valuation" topics under .

Bond valuation, in that cashflows (coupons and return of principal, or "Face value") are deterministic, may proceed in the same fashion. An immediate extension, Arbitrage-free bond pricing, discounts each cashflow at the market derived rate – i.e. at each coupon's corresponding zero rate, and of equivalent credit worthiness – as opposed to an overall rate.

In many treatments bond valuation precedes equity valuation, under which cashflows (dividends) are not "known" per se. Williams and onward allow for forecasting as to these – based on historic ratios or published dividend policy – and cashflows are then treated as essentially deterministic; see below under .

For both stocks and bonds, "under certainty, with the focus on cash flows from securities over time," valuation based on a term structure of interest rates is in fact consistent with arbitrage-free pricing.

Indeed, a corollary of the above is that "the law of one price implies the existence of a discount factor".

Corresponding to these: ; and equivalently, for the above "numeraire bond", . In practice, the latter is interchangeable with the risk-free yield curve: this ensures consistency between the theoretical no-arbitrage framework and applied valuation, providing a common benchmark for discounting future cash flows.

Whereas these "certainty" results are all commonly employed under corporate finance, uncertainty is the focus of "asset pricing models" as follows. Fisher's formulation of the theory here - developing an intertemporal equilibrium model - underpins also for the development.

Uncertainty

thumb|right|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. The graphic displays the CAL, [[Capital allocation line, formed when the risky asset is a single-asset rather than the market, in which case the line is the CML.]]

thumb|right|The [[Capital market line is the tangent line drawn from the point of the risk-free asset to the feasible region for risky assets. The tangency point M represents the market portfolio. The CML results from the combination of the market portfolio and the risk-free asset (the point L). Addition of leverage (the point R) creates levered portfolios that are also on the CML.]]

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</math>), the asset's correlated volatility relative to the overall market <math>m</math>.

thumb|right|[[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.]]

For "choice under uncertainty" the twin assumptions of rationality and market efficiency, as more closely defined, lead to modern portfolio theory (MPT) with its 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. As above, the (intuitive) link between these, is that the latter derivative prices are calculated such that they are arbitrage-free with respect to the more fundamental, equilibrium determined, securities prices; see .

Briefly, and intuitively – and consistent with above – the relationship between rationality and efficiency is as follows.

Given the ability to profit from private information, self-interested traders are motivated to acquire and act on their private information. In doing so, traders contribute to more and more "correct", i.e. efficient, prices: the efficient-market hypothesis, or EMH. Thus, if prices of financial assets are (broadly) efficient, then deviations from these (equilibrium) values could not last for long. (See earnings response coefficient.)

The EMH (implicitly) assumes that average expectations constitute an "optimal forecast", i.e. prices using all available information are identical to the best guess of the future: the assumption of rational expectations.

The EMH does allow that when faced with new information, some investors may overreact and some may underreact,

but what is required, however, is that investors' reactions follow a normal distribution – so that the net effect on market prices cannot be reliably exploited consolidating previous works re random walks in stock prices: Jules Regnault (1863); Louis Bachelier (1900); Maurice Kendall (1953); Paul Cootner (1964); and Paul Samuelson (1965), among others.

Under these conditions, investors can then be assumed to act rationally: their investment decision must be calculated or a loss is sure to follow; had described the mean-variance method, in the context of reinsurance.

This result will be independent of the investor's level of risk aversion and assumed utility function, thus providing a readily determined discount rate for corporate finance decision makers as above, and for other investors.

The argument proceeds as follows:

If one can construct an efficient frontier – i.e. each combination of assets offering the best possible expected level of return for its level of risk, see diagram – then mean-variance efficient portfolios can be formed simply as a combination of holdings of the risk-free asset and the "market portfolio" (the Mutual fund separation theorem), with the combinations here plotting as the capital market line, or CML.

Then, given this CML, the required return on a risky security will be independent of the investor's utility function, and solely determined by its covariance ("beta") with aggregate, i.e. market, risk.

This is because investors here can then maximize utility through leverage as opposed to stock selection; see Separation property (finance), and CML diagram aside.

As can be seen in the formula aside, this result is consistent with the preceding, equaling the riskless return plus an adjustment for risk. and Robert C. Merton – is consistent with "previous versions of the formula" of Louis Bachelier (1900) and Edward O. Thorp (1967); although these were more "actuarial" in flavor, and had not established risk-neutral discounting. had published a formula for the price of a call-option which, with adjustments, satisfied the BSM partial differential equation.

James Boness (1964),

in fact, derived a formula identical to BSM, though through a different argument. introduced this area of mathematics into finance in 1965;

Robert Merton promoted continuous stochastic calculus and continuous-time processes from 1969.

