# Finance

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Academic discipline studying businesses and investments

For other uses, see [Finance (disambiguation)](/source/Finance_(disambiguation)). "Financial" redirects here. For the Georgian newspaper, see [*The Financial*](/source/The_Financial).

Part of a series on Finance Markets Assets Asset (economics) Bond Asset growth Capital asset Commodity Derivatives Domains Equity Foreign exchange Money Over-the-counter Private equity Real estate Spot Stock Participants Angel investor Bull (stock market speculator) Financial planner Investor institutional Retail Speculator Locations Financial centres Offshore financial centres Conduit and sink OFCs Instruments Bond Cash Collateralized debt obligation Credit default swap Time deposit (certificate of deposit) Credit line Deposit Derivative Futures contract Indemnity Insurance Letter of credit Loan Mortgage Option (call exotic put) Performance bonds Repurchase agreement Stock Security Syndicated loan Synthetic CDO Corporate General Accounting Audit Capital budgeting Capital structure Corporate finance Credit rating agency Enterprise risk management Enterprise value Risk management Financial statements Transactions Leveraged buyout Mergers and acquisitions Structured finance Venture capital Taxation Base erosion and profit shifting (BEPS) Corporate tax haven Tax inversion Tax haven Transfer pricing Personal Credit / Debt Employment contract Financial planning Retirement Student loan Public Government spending Final consumption expenditure Operations Redistribution Transfer payment Government revenue Taxation Deficit spending Budget (balance) Debt Non-tax revenue Warrant of payment Banking Central bank Deposit account Fractional-reserve Full-reserve Investment banking Loan Money supply Lists of banks Bank regulation Banking license Basel Accords Bank for International Settlements Financial Stability Board Deposit insurance Separation of investment and retail banking Regulation · Financial law International Financial Reporting Standards ISO 31000 Professional certification Fund governance Economic history Private equity and venture capital Recession Stock market bubble Stock market crash Accounting scandals Outline Business and Economics portal Money portal v t e

**Finance** refers to resources and the [discipline](/source/Academic_discipline) that studies such resources, allowing an entity to gain the [consumption](/source/Consumption_(economics)) and [saving](/source/Saving) opportunity within a specified timeframe, with related concepts such as [income](/source/Income), [money](/source/Money), [currency](/source/Currency), [assets](/source/Asset) and [liabilities](/source/Liability_(financial_accounting)).[a] As a subject of study, it is a field of [business administration](/source/Business_administration) which involves the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in [financial systems](/source/Financial_system), the discipline can be divided into [personal](/source/Personal_finance), [corporate](/source/Corporate_finance), and [public finance](/source/Public_finance).

In these financial systems, assets are bought, sold, or traded as [financial instruments](/source/Financial_instrument), such as [currencies](/source/Currency), [loans](/source/Loan), [bonds](/source/Bond_(finance)), [shares](/source/Share_(finance)), [stocks](/source/Stock), [options](/source/Option_(finance)), [futures](/source/Futures_contract), [swaps](/source/Swap_(finance)), etc. Assets can also be [banked](/source/Bank), [invested](/source/Investment), and [insured](/source/Insurance) to maximize value and minimize loss. In practice, [risks](/source/Financial_risk) are always present in any financial action and entities.

Due to its wide scope, a broad range of subfields exists within finance. [Asset-](/source/Asset_management), [money-](/source/Money_management), [risk-](/source/Financial_risk_management) and [investment management](/source/Investment_management) aim to maximize value and minimize [volatility](/source/Volatility_(finance)). [Financial analysis](/source/Financial_analysis) assesses the viability, stability, and profitability of an action or entity. Some fields are multidisciplinary, such as [mathematical finance](/source/Mathematical_finance), [financial law](/source/Financial_law), [financial economics](/source/Financial_economics), [financial engineering](/source/Financial_engineering) and [financial technology](/source/Financial_technology). These fields are the foundation of [business](/source/Business) and [accounting](/source/Accounting). In some cases, [theories in finance](/source/Financial_economics) can be tested using the [scientific method](/source/Scientific_method), covered by [experimental finance](/source/Experimental_finance).

The early history of finance parallels the early [history of money](/source/History_of_money), which is [prehistoric](/source/Prehistory). Ancient and medieval civilizations incorporated basic functions of finance, such as banking, trading and accounting, into their economies. In the late 19th century, the [global financial system](/source/Global_financial_system) was formed.

In the middle of the 20th century, finance emerged as a distinct academic discipline,[b] separate from economics.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] The earliest doctoral programs in finance were established in the 1960s and 1970s.[1] Today, finance is also [widely studied](/source/Outline_of_finance#Education) through career-focused undergraduate and [master's level](/source/Master_of_Finance) programs.[2][3]

## The financial system

Main article: [Financial system](/source/Financial_system)

See also: [Financial services](/source/Financial_services), [financial market](/source/Financial_market), and [Circular flow of income](/source/Circular_flow_of_income)

[Bond](/source/Bond_(finance)) issued by The Baltimore and Ohio Railroad. Bonds are a form of borrowing used by corporations to finance their operations.

[Share certificate](/source/Share_certificate) dated 1913 issued by the Radium Hill Company

NYSE's stock exchange [traders](/source/Trader_(finance)) floor in 1963, before the introduction of electronic readouts and computer screens

[Chicago Board of Trade](/source/Chicago_Board_of_Trade) [Corn Futures](/source/Maize#Commodity) market, 1993

[Oil traders](/source/Price_of_oil#Speculative_trading_and_crude_oil_futures), Houston, 2009

As outlined, the financial system consists of the flows of capital that take place between individuals and households ([personal finance](/source/Personal_finance)), governments ([public finance](/source/Public_finance)), and businesses ([corporate finance](/source/Corporate_finance)). "Finance" thus studies the process of channeling money from savers and investors to entities that need it.[c] Savers and investors have money available which could earn interest or dividends if put to productive use. Individuals, companies and governments must obtain money from some external source, such as loans or credit, when they lack sufficient funds to run their operations.

In general, an entity whose income exceeds its expenditure can lend or invest the surplus with the aim of earning a fair return. Correspondingly, an entity where income is less than expenditure can raise capital usually in one of two ways: (i) by borrowing in the form of a loan (private individuals), or by selling [government or corporate bonds](/source/Bond_(finance)); (ii) by a corporation selling [equity](/source/Equity_(finance)), also called stock or shares (which may take various forms: [preferred stock](/source/Preferred_stock) or [common stock](/source/Common_stock)). The owners of both bonds and stock may be [institutional investors](/source/Institutional_investor)—financial institutions such as investment banks and [pension funds](/source/Pension_funds)—or private individuals, called [private investors](/source/Private_investors) or retail investors. (See [Financial market participants](/source/Financial_market_participants).)

The [lending](/source/Lender) is often indirect, through a [financial intermediary](/source/Financial_intermediary) such as a [bank](/source/Bank), or via the purchase of notes or [bonds](/source/Bond_(finance)) ([corporate bonds](/source/Corporate_bonds), [government bonds](/source/Government_bond), or mutual bonds) in the [bond market](/source/Bond_market). The lender receives interest, the [borrower](/source/Debtor) pays a higher interest than the lender receives, and the financial intermediary earns the difference for arranging the loan.[5][6] A bank aggregates the activities of many borrowers and lenders. Banks accept deposits from individuals and businesses, paying interest on these funds. The bank then lends these deposits to borrowers, facilitating transactions between borrowers and lenders of various sizes and enabling efficient financial coordination. Investing typically entails the purchase of [stock](/source/Equity_(finance)), either individual securities or via a [mutual fund](/source/Mutual_fund), for example. Stocks are usually sold by corporations to investors so as to raise required capital in the form of "[equity financing](/source/Equity_financing)", as distinct from the debt financing described above. The financial intermediaries here are the [investment banks](/source/Investment_bank) (which [find the initial investors](/source/Investment_banking#Corporate_finance) and facilitate the listing of the securities, typically shares and bonds), the [securities exchanges](/source/Securities_exchange) (which allow their trade thereafter), and the various investment service providers (including [mutual funds](/source/Mutual_funds), [pension funds](/source/Pension_funds), [wealth managers](/source/Wealth_management), and [stock brokers](/source/Stock_brokers), typically servicing retail investors).