As implied by the Fundamental Theorem, the two major results are consistent.

Here, the Black-Scholes equation can alternatively be derived from the CAPM, and the price obtained from the Black–Scholes model is thus consistent with the assumptions of the CAPM.

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 can be derived via state-pricing – essentially, by expanding the above fundamental equations – further explaining, and if required demonstrating, this consistency.

Here, the CAPM is derived by attaching a binomial probability It returns the required (expected) return of a financial asset as a linear function of various macro-economic factors, and assumes that arbitrage should bring incorrectly priced assets back into line.

The linear factor model structure of the APT is used as the basis for many of the commercial risk and fund management systems employed by asset managers. Here,

managers apply various of the abovementioned multi-factor models - often

bespoke extensions - such that their portfolio has the desired exposure ("tilt") to macroeconomic, market and / or fundamental risk factors; respectively: Macro-, Factor-, and Style Funds.

Research here, and application (e.g. "Smart Beta"), is ongoing, and over the years "hundreds of factors attempt to explain the cross-section of expected returns";

with this "factor zoo",

there is a risk of data mining, and researchers have proposed various criteria for establishing significance.

At the same time, "classic" mean-variance optimization — i.e. building an efficient portfolio as described above — is still widely used by Asset Allocation Funds. Here, given issues noted with this approach, the application is typically in combination with other techniques.

The Black–Litterman model is often employed.

Black–Litterman departs from the original Markowitz model approach: it starts with an equilibrium assumption, as for the latter, but this is then modified to take into account the "views" (i.e., the specific opinions about asset returns) of the investor in question to arrive at a bespoke asset allocation.

A further modification often used relates to the subsequent optimization: under (Tail) risk parity, the focus is on the allocation of risk, rather than the allocation of capital.

Other developments re portfolio optimization include the following.

Where factors additional to volatility are considered (kurtosis, skew...) then multiple-criteria decision analysis can be applied; here deriving a Pareto efficient portfolio. The universal portfolio algorithm identifies the "growth optimal portfolio" per the Kelly criterion, applying information theory to asset selection. Behavioral portfolio theory recognizes that investors have varied aims and create an investment portfolio that meets a broad range of goals. Copulas have lately been applied here; recently this is the case also for genetic algorithms and

Derivative pricing

thumb|right| Binomial Lattice with [[Binomial options pricing model#STEP 1: Create the binomial price tree|CRR formulae ]]

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thumb|right|Stylized volatility smile: showing the (implied) volatility by strike-price, for which the [[Black–Scholes formula returns market prices.]]

In pricing derivatives, 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 – at least implicitly – using state-prices (as above); relatedly, a large number of researchers have used options to extract state-prices for a variety of other applications in financial economics. For path dependent derivatives, Monte Carlo methods for option pricing are employed; here the modelling is in continuous time, but similarly uses 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.

Drawing on these techniques, models for various other underlyings and applications have also been developed, all based on the same logic (using "contingent claim analysis"). 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 or delivery requirements might not be honored. Exotic derivatives are now routinely valued. Multi-asset underlyers are handled via simulation or copula based analysis.

Similarly, the various short-rate models allow for an extension of these techniques 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.) The more general HJM Framework describes the dynamics of the full forward-rate curve – as opposed to working with short rates – and is then more widely applied. The valuation of the underlying instrument – additional to its derivatives – is relatedly extended, particularly for hybrid securities, where credit risk is combined with uncertainty re future rates; see and .

Following the Crash of 1987, equity options traded in American markets began to exhibit what is known as a "volatility smile"; that is, for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices, and thus implied volatilities, than what is suggested by BSM. (The pattern differs across various markets.) Modelling the volatility smile is an active area of research, and developments here – as well as implications re the standard theory – are discussed in the next section.

After the 2008 financial crisis, a further development: as outlined, (over the counter) derivative pricing had relied on the BSM risk neutral pricing framework, under the assumptions of funding at the risk free rate and the ability to perfectly replicate cashflows so as to fully hedge. This, in turn, is built on the assumption of a credit-risk-free environment – called into question during the crisis.

Addressing this, therefore, issues such as counterparty credit risk, funding costs and costs of capital are now additionally considered when pricing, and a credit valuation adjustment, or CVA – and potentially other valuation adjustments, collectively xVA – is generally added to the risk-neutral derivative value.

The standard economic arguments can be extended to incorporate these various adjustments.