Inter-institutional trade and investment, and [fund-management at this scale](/source/Investment_management), is referred to as "wholesale finance". Institutions here [extend the products offered](/source/Structured_finance), with related trading, to include bespoke [options](/source/Option_(finance)), [swaps](/source/Swap_(finance)), and [structured products](/source/Structured_products), as well as [specialized financing](/source/Special-purpose_entity#Types); this "[financial engineering](/source/Financial_engineering)" is [inherently mathematical](/source/Outline_of_finance#Mathematical_tools), and these institutions are then the major employers of [quantitative analysts](/source/Quantitative_analyst) (or "quants", see [below](#Financial_mathematics)). In these institutions, [risk management](/source/Financial_risk_management), [regulatory capital](/source/Capital_requirement), and [compliance](/source/Regulatory_compliance) play major roles.

## Areas of finance

As outlined, finance broadly comprises three areas: personal finance, corporate finance, and public finance. These, in turn, overlap and employ various activities and sub-disciplines—chiefly [investments](/source/Investment), risk management, and [quantitative finance](/source/Quantitative_finance).

### Personal finance

Main article: [Personal finance](/source/Personal_finance)

Further information: [Financial planner](/source/Financial_planner) and [Investment advisory](/source/Investment_advisory)

[Wealth management](/source/Wealth_management) consultation—here, the [financial advisor](/source/Financial_planner) counsels the client on an appropriate [investment strategy](/source/Investment_strategy).

Personal finance refers to the practice of budgeting to ensure enough funds are available to meet basic needs, while ensuring there is only a reasonable level of risk to lose said capital. Personal finance may involve paying for education, financing [durable goods](/source/Durable_good) such as [real estate](/source/Real_estate) and cars, buying [insurance](/source/Insurance), investing, and saving for [retirement](/source/Retirement).[7] Personal finance may also involve paying for a loan or other debt obligations. The main areas of personal finance are considered to be income, spending, saving, investing, and protection. The following steps, as outlined by the Financial Planning Standards Board, suggest that an individual will understand a potentially secure personal finance plan after:

- Purchasing insurance to ensure protection against unforeseen personal events;

- Understanding the effects of tax policies, subsidies, or penalties on the management of personal finances;

- Understanding the effects of credit on individual financial standing;

- Developing a savings plan or financing for large purchases (auto, education, home);

- Planning a secure financial future in an environment of economic instability;

- Pursuing a checking or a savings account;

- Preparing for retirement or other long term expenses.[8]

### Corporate finance

Main articles: [Corporate finance](/source/Corporate_finance) and [Financial management](/source/Financial_management)

Further information: [Strategic financial management](/source/Strategic_financial_management)

Corporate finance deals with the actions that managers take to increase the value of the firm to the shareholders, the sources of funding and the [capital structure](/source/Capital_structure) of corporations, and the tools and analysis used to allocate financial resources. While corporate finance is in principle different from [managerial finance](/source/Managerial_finance), which studies the [financial management](/source/Financial_management) of all firms rather than corporations alone, the concepts are applicable to the financial problems of all firms,[9] and this area is then often referred to as "business finance".

Typically, "corporate finance" relates to the *long term* objective of maximizing the value of the [entity's assets](/source/Enterprise_value), its [stock](/source/Stock), and its [return to shareholders](/source/Return_on_equity), while also [balancing risk and profitability](/source/Risk%E2%80%93return_spectrum). This entails[10] three primary areas:

1. [Capital budgeting](/source/Capital_budgeting): selecting which projects to invest in—here, accurately [determining value](/source/Corporate_finance#Investment_and_project_valuation) is crucial, as judgements about asset values can be "make or break".[11]

1. [Dividend policy](/source/Dividend_policy): the use of "excess" funds—these are to be reinvested in the business or returned to shareholders.

1. [Capital structure](/source/Capital_structure): deciding on the mix of funding to be used—here attempting to find the [optimal capital mix](/source/Capital_structure#Optimal_capital_structure) re debt-commitments vs [cost of capital](/source/Cost_of_capital). (This consists in understanding how much the firm has to generate [to satisfy investors](/source/Return_on_equity), and by minimizing the [weighted average cost of capital](/source/Weighted_average_cost_of_capital) (WACC) so that the value of the company increases.)

The latter [creates the link](/source/Investment_banking#Corporate_finance) with [investment banking](/source/Investment_banking) and [securities trading](/source/Securities_trading), as above, in that the capital raised will generically comprise debt, i.e. [corporate bonds](/source/Corporate_bond), and [equity](/source/Equity_(finance)), often [listed shares](/source/Stock_(finance)). Re risk management within corporates, see [below](#Risk_management).

Financial managers—i.e. as distinct from corporate financiers—focus more on the *short term* elements of profitability, cash flow, and "[working capital management](/source/Working_capital_management)" ([inventory](/source/Inventory), credit and [debtors](/source/Debtor)), which is concerned about the daily funding operations, and the goal is to maintain liquidity, minimize risk and maximize efficiency ensuring that the firm can [safely and profitably](/source/Corporate_finance#Working_capital_management) carry out its financial *and operational* objectives; i.e. that it: (1) can service both maturing short-term debt repayments, and scheduled long-term debt payments, and (2) has sufficient cash flow for ongoing and upcoming [operational expenses](/source/Operations_management). (See [Financial management](/source/Financial_management) and [FP&A](/source/FP%26A).)

### Public finance

Main article: [Public finance](/source/Public_finance)

President [George W. Bush](/source/George_W._Bush), speaking on the [Federal Budget](/source/United_States_federal_budget) in 2007, [requesting additional funds](https://en.wikinews.org/wiki/US_Congress_debates_Iraq_funding) from [Congress](/source/United_States_Congress)

CBO: 2023 US Federal Budget Infographic

Public finance refers to the management of finances related to sovereign states, sub-national entities, and associated public agencies or bodies. It generally encompasses a long-term strategic perspective regarding investment decisions that affect public entities.[12] These long-term strategic periods typically encompass five or more years.[13] Public finance is primarily concerned with:[14]

- Identification of [required expenditures](/source/Government_expenditures) of a public sector entity;

- Source(s) of that [entity's revenue](/source/Government_revenue) - both from tax, and from non-tax sources;

- The [budgeting process](/source/Government_budget);

- Sovereign [debt issuance](/source/Government_bond), or [municipal bonds](/source/Municipal_bond) for [public works](/source/Public_works) projects.

Central banks, such as the [Federal Reserve System](/source/Federal_Reserve_System) banks in the [United States](/source/United_States), the [European Central Bank](/source/European_Central_Bank) and the [Bank of England](/source/Bank_of_England) in the [United Kingdom](/source/United_Kingdom), are strong players in public finance. They act as [lenders of last resort](/source/Lender_of_last_resort) as well as strong influences on monetary and credit conditions in the economy.[15]

[Development finance](/source/Development_finance), which is related, concerns investment in [economic development](/source/Economic_development) projects provided by a [(quasi) governmental institution](/source/Development_finance_institution#Typology) on a non-commercial basis; these projects would otherwise not be able [to get financing](/source/Public_utility#Finance). A [public–private partnership](/source/Public%E2%80%93private_partnership) is primarily used for [infrastructure](/source/Infrastructure) projects: a private sector corporate [provides the financing](/source/Infrastructure_and_economics#Ownership_and_financing_of_infrastructure) up-front, and then draws profits from taxpayers or users. [Climate finance](/source/Climate_finance), and the related [Environmental finance](/source/Environmental_finance), address the financial strategies, resources [and instruments](/source/Climate_finance#Financial_instruments) used in [climate change mitigation](/source/Climate_change_mitigation).

### Investment management

Main article: [Investment management](/source/Investment_management)

See also: [Active management](/source/Active_management) and [Passive management](/source/Passive_management)

[Share prices](/source/Share_price) listed in a Korean newspaper

"The excitement before the bubble burst"—viewing prices via [ticker tape](/source/Ticker_tape), shortly before the [Wall Street crash of 1929](/source/Wall_Street_crash_of_1929)

A modern price-ticker. This infrastructure underpins contemporary exchanges, evidencing prices and related ticker symbols. The ticker symbol is represented by a unique set of characters used to identify the subject of the financial transaction.

Investment management[9] is the professional asset management of various securities—typically shares and bonds, but also other assets, such as real estate, commodities and [alternative investments](/source/Alternative_investment)—in order to meet specified investment goals for the benefit of investors.

As above, investors may be institutions, such as insurance companies, pension funds, corporations, charities, educational establishments, or private investors, either directly via investment contracts or, more commonly, via collective investment schemes like mutual funds, [exchange-traded funds](/source/Exchange-traded_funds), or [real estate investment trusts](/source/Real_estate_investment_trust).

At the heart of investment management[9] is [asset allocation](/source/Asset_allocation)—[diversifying the exposure](/source/Diversification_(finance)) among these [asset classes](/source/Asset_classes), and among individual securities within each asset class—as appropriate to the client's [investment policy](/source/Investment_policy), in turn, a function of risk profile, investment goals, and investment horizon (see [Investor profile](/source/Investor_profile)). Here:

- [Portfolio optimization](/source/Portfolio_optimization) is the process of selecting the best portfolio given the client's objectives and constraints.

- [Fundamental analysis](/source/Fundamental_analysis) is the approach typically applied in [valuing](/source/Valuation_(finance)) and evaluating the individual securities.

- [Technical analysis](/source/Technical_analysis) is about forecasting future asset prices with past data.[16]

Overlaid is the portfolio manager's [investment style](/source/Investment_style)—broadly, [active](/source/Active_management) vs [passive](/source/Passive_management), [value](/source/Value_investing) vs [growth](/source/Growth_investing), and [small cap](/source/Small_cap_company) vs. [large cap](/source/Large_cap)—and [investment strategy](/source/Investment_strategy).

In a well-diversified portfolio, achieved [investment performance](/source/Investment_performance) will, in general, largely be a function of the asset mix selected, while the individual securities are less impactful. The specific approach or philosophy will also be significant, depending on the extent to which it is complementary with the [market cycle](/source/Stock_market_cycles).

Additional to this [diversification](/source/Diversification_(finance)), the fundamental risk mitigant employed, [investment managers will apply](/source/Financial_risk_management#Investment_management) various hedging techniques as appropriate,[9] these may relate to the [portfolio as a whole](/source/Portfolio_insurance) or [to individual stocks](/source/Hedge_(finance)#Hedging_a_stock_price). [Bond portfolios](/source/Bond_fund) are often (instead) managed via [cash flow matching](/source/Cashflow_matching) or [immunization](/source/Immunization_(finance)), while for derivative portfolios and positions, traders use ["the Greeks"](/source/Greeks_(finance)#Use_of_the_Greeks) to measure and then offset sensitivities. In parallel, managers – [active](/source/Active_management) and [passive](/source/Passive_management) – [will monitor](/source/Performance_attribution) [tracking error](/source/Tracking_error), thereby minimizing and preempting any underperformance [vs their "benchmark"](/source/Investment_management#Risk-adjusted_performance_measurement).

A [quantitative fund](/source/Quantitative_fund) is managed using [computer-based mathematical techniques](/source/Quantitative_fund#Investment_process) (increasingly, [machine learning](/source/Machine_learning)) instead of human judgment. The actual trading [is typically automated](/source/Automated_trading_system) via [sophisticated algorithms](/source/Algorithmic_trading).

### Risk management

Main article: [Financial risk management](/source/Financial_risk_management)

Crowds gathering outside the New York Stock Exchange after the [Wall Street crash of 1929](/source/Wall_Street_crash_of_1929)

Customers queuing outside a [Northern Rock](/source/Northern_Rock) branch in the [United Kingdom](/source/United_Kingdom) to withdraw their savings during the [2008 financial crisis](/source/2008_financial_crisis)

[Risk management](/source/Risk_management), in general, is the study of how to control risks and balance the possibility of gains; it is the process of measuring risk and then developing and implementing strategies to manage that risk. [Financial risk management](/source/Financial_risk_management)[17][18] is the practice of protecting [corporate value](/source/Enterprise_value) against [financial risks](/source/Financial_risk), often by ["hedging"](/source/Hedge_(finance)) exposure to these using financial instruments. The focus is particularly on credit and market risk, and in banks, through regulatory capital, includes operational risk.

- [Credit risk](/source/Credit_risk) is the risk of [default on a debt](/source/Default_(finance)) that may arise from a borrower failing to make required payments;

- [Market risk](/source/Market_risk) relates to losses arising from movements in market variables such as prices and exchange rates;

- [Operational risk](/source/Operational_risk) relates to failures in internal processes, people, and systems, or to external events (these risks will often be [insured](/source/Insurance)).

Financial risk management is [related to corporate finance](/source/Corporate_finance#Financial_risk_management)[9] in two ways. Firstly, firm exposure to market risk is a direct result of previous capital investments and funding decisions; while credit risk arises from the business's credit policy and is often addressed through [credit insurance](/source/Trade_credit_insurance) and [provisioning](/source/Bad_debt#Doubtful_debt_reserve). Secondly, both disciplines share the goal of enhancing or at least preserving, the firm's [economic value](/source/Economic_value), and in this context[19] overlaps also [enterprise risk management](/source/Enterprise_risk_management), typically the domain of [strategic management](/source/Strategic_management). Here, businesses devote much time and effort to [forecasting](/source/Financial_forecast), [analytics](/source/FP%26A) and [performance monitoring](/source/Managerial_finance#Managerial_accounting_techniques). (See [ALM](/source/Asset_and_liability_management) and [treasury management](/source/Treasury_management).)

[For banks](/source/Financial_risk_management#Banking) and other wholesale institutions,[20] risk management [focuses on](/source/Quantitative_analysis_(finance)#Risk_management) managing, and as necessary hedging, the various positions held by the institution—both [trading positions](/source/Trading_book) and [long term exposures](/source/Banking_book)—and on calculating and monitoring the resultant [economic capital](/source/Economic_capital), and [regulatory capital](/source/Regulatory_capital) under [Basel III](/source/Basel_III). The calculations here are mathematically sophisticated, and within the domain of [quantitative finance](/source/Quantitative_finance) as below. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed to [counterparty credit risk](/source/Counterparty_credit_risk). Banks typically employ [Middle office](/source/Middle_office) ["Risk Groups"](/source/Investment_banking#Risk_management), whereas [front office](/source/Front_office) risk teams provide risk "services" (or "solutions") to customers.

[Insurers](/source/Insurers)[21] [manage their own risks](/source/Financial_risk_management#Insurance) with a focus on [solvency](/source/Solvency_ratio) and the ability to pay claims: [life insurers](/source/Life_insurer) are concerned more with [longevity risk](/source/Longevity_risk) and [interest rate risk](/source/Interest_rate_risk); short-term insurers ([property](/source/Property_insurance), [health](/source/Health_insurance), [casualty](/source/Casualty_insurance)) emphasize [catastrophe-](/source/Catastrophe_modeling) and claims volatility risks. For expected claims [reserves](/source/Actuarial_reserve) are set aside periodically, while to absorb unexpected losses, a minimum [level of capital](/source/Solvency_II) is maintained.