A related, and perhaps more fundamental change, is that discounting is now on the Overnight Index Swap (OIS) curve, as opposed to LIBOR as used previously. (Also, practically, the interest paid on cash collateral is usually the overnight rate; OIS discounting is then, sometimes, referred to as "CSA discounting".) Swap pricing – and, therefore, yield curve construction – is further modified: previously, swaps were valued off a single "self discounting" interest rate curve; whereas post crisis, to accommodate OIS discounting, valuation is now under a "multi-curve framework" where "forecast curves" are constructed for each floating-leg LIBOR tenor, with discounting on the common OIS curve.

Corporate finance theory

right|thumb|Project valuation via decision tree.

Mirroring the above developments, corporate finance valuations and decisioning no longer need assume "certainty".

Monte Carlo methods in finance allow financial analysts to construct "stochastic" or probabilistic corporate finance models, as opposed to the traditional static and deterministic models; the correct discount rate here reflecting each decision-point's "non-diversifiable risk looking forward." as opposed to a theoretically correct state-by-state treatment under uncertainty; see comments under Financial modeling § Accounting.

In more modern treatments, then, it is the expected cashflows (in the mathematical sense: <math display=inline>\sum_{s}p_{s}X_{sj}</math>) combined into an overall value per forecast period which are discounted. recognizing Modigliani and Miller's Irrelevance principle.

"Corporate finance" as a discipline more broadly, building on Fisher above, relates to the long term objective of maximizing the value of the firm - and its return to shareholders - and thus also incorporates the areas of capital structure and dividend policy.

Extensions of the theory here then also consider these latter, as follows:

(i) Optimization re capitalization structure, and theories here as to corporate choices and behavior: Capital structure substitution theory, Pecking order theory, Market timing hypothesis, Trade-off theory.

(ii) Considerations and analysis re dividend policy, additional to - and sometimes contrasting with - Modigliani-Miller, include: the Walter model, Lintner model, Residuals theory and signaling hypothesis, as well as discussion re the observed clientele effect and dividend puzzle.

A significant development

Stephen Ross in 1973 and Barry Mitnick in 1975.

In 1976, Michael Jensen and William Meckling built an agency theory of the firm, see contract theory.

The resultant (unseen) "agency costs" may impact firm value - as well as overall market efficiency.

A related emphasis is placed on the agency issues interrelated with capital structure and with dividends.

Given this scope, all corporate finance decisions may (must), in fact, be viewed through an agency lens.

Although, as described, the typical "use case" for real options is capital budgeting, they may also be applied

to problems of capital structure and dividend policy (here it is stockholders and bondholders who have different objective functions) and to the related design of corporate securities. Further, they are often used in the analysis of the related agency problems.

The basis for these analyses is that equity may be viewed as a call option on the firm,

Financial markets

thumb|[[$SPY|SPY daily closing prices (2018-2025) with corresponding machine learning produced "trend-scanning" labels and related statistics, used in subsequent classification- and regression problems.]]

The discipline, as outlined, also includes a formal study of financial markets. Of interest especially are market regulation and market microstructure, and their relationship to price efficiency.

Regulatory economics studies, in general, the economics of regulation. In the context of finance, it will address the impact of financial regulation on the functioning of markets and the efficiency of prices, while also weighing the corresponding increases in market confidence and financial stability.

Research here considers how, and to what extent, regulations relating to disclosure (earnings guidance, annual reports), insider trading, and short-selling will impact price efficiency, the cost of equity, and market liquidity.

Market microstructure is concerned with the details of how exchange occurs in markets

(with Walrasian-, matching-, Fisher-, and

Arrow-Debreu markets as prototypes),

and "analyzes how specific trading mechanisms affect the price formation process", examining the ways in which the processes of a market affect determinants of transaction costs, prices, quotes, volume, and trading behavior.

It has been used, for example, in providing explanations for long-standing exchange rate puzzles, and for the equity premium puzzle.

In contrast to the above classical approach, models here explicitly allow for (testing the impact of) market frictions and other imperfections;

Departures from rationality

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|colspan="1" | Market anomalies and economic puzzles

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Calendar effect
January effect
Sell in May
Mark Twain effect
Santa Claus rally
Closed-end fund puzzle
Dividend puzzle
Equity home bias puzzle
Equity premium puzzle
Excess volatility puzzle
Forward premium anomaly
Low-volatility anomaly
Momentum anomaly
Neglected firm effect
Post-earnings-announcement drift
Real exchange-rate puzzles

As seen, a common assumption is that financial decision makers act rationally; see Homo economicus. Recently, however, 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.

For related criticisms re corporate finance theory vs its practice see:.

Various market anomalies have been documented in parallel. These comprise price "distortions", e.g. size premiums, or return "predictability" as exemplified by the various calendar effects, and are anomalous in the sense that

also to the institutional

aspects of finance - including academic.