### Quantitative finance

Main article: [Quantitative analysis (finance)](/source/Quantitative_analysis_(finance))

[Dōjima Rice Exchange](/source/D%C5%8Djima_Rice_Exchange), the world's first [futures exchange](/source/Futures_exchange), established in [Osaka](/source/Osaka) in 1697

Quantitative finance—also referred to as "mathematical finance"—includes those finance activities where [a sophisticated mathematical model](/source/Financial_modeling#Quantitative_finance) is required,[22] and thus overlaps several of the above.

As a specialized practice area, quantitative finance comprises primarily three sub-disciplines; the underlying theory and techniques [are discussed](#Financial_mathematics) in the next section:

1. Quantitative finance is often synonymous with [financial engineering](/source/Financial_engineering). This area generally underpins a bank's [customer-driven derivatives business](/source/Investment_banking#Sales_and_trading)—delivering bespoke [OTC-contracts](/source/Over-the-counter_(finance)#Contracts) and ["exotics"](/source/Exotic_derivative), and [designing](/source/Structured_product#Product_design_and_manufacture) the various structured products and solutions mentioned—and encompasses [modeling and programming](/source/Financial_modeling#Quantitative_finance) in support of the initial trade, and its subsequent hedging and management.

1. Quantitative finance also significantly overlaps [financial risk management](/source/Financial_risk_management) in banking, as [mentioned](#Risk_management), both as regards this hedging, and as regards economic capital as well as compliance with regulations and [the Basel capital / liquidity requirements](/source/Basel_III).

1. "Quants" are also responsible for building and deploying the investment strategies at the quantitative funds [mentioned](#Investment_management); they are also involved in [quantitative investing](/source/Outline_of_finance#Quantitative_investing) more generally, in areas such as [trading strategy](/source/Trading_strategy) formulation, and in [automated trading](/source/Automated_trading), [high-frequency trading](/source/High-frequency_trading), [algorithmic trading](/source/Algorithmic_trading), and [program trading](/source/Program_trading).

## Financial theory

∑ t = 1 n F C F F t ( 1 + W A C C t ) t + [ F C F F n + 1 ( W A C C n + 1 − g n + 1 ) ] ( 1 + W A C C n ) n {\displaystyle \sum _{t=1}^{n}{\frac {FCFF_{t}}{(1+WACC_{t})^{t}}}+{\frac {\left[{\frac {FCFF_{n+1}}{(WACC_{n+1}-g_{n+1})}}\right]}{(1+WACC_{n})^{n}}}} DCF valuation formula widely applied in business and finance, since articulated in 1938. Here, to get the value of the firm, its forecasted free cash flows are discounted to the present using the weighted average cost of capital for the discount factor. For share valuation investors use the related dividend discount model.

Financial theory is studied and developed within the disciplines of [management](/source/Management#Training_and_education), [(financial)](/source/Financial_economics) [economics](/source/Economics), [accountancy](/source/Accountancy) and [applied mathematics](/source/Applied_mathematics). In the abstract,[9][23] *finance* is concerned with the investment and deployment of [assets](/source/Asset) and [liabilities](/source/Liability_(financial_accounting)) over "space and time"; i.e., it is about performing [valuation](/source/Valuation_(finance)) and [asset allocation](/source/Asset_allocation) today, based on the risk and uncertainty of future outcomes while appropriately incorporating the [time value of money](/source/Time_value_of_money).[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

### Managerial finance

Main article: [Managerial finance](/source/Managerial_finance)

Managerial finance is the branch of finance that deals with the financial aspects of the [management](/source/Management) of a company, and the financial dimension of managerial decision-making more broadly. It provides the [theoretical underpin](/source/Management#Theoretical_scope) for the practice [described above](#Corporate_finance), concerning itself with the [managerial application](/source/Management#Implementation_of_policies_and_strategies) of the various [finance techniques](/source/Financial_analysis).[24] Academics working in this area are typically based in [business school](/source/Business_school) finance departments, in [accounting](/source/Accounting), or in [management science](/source/Management_science).

The tools addressed and developed relate in the main to [managerial accounting](/source/Managerial_accounting) and [corporate finance](/source/Corporate_finance): the former allow management to better understand, and hence act on, financial information relating to [profitability](/source/Profitability) and performance; the latter, as above, are about optimizing the overall financial structure, including its impact on working capital. Key aspects of managerial finance thus include:

- [Capital budgeting](/source/Capital_budgeting)

- [Capital structure](/source/Capital_structure)

- [Working capital management](/source/Working_capital_management)

- [Risk management](/source/Risk_management)

- Financial analysis and reporting

The discussion, however, also extends to the broader field of [business strategy](/source/Business_strategy), emphasizing the need for alignment with the overall strategic objectives of the company. It likewise incorporates [managerial perspectives](/source/Management#Theoretical_scope) related to planning, directing, and controlling.[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*]

### Financial economics

Main article: [Financial economics](/source/Financial_economics)

The "[efficient frontier](/source/Efficient_frontier)", was first formulated by [Harry Markowitz](/source/Harry_Markowitz) in 1952 as a prototypical concept in [modern portfolio theory](/source/Modern_portfolio_theory). In the [Markowitz model](/source/Markowitz_model),  an "efficient" portfolio has the best possible expected return for its level of risk (represented by the standard deviation of return).

[Modigliani–Miller theorem](/source/Modigliani%E2%80%93Miller_theorem), a foundational element of finance theory, introduced in 1958; it forms the basis for modern thinking on [capital structure](/source/Capital_structure). Even if [leverage](/source/Leverage_(finance)) ([D/E](/source/Debt_to_equity_ratio)) increases, the [weighted average cost of capital](/source/Weighted_average_cost_of_capital) (k0) stays constant.

Financial economics[25] is the branch of [economics](/source/Economics) that studies the interrelation of financial [variables](/source/Variable_(mathematics)), such as [prices](/source/Price), [interest rates](/source/Interest_rate) and shares, as opposed to [real](/source/Real_vs._nominal_in_economics) economic variables, i.e. [goods and services](/source/Goods_and_services). It thus centers on pricing, decision making, and risk management in the [financial markets](/source/Financial_market),[25][23] and produces many of the commonly employed [financial models](/source/Financial_model). ([Financial econometrics](/source/Financial_econometrics) is the branch of financial economics that uses econometric techniques to [parameterize](/source/Parametrization_(geometry)) the relationships suggested.)

The discipline has two main areas of focus:[23] [asset pricing](/source/Asset_pricing) and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:

1. Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the [portfolio-](/source/Outline_of_finance#Portfolio_theory) and [investment theory](/source/Investment_theory) applied in asset management. The analysis essentially explores how [rational investors](/source/Homo_economicus) would apply [risk and return](/source/Risk-return_spectrum) to the problem of [investment](/source/Investment) under uncertainty, producing the key "[Fundamental theorem of asset pricing](/source/Fundamental_theorem_of_asset_pricing)". Here, the twin assumptions of [rationality](/source/Rational_pricing) and [market efficiency](/source/Efficient-market_hypothesis) lead to [modern portfolio theory](/source/Modern_portfolio_theory) (the [CAPM](/source/Capital_asset_pricing_model)), and to the [Black–Scholes](/source/Black%E2%80%93Scholes_model) theory for [option valuation](/source/Valuation_of_options). At more advanced levels—and often in response to [financial crises](/source/Financial_crisis)—the study [then extends](/source/Financial_economics#Extensions) these ["neoclassical" models](/source/Neoclassical_economics#Rational_Behavior_Assumptions) to incorporate phenomena where their assumptions do not hold, or to more general settings.

1. Much of [corporate finance theory](/source/Outline_of_finance#Corporate_finance_theory), by contrast, considers investment under "[certainty](/source/Certainty)" ([Fisher separation theorem](/source/Fisher_separation_theorem), ["theory of investment value"](/source/The_Theory_of_Investment_Value), and [Modigliani–Miller theorem](/source/Modigliani%E2%80%93Miller_theorem)). Here, theory and methods are developed for the decisions about funding, dividends, and capital structure discussed above. A recent development is [to incorporate uncertainty](/source/Financial_economics#Corporate_finance_theory) and [contingency](/source/Contingent_claim_valuation)—and thus various elements of asset pricing—into these decisions, employing for example [real options analysis](/source/Real_options_analysis).

### Financial mathematics

C ( S , t ) = N ( d 1 ) S − N ( d 2 ) K e − r ( T − t ) d 1 = 1 σ T − t [ ln ⁡ ( S K ) + ( r + σ 2 2 ) ( T − t ) ] d 2 = d 1 − σ T − t {\displaystyle {\begin{aligned}C(S,t)&=N(d_{1})S-N(d_{2})Ke^{-r(T-t)}\\d_{1}&={\frac {1}{\sigma {\sqrt {T-t}}}}\left[\ln \left({\frac {S}{K}}\right)+\left(r+{\frac {\sigma ^{2}}{2}}\right)(T-t)\right]\\d_{2}&=d_{1}-\sigma {\sqrt {T-t}}\\\end{aligned}}} The Black–Scholes formula for the value of a call option. Although lately its use is considered naive, it has underpinned the development of derivatives-theory, and financial mathematics more generally, since its introduction in 1973.[26]

["Trees"](/source/Lattice_model_(finance)) are widely applied in mathematical finance; here used in calculating an [OAS](/source/Option_adjusted_spread). Other common pricing-methods are [simulation](/source/Monte_Carlo_methods_in_finance#Overview) and [PDEs](/source/Finite_difference_methods_for_option_pricing). These are used for settings beyond [those envisaged](/source/Black%E2%80%93Scholes_model#Fundamental_hypotheses) by Black-Scholes. [Post crisis](/source/Valuation_of_options#Post_crisis), even in those settings, banks use [local](/source/Local_volatility) and [stochastic volatility](/source/Stochastic_volatility) models to incorporate the [volatility surface](/source/Volatility_surface), while the [xVA](/source/XVA) adjustments accommodate [counterparty](/source/Counterparty_credit_risk) and capital considerations.

Main article: [Mathematical finance](/source/Mathematical_finance)

See also: [Quantitative analysis (finance)](/source/Quantitative_analysis_(finance)) and [Financial modeling § Quantitative finance](/source/Financial_modeling#Quantitative_finance)

Financial mathematics[27] is the field of [applied mathematics](/source/Applied_mathematics) concerned with [financial markets](/source/Financial_market); [Louis Bachelier's doctoral thesis](/source/Louis_Bachelier#The_doctoral_thesis), defended in 1900, is considered to be the first scholarly work in this area. The field is largely focused on the [modeling of derivatives](/source/Outline_of_finance#Derivatives_pricing)—with much emphasis on [interest rate-](/source/Interest_rate_derivative) and [credit risk modeling](/source/Credit_derivative)—while other important areas include [insurance mathematics](/source/Actuarial_science) and [quantitative portfolio management](/source/Outline_of_finance#Mathematical_techniques). Relatedly, the techniques developed [are applied](/source/Contingent_claim_analysis) to pricing and hedging a wide range of [asset-backed](/source/Asset-backed_security), [government](/source/Government_bond), and [corporate](/source/Capital_structure)-securities.

As [above](#Quantitative_finance), in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed. The [main mathematical tools](/source/Outline_of_finance#Mathematical_tools) and techniques are, correspondingly:

- for derivatives,[28] [Itô's stochastic calculus](/source/It%C3%B4_calculus), [simulation](/source/Monte_Carlo_methods_in_finance), and [partial differential equations](/source/Partial_differential_equation); see aside boxed discussion re the prototypical [Black-Scholes model](/source/Black-Scholes_model) and [the various numeric techniques](/source/Valuation_of_options#Pricing_models) now applied

- for risk management,[20] [value at risk](/source/Value_at_risk), [stress testing](/source/Stress_test_(financial)) and ["sensitivities" analysis](/source/PnL_Explained#Sensitivities_method) (applying the "greeks"); the underlying mathematics comprises [mixture models](/source/Mixture_model#A_financial_model), [PCA](/source/Principal_component_analysis#Quantitative_finance), [volatility clustering](/source/Volatility_clustering) and [copulas](/source/Copula_(probability_theory)#Quantitative_finance).[29]

- in both of these areas, and particularly for portfolio problems, quants employ [sophisticated optimization techniques](/source/Outline_of_finance#Mathematical_techniques)

Mathematically, these separate into [two analytic branches](/source/Mathematical_finance#History:_Q_versus_P): derivatives pricing uses [risk-neutral probability](/source/Risk-neutral_measure) (or [arbitrage-pricing](/source/Rational_pricing) probability), denoted by "Q"; while risk and portfolio management generally use physical (or actual or actuarial) probability, denoted by "P". These are interrelated through the above "[Fundamental theorem of asset pricing](/source/Fundamental_theorem_of_asset_pricing)".

The subject is closely related to financial economics, which, as outlined, focuses on much of the underlying theory involved in financial mathematics: generally, financial mathematics will derive and extend the [mathematical models](/source/Mathematical_model) suggested. [Computational finance](/source/Computational_finance) is the branch of (applied) [computer science](/source/Computer_science) that deals with problems of practical interest in finance, and especially[27] emphasizes the [numerical methods](/source/Numerical_methods) applied here.

### Experimental finance

Main article: [Experimental finance](/source/Experimental_finance)

[Experimental finance](/source/Experimental_finance)[30] aims to establish different market settings and environments to experimentally observe and provide a lens through which science can analyze agents' behavior and the resulting characteristics of trading flows, information diffusion, and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance study how well existing financial economics theories make accurate predictions and seek to validate them. They also aim to discover new principles to extend these theories for future financial decisions. This research often involves conducting trading simulations or observing human behavior in artificial, competitive, market-like environments.

### Behavioral finance

Main article: [Behavioral economics](/source/Behavioral_economics)

[Behavioral finance](/source/Behavioral_finance) studies how the *[psychology](/source/Psychology)* of investors or managers affects financial decisions and markets[31] and is relevant when making a decision that can impact either negatively or positively on one of their areas. With more in-depth research into behavioral finance, it is possible to bridge what actually happens in financial markets with analysis based on financial theory.[32] Behavioral finance has grown over the last few decades to become an integral aspect of finance. Nowadays there is a need for more theory and testing of the effects of feelings on financial decisions. Especially, because now the time has come to move beyond behavioral finance to social finance, which studies the structure of social interactions, how financial ideas spread, and how social processes affect financial decisions and outcomes.[33][34]

Behavioral finance includes such topics as:

1. Empirical studies that demonstrate significant deviations from classical theories;

1. Models of how psychology affects and impacts trading and prices;

1. Forecasting based on these methods;

1. Studies of experimental asset markets and the use of models to forecast experiments.

A strand of behavioral finance has been dubbed [quantitative behavioral finance](/source/Quantitative_behavioral_finance), which uses mathematical and statistical methodologies to understand behavioral biases in conjunction with valuation.

### Quantum finance

Main article: [Quantum finance](/source/Quantum_finance)

This section needs more citations. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. (April 2025) (Learn how and when to remove this message)

Quantum finance involves applying quantum mechanical approaches to financial theory, providing novel methods and perspectives in the field.[35] *Quantum* *finance* is an interdisciplinary field, in which theories and methods developed by *quantum* physicists and economists are applied to solve financial problems. It represents a branch known as econophysics. Although *quantum* computational methods have been around for quite some time and use the basic principles of physics to better understand the ways to implement and manage cash flows, it is mathematics that is actually important in this new scenario.[36] Finance theory is heavily based on [financial instrument](/source/Financial_instrument) pricing such as [stock option](/source/Stock_option) pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as [computational finance](/source/Computational_finance). Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Most commonly used quantum financial models are quantum continuous model, quantum binomial model, multi-step quantum binomial model etc.