Here, financial crises have been a topic of interest

and, in particular, the failure market microstructure and Heterogeneous agent models, as above. The latter is extended to agent-based computational models; here, as mentioned, price is treated as an emergent phenomenon, resulting from the interaction of the various market participants (agents). The noisy market hypothesis argues that prices can be influenced by speculators and momentum traders, as well as by insiders and institutions that often buy and sell stocks for reasons unrelated to fundamental value; see Noise (economic) and Noise trader. The adaptive market hypothesis is an attempt to reconcile the efficient market hypothesis with behavioral economics, by applying the principles of evolution to financial interactions. An information cascade, alternatively, shows market participants engaging in the same acts as others ("herd behavior"), despite contradictions with their private information. Copula-based modelling has similarly been applied. See also Hyman Minsky's "financial instability hypothesis", as well as George Soros' application of "reflexivity".

In the alternative, institutionally inherent limits to arbitrage - i.e. as opposed to factors directly contradictory to the theory - are sometimes referenced.

Note however, that despite the above inefficiencies, asset prices do effectively

Thus after fund costs - and given other considerations - it is difficult to consistently outperform market averages

and achieve "alpha".

The practical implication is that passive investing, i.e. via low-cost index funds, should, on average, serve better than any other active strategy -

and, in fact, this practice is now widely adopted.

Here, however, the following concern is posited:

although in concept, it is "the research undertaken by active managers [that] keeps prices closer to value... [and] thus there is a fragile equilibrium in which some investors choose to index while the rest continue to search for mispriced securities"; potentially leading to asset bubbles.

See Grossman-Stiglitz paradox.

Historical notes

References

Bibliography

Financial economics

Volume I ; Volume II .

Asset pricing

Corporate finance

External links

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;Surveys

Great Moments in Financial Economics I, II, III, IVa, IVb (archived, 2007-06-27). Mark Rubinstein
The Scientific Evolution of Finance (archived, 2003-04-03). Don Chance and Pamela Peterson
The Early History of Portfolio Theory: 1600-1960, Harry M. Markowitz. Financial Analysts Journal, Vol. 55, No. 4 (Jul. – Aug., 1999), pp. 5–16
The Theory of Corporate Finance: A Historical Overview, Michael C. Jensen and Clifford W. Smith.
A Stylized History of Quantitative Finance, Emanuel Derman
Financial Engineering: Some Tools of the Trade (discusses historical context of derivative pricing). Ch 10 in Phelim Boyle and Feidhlim Boyle (2001). "Derivatives: The Tools That Changed Finance". Risk Books (June 2001).
What We Do Know: The Seven Most Important Ideas in Finance; What We Do Not Know: 10 Unsolved Problems in Finance, Richard A. Brealey, Stewart Myers and Franklin Allen.
An Overview of Modern Financial Economics (MIT Working paper). Chi-fu Huang
Irving Fisher's Theory of Investment Gonçalo L. Fonseca, The New School
Financial Economics, Perry Mehrling. (From "Handbook of the History of Economic Analysis", 2016.)

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Course material

Fundamentals of Asset Pricing, David K. Backus, NYU, Stern
Financial Economics: Classics and Contemporary , Antonio Mele, Università della Svizzera Italiana
Microfoundations of Financial Economics André Farber, Solvay Business School
An introduction to investment theory, William Goetzmann, Yale School of Management
Macro-Investment Analysis. William F. Sharpe, Stanford Graduate School of Business
Finance Theory (MIT OpenCourseWare). Andrew Lo, MIT.
Financial Theory (Open Yale Courses). John Geanakoplos, Yale University.
. G.L. Fonseca, New School for Social Research
Introduction to Financial Economics. Gordan Zitkovi, University of Texas at Austin
An Introduction to Asset Pricing Theory, Junhui Qian, Shanghai Jiao Tong University

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Links and portals

JEL Classification Codes Guide
Financial Economics Links on AEA's RFE
SSRN Financial Economics Network
Financial Economics listings on economicsnetwork.ac.uk
Financial Economists Roundtable
NBER Working Papers in Financial Economics
Financial Economics Resources on QFINANCE (archived 2014-03-13)
Financial Economics Links on WebEc (archived 2016-03-24)

Actuarial resources

"Models for Financial Economics (MFE)" , Society of Actuaries
"Financial Economics (CT8)", Institute and Faculty of Actuaries
"A Primer In Financial Economics", S. F. Whelan, D. C. Bowie and A. J. Hibbert. British Actuarial Journal, Volume 8, Issue 1, April 2002, pp. 27–65.
"Pension Actuary's Guide to Financial Economics". Gordon Enderle, Jeremy Gold, Gordon Latter and Michael Peskin. Society of Actuaries and American Academy of Actuaries.