## History of finance

Further information: [History of money](/source/History_of_money), [History of banking](/source/History_of_banking), [History of investment](/source/History_of_investment), [Financial centre § History](/source/Financial_centre#History), [Corporate finance § History](/source/Corporate_finance#History), [Quantitative analysis (finance) § History](/source/Quantitative_analysis_(finance)#History), [Financial crisis § History](/source/Financial_crisis#History), and [Global financial system § History of international financial architecture](/source/Global_financial_system#History_of_international_financial_architecture)

See also: [Category:History of finance](https://en.wikipedia.org/wiki/Category:History_of_finance)

The origin of finance can be traced to the beginning of state formation and trade during the [Bronze Age](/source/Bronze_Age). The earliest historical evidence of finance is dated to around 3000 BCE. Banking originated in [West Asia](/source/West_Asia), where temples and palaces were used as safe places for the storage of valuables. Initially, the only valuable that could be deposited was grain, but cattle and precious materials were eventually included. During the same period, the [Sumerian city](/source/History_of_Sumer) of [Uruk](/source/Uruk) in [Mesopotamia](/source/Mesopotamia) supported trade by lending as well as the use of interest. In Sumerian, "interest" was *mas*, which translates to "calf". In [Greece](/source/Greece) and [Egypt](/source/Egypt), the words used for interest, *tokos* and *ms* respectively, meant "to give birth". In these cultures, interest indicated a valuable increase, and seemed to consider it from the lender's point of view.[37] The [Code of Hammurabi](/source/Code_of_Hammurabi) (1792–1750 BCE) included laws governing banking operations. The Babylonians were accustomed to charging interest at the rate of 20 percent per year. By 1200 BCE, [cowrie](/source/Cowrie) shells were used as a form of money in [China](/source/China).

The use of coins as a means of representing money began in the years between 700 and 500 BCE.[38] Herodotus mentions the use of crude coins in [Lydia](/source/Lydia) around 687 BCE and, by 640 BCE, the Lydians had started to use coin money more widely and opened permanent retail shops.[39] Shortly after, cities in [Classical Greece](/source/Classical_Greece), such as [Aegina](/source/Aegina), [Athens](/source/Athens), and [Corinth](/source/Ancient_Corinth), started minting their own coins between 595 and 570 BCE. During the [Roman Republic](/source/Roman_Republic), interest was outlawed by the *Lex Genucia* reforms in 342 BCE, though the provision went largely unenforced. Under [Julius Caesar](/source/Julius_Caesar), a ceiling on interest rates of 12% was set, and much later under [Justinian](/source/Justinian) it was lowered even further to between 4% and 8%.[40]

The first stock exchange was opened in [Antwerp](/source/Antwerp) in 1531.[41] Since then, popular exchanges such as the [London Stock Exchange](/source/London_Stock_Exchange) (founded in 1773) and the [New York Stock Exchange](/source/New_York_Stock_Exchange) (founded in 1793) were created.[42][43]

## See also

- [2008 financial crisis](/source/2008_financial_crisis)

- [Outline of finance](/source/Outline_of_finance)

## Notes

1. **[^](#cite_ref-1)** The following are definitions of 'finance' as crafted by the authors indicated: - [Fama and Miller](https://faculty.chicagobooth.edu/eugene.fama/research/Theory%20of%20Finance/The%20Theory%20of%20Finance%20Preface%20and%20Table%20of%20Contents.pdf): "The theory of finance is concerned with how individuals and firms allocate resources through time. In particular, it seeks to explain how solutions to the problems faced in allocating resources through time are facilitated by the existence of capital markets (which provide a means for individual economic agents to exchange resources to be available of different points In time) and of firms (which, by their production-investment decisions, provide a means for individuals to transform current resources physically into resources to be available in the future)." - [Guthmann and Dougall](https://afajof.org/wp-content/uploads/files/historical-texts/guthmann-dougall-1940-ocr.pdf): "Finance is concerned with the raising and administering of funds and with the relationships between private profit-seeking enterprise on the one hand and the groups which supply the funds on the other. These groups, which include investors and speculators – that is, capitalists or property owners – as well as those who advance short-term capital, place their money in the field of commerce and industry and in return expect a stream of income." - [Drake and Fabozzi](https://www.wiley.com/en-in/Finance:+Capital+Markets,+Financial+Management,+and+Investment+Management-p-9780470407356): "Finance is the application of economic principles to decision-making that involves the allocation of money under conditions of uncertainty." - [F.W. Paish](https://openlibrary.org/authors/OL1637242A/Frank_Walter_Paish): "Finance may be defined as the position of money at the time it is wanted". - [John J. Hampton](https://openlibrary.org/authors/OL835181A/John_J._Hampton): "The term finance can be defined as the management of the flows of money through an organisation, whether it will be a corporation, school, or bank or government agency". - [Howard and Upton](https://www.worldcat.org/oclc/976723372): "Finance may be defined as that administrative area or set of administrative functions in an organisation which relates with the arrangement of each debt and credit so that the organisation may have the means to carry out the objectives as satisfactorily as possible". - [Pablo Fernandez](https://education.wbstraining.com/pluginfile.php/2808/mod_resource/content/1/PabloFernandez_Finance%20and%20Financial%20Economics.pdf): "Finance is a profession that requires interdisciplinary training and helps company managers make sound decisions regarding financing, investment, continuity, and other issues that affect the inflow and outflow of money, as well as the company’s risk. It also helps individuals and institutions invest wisely and plan money-related matters effectively."

1. **[^](#cite_ref-2)** The first academic journal, *[The Journal of Finance](/source/The_Journal_of_Finance)*,[*[citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citation_needed)*] began publication in 1946.

1. **[^](#cite_ref-7)** Finance thus allows production and consumption in society to operate independently from each other. Without the use of financial allocation, production would have to happen at the same time and space as consumption. Through finance, distances in timespace between production and consumption are then possible.[4]

## References

1. **[^](#cite_ref-3)** Gippel, Jennifer K (7 November 2012). ["A revolution in finance?"](https://doi.org/10.1177%2F0312896212461034). *[Australian Journal of Management](/source/Australian_Journal_of_Management)*. **38** (1): 125–146. [doi](/source/Doi_(identifier)):[10.1177/0312896212461034](https://doi.org/10.1177%2F0312896212461034). [ISSN](/source/ISSN_(identifier)) [0312-8962](https://search.worldcat.org/issn/0312-8962). [S2CID](/source/S2CID_(identifier)) [154759424](https://api.semanticscholar.org/CorpusID:154759424).

1. **[^](#cite_ref-4)** ["Finance"](https://www.ucas.com/explore/subjects/finance) [Archived](https://web.archive.org/web/20230131091501/https://www.ucas.com/explore/subjects/finance) 31 January 2023 at the [Wayback Machine](/source/Wayback_Machine), [UCAS](/source/UCAS) Subject Guide.

1. **[^](#cite_ref-5)** Anthony P. Carnevale, Ban Cheah, Andrew R. Hanson (2015). ["The Economic Value of College Majors"](https://1gyhoq479ufd3yna29x7ubjn-wpengine.netdna-ssl.com/wp-content/uploads/The-Economic-Value-of-College-Majors-Full-Report-web-FINAL.pdf) [Archived](https://web.archive.org/web/20221108144220/https://1gyhoq479ufd3yna29x7ubjn-wpengine.netdna-ssl.com/wp-content/uploads/The-Economic-Value-of-College-Majors-Full-Report-web-FINAL.pdf) 8 November 2022 at the [Wayback Machine](/source/Wayback_Machine). [Georgetown University](/source/Georgetown_University).

1. **[^](#cite_ref-6)** Allen, Michael; Price, John (2000). ["Monetized time-space: derivatives – money's 'new imaginary'?"](https://www.tandfonline.com/doi/abs/10.1080/030851400360497). *Economy and Society*. **29** (2): 264–284. [doi](/source/Doi_(identifier)):[10.1080/030851400360497](https://doi.org/10.1080%2F030851400360497). [S2CID](/source/S2CID_(identifier)) [145739812](https://api.semanticscholar.org/CorpusID:145739812). [Archived](https://web.archive.org/web/20220320050529/https://www.tandfonline.com/doi/abs/10.1080/030851400360497) from the original on 20 March 2022. Retrieved 3 June 2022.

1. **[^](#cite_ref-8)** See e.g., [Bank of Finland](/source/Bank_of_Finland). ["Financial system"](https://www.suomenpankki.fi/en/financial-stability/the-financial-system-in-brief/). [Archived](https://web.archive.org/web/20200602105013/https://www.suomenpankki.fi/en/financial-stability/the-financial-system-in-brief/) from the original on 2 June 2020. Retrieved 18 May 2020.

1. **[^](#cite_ref-9)** ["What is the financial system?"](https://www.ecnmy.org/learn/your-money/banking-and-finance/what-is-the-financial-system/). *Economy*. [Archived](https://web.archive.org/web/20200731162128/https://www.ecnmy.org/learn/your-money/banking-and-finance/what-is-the-financial-system/) from the original on 31 July 2020. Retrieved 18 May 2020.

1. **[^](#cite_ref-10)** Publishing, Speedy (2015). [*Finance (Speedy Study Guides)*](https://books.google.com/books?id=DF7FCQAAQBAJ). Speedy Publishing LLC. [ISBN](/source/ISBN_(identifier)) [978-1-68185-667-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-68185-667-4).

1. **[^](#cite_ref-11)** Snowdon, Michael, ed. (2019), "Financial Planning Standards Board", *Financial Planning Competency Handbook*, John Wiley & Sons, Ltd, pp. 709–735, [doi](/source/Doi_(identifier)):[10.1002/9781119642497.ch80](https://doi.org/10.1002%2F9781119642497.ch80), [ISBN](/source/ISBN_(identifier)) [978-1-119-64249-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-119-64249-7), [S2CID](/source/S2CID_(identifier)) [242623141](https://api.semanticscholar.org/CorpusID:242623141)

1. ^ [***a***](#cite_ref-Drake_Fabozzi_12-0) [***b***](#cite_ref-Drake_Fabozzi_12-1) [***c***](#cite_ref-Drake_Fabozzi_12-2) [***d***](#cite_ref-Drake_Fabozzi_12-3) [***e***](#cite_ref-Drake_Fabozzi_12-4) [***f***](#cite_ref-Drake_Fabozzi_12-5) Pamela Drake and [Frank Fabozzi](/source/Frank_Fabozzi) (2009). [What Is Finance?](https://media.wiley.com/product_data/excerpt/52/04704073/0470407352.pdf) [Archived](https://web.archive.org/web/20230223003858/https://media.wiley.com/product_data/excerpt/52/04704073/0470407352.pdf) 2023-02-23 at the [Wayback Machine](/source/Wayback_Machine)

1. **[^](#cite_ref-13)** See [Aswath Damodaran](/source/Aswath_Damodaran), [Corporate Finance: First Principles](http://pages.stern.nyu.edu/~adamodar/New_Home_Page/AppldCF/other/Image2.gif) [Archived](https://web.archive.org/web/20161017190714/http://pages.stern.nyu.edu/~adamodar/New_Home_Page/AppldCF/other/Image2.gif) 2016-10-17 at the [Wayback Machine](/source/Wayback_Machine)

1. **[^](#cite_ref-Irons_14-0)** Irons, Robert (July 2019). [*The Fundamental Principles of Finance*](https://play.google.com/store/books/details/Robert_Irons_The_Fundamental_Principles_of_Finance?id=tzr3DwAAQBAJ&hl=en_US&gl=US). Google Books: Routledge. [ISBN](/source/ISBN_(identifier)) [978-1-000-02435-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-000-02435-7). [Archived](https://web.archive.org/web/20211111150837/https://play.google.com/store/books/details/Robert_Irons_The_Fundamental_Principles_of_Finance?id=tzr3DwAAQBAJ&hl=en_US&gl=US) from the original on 11 November 2021. Retrieved 3 April 2021.

1. **[^](#cite_ref-15)** Doss, Daniel; Sumrall, William; Jones, Don (2012). *Strategic Finance for Criminal Justice Organizations* (1st ed.). Boca Raton, Florida: CRC Press. p. 23. [ISBN](/source/ISBN_(identifier)) [978-1-4398-9223-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-4398-9223-7).

1. **[^](#cite_ref-16)** Doss, Daniel; Sumrall, William; Jones, Don (2012). *Strategic Finance for Criminal Justice Organizations* (1st ed.). Boca Raton, Florida: CRC Press. pp. 53–54. [ISBN](/source/ISBN_(identifier)) [978-1-4398-9223-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-4398-9223-7).

1. **[^](#cite_ref-17)** Kioko, Sharon; Marlowe, Justin (2016). [*Financial Strategy for Public Managers*](https://press.rebus.community/financialstrategy/). Rebus Foundation. [ISBN](/source/ISBN_(identifier)) [978-1-927472-59-0](https://en.wikipedia.org/wiki/Special:BookSources/978-1-927472-59-0). [Archived](https://web.archive.org/web/20220615185910/https://press.rebus.community/financialstrategy/) from the original on 15 June 2022. Retrieved 5 July 2022.

1. **[^](#cite_ref-18)** Board of Governors of Federal Reserve System of the United States. Mission of the Federal Reserve System. [Federalreserve.gov](https://www.federalreserve.gov/aboutthefed/mission.htm) Accessed: 2010-01-16. (Archived by WebCite at [Archived](https://web.archive.org/web/20100114154328/http://www.federalreserve.gov/aboutthefed/mission.htm) 2010-01-14 at the [Wayback Machine](/source/Wayback_Machine))

1. **[^](#cite_ref-19)** Han, Yufeng; Liu, Yang; Zhou, Guofu; Zhu, Yingzi (21 May 2021). ["Technical Analysis in the Stock Market: A Review"](https://doi.org/10.2139%2Fssrn.3850494). Rochester, NY. [doi](/source/Doi_(identifier)):[10.2139/ssrn.3850494](https://doi.org/10.2139%2Fssrn.3850494). [S2CID](/source/S2CID_(identifier)) [235195430](https://api.semanticscholar.org/CorpusID:235195430). [SSRN](/source/SSRN_(identifier)) [3850494](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3850494). {{[cite journal](https://en.wikipedia.org/wiki/Template:Cite_journal)}}: Cite journal requires |journal= ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#missing_periodical))

1. **[^](#cite_ref-Christoffersen2011_20-0)** Peter F. Christoffersen (2011). [*Elements of Financial Risk Management*](https://books.google.com/books?id=YkcMBGYbRasC). Academic Press. [ISBN](/source/ISBN_(identifier)) [978-0-12-374448-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-374448-7).

1. **[^](#cite_ref-Malz2011_21-0)** Allan M. Malz (2011). [*Financial Risk Management: Models, History, and Institutions*](https://books.google.com/books?id=rFX2f6AxH1QC). John Wiley & Sons. [ISBN](/source/ISBN_(identifier)) [978-1-118-02291-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-118-02291-7).

1. **[^](#cite_ref-22)** John Hampton (2011). *The AMA Handbook of Financial Risk Management*. [American Management Association](/source/American_Management_Association). [ISBN](/source/ISBN_(identifier)) [978-0-8144-1744-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-8144-1744-7)

1. ^ [***a***](#cite_ref-DeMeo_23-0) [***b***](#cite_ref-DeMeo_23-1) See generally, Roy E. DeMeo (N.D.) [Quantitative Risk Management: VaR and Others](https://mathfinance.charlotte.edu/sites/mathfinance.charlotte.edu/files/media/An%20Introduction%20to%20Value%20At%20Risk%20New.pdf) [Archived](https://web.archive.org/web/20211112082350/https://mathfinance.charlotte.edu/sites/mathfinance.charlotte.edu/files/media/An%20Introduction%20to%20Value%20At%20Risk%20New.pdf) 2021-11-12 at the [Wayback Machine](/source/Wayback_Machine)

1. **[^](#cite_ref-24)** Thomas M. Grondin (2001). ["Risk Management Practices in the Insurance Industry"](https://www.soa.org/globalassets/assets/library/proceedings/record-of-the-society-of-actuaries/2000-09/2001/january/RSA01V27N218PD.PDF) [Archived](https://web.archive.org/web/20250320092151/https://www.soa.org/globalassets/assets/library/proceedings/record-of-the-society-of-actuaries/2000-09/2001/january/RSA01V27N218PD.PDF) 20 March 2025 at the [Wayback Machine](/source/Wayback_Machine). [Society of Actuaries](/source/Society_of_Actuaries)

1. **[^](#cite_ref-SIAM_25-0)** See discussion here: ["Careers in Applied Mathematics"](https://www.siam.org/Portals/0/Student%20Programs/Thinking%20of%20a%20Career/brochure.pdf) (PDF). [Society for Industrial and Applied Mathematics](/source/Society_for_Industrial_and_Applied_Mathematics). [Archived](https://web.archive.org/web/20190305095047/https://www.siam.org/Portals/0/Student%20Programs/Thinking%20of%20a%20Career/brochure.pdf) (PDF) from the original on 5 March 2019.

1. ^ [***a***](#cite_ref-Fama_and_Miller_26-0) [***b***](#cite_ref-Fama_and_Miller_26-1) [***c***](#cite_ref-Fama_and_Miller_26-2) See the discussion re finance theory by Fama and Miller under [§ Notes](#Notes).

1. **[^](#cite_ref-cfi_27-0)** [What is managerial finance?](https://corporatefinanceinstitute.com/resources/knowledge/finance/managerial-finance/) [Archived](https://web.archive.org/web/20220704085037/https://corporatefinanceinstitute.com/resources/knowledge/finance/managerial-finance/) 4 July 2022 at the [Wayback Machine](/source/Wayback_Machine), [Corporate Finance Institute](/source/Corporate_Finance_Institute)

1. ^ [***a***](#cite_ref-Sharpe_28-0) [***b***](#cite_ref-Sharpe_28-1) For an overview, see ["Financial Economics"](http://www.stanford.edu/~wfsharpe/mia/int/mia_int2.htm) [Archived](https://web.archive.org/web/20040604105441/http://www.stanford.edu/~wfsharpe/mia/int/mia_int2.htm) 2004-06-04 at the [Wayback Machine](/source/Wayback_Machine), [William F. Sharpe](/source/William_F._Sharpe) (Stanford University manuscript)

1. **[^](#cite_ref-29)** ["The History of the Black-Scholes Formula"](https://priceonomics.com/the-history-of-the-black-scholes-formula/) [Archived](https://web.archive.org/web/20211126125626/https://priceonomics.com/the-history-of-the-black-scholes-formula/) 2021-11-26 at the [Wayback Machine](/source/Wayback_Machine), priceonomics.com

1. ^ [***a***](#cite_ref-SIAM2_30-0) [***b***](#cite_ref-SIAM2_30-1) [Research Area: Financial Mathematics and Engineering](https://www.siam.org/research-areas/detail/financial-mathematics-and-engineering#) [Archived](https://web.archive.org/web/20220516114958/https://www.siam.org/research-areas/detail/financial-mathematics-and-engineering) 2022-05-16 at the [Wayback Machine](/source/Wayback_Machine), Society for Industrial and Applied Mathematics

1. **[^](#cite_ref-Mastro_31-0)** For a survey, see ["Financial Models"](https://catalogimages.wiley.com/images/db/pdf/9781118487716.excerpt.pdf) [Archived](https://web.archive.org/web/20211113134700/https://catalogimages.wiley.com/images/db/pdf/9781118487716.excerpt.pdf) 2021-11-13 at the [Wayback Machine](/source/Wayback_Machine), from Michael Mastro (2013). *Financial Derivative and Energy Market Valuation*, John Wiley & Sons. [ISBN](/source/ISBN_(identifier)) [978-1-118-48771-6](https://en.wikipedia.org/wiki/Special:BookSources/978-1-118-48771-6).

1. **[^](#cite_ref-32)** See for example III.A.3, in Carol Alexander, ed. (2005). *The Professional Risk Managers' Handbook*. PRMIA Publications. [ISBN](/source/ISBN_(identifier)) [978-0-9766097-0-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-9766097-0-4)

1. **[^](#cite_ref-ssrn_33-0)** Bloomfield, Robert and Anderson, Alyssa. ["Experimental finance"](http://fasri.net/wp-content/uploads/2009/10/experimental-finance-chapter-_wiley_.pdf) [Archived](https://web.archive.org/web/20160304033849/http://fasri.net/wp-content/uploads/2009/10/experimental-finance-chapter-_wiley_.pdf) 2016-03-04 at the [Wayback Machine](/source/Wayback_Machine). In Baker, H. Kent, and Nofsinger, John R., eds. Behavioral finance: investors, corporations, and markets. Vol. 6. John Wiley & Sons, 2010. pp. 113–131. [ISBN](/source/ISBN_(identifier)) [978-0-470-49911-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-49911-5)

1. **[^](#cite_ref-34)** Glaser, Markus and Weber, Martin and Noeth, Markus. (2004). ["Behavioral Finance"](https://madoc.bib.uni-mannheim.de/2770/1/dp03_14.pdf) [Archived](https://web.archive.org/web/20230209093116/https://madoc.bib.uni-mannheim.de/2770/1/dp03_14.pdf) 2023-02-09 at the [Wayback Machine](/source/Wayback_Machine), pp. 527–546 in *Handbook of Judgment and Decision Making*, Blackwell Publishers [ISBN](/source/ISBN_(identifier)) [978-1-405-10746-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-405-10746-4)

1. **[^](#cite_ref-35)** Zahera, Syed Aliya; Bansal, Rohit (8 May 2018). ["Do investors exhibit behavioral biases in investment decision making? A systematic review"](https://www.emerald.com/insight/content/doi/10.1108/QRFM-04-2017-0028/full/html). *Qualitative Research in Financial Markets*. **10** (2): 210–251. [doi](/source/Doi_(identifier)):[10.1108/QRFM-04-2017-0028](https://doi.org/10.1108%2FQRFM-04-2017-0028). [ISSN](/source/ISSN_(identifier)) [1755-4179](https://search.worldcat.org/issn/1755-4179). [Archived](https://web.archive.org/web/20220408144635/https://www.emerald.com/insight/content/doi/10.1108/QRFM-04-2017-0028/full/html) from the original on 8 April 2022. Retrieved 8 April 2022.

1. **[^](#cite_ref-36)** Shefrin, Hersh (2002). [*Beyond greed and fear: Understanding behavioral finance and the psychology of investing*](https://archive.org/details/beyondgreedfearu00shef). New York: Oxford University Press. p. ix. [ISBN](/source/ISBN_(identifier)) [978-0-19-530421-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-530421-3). Retrieved 8 May 2017. growth of behavioral finance.

1. **[^](#cite_ref-37)** Hirshleifer, David (2015). ["Behavioral Finance"](https://doi.org/10.1146%2Fannurev-financial-092214-043752). *Annual Review of Financial Economics*. **7**: 133–159. [doi](/source/Doi_(identifier)):[10.1146/annurev-financial-092214-043752](https://doi.org/10.1146%2Fannurev-financial-092214-043752). [ISSN](/source/ISSN_(identifier)) [1941-1367](https://search.worldcat.org/issn/1941-1367).

1. **[^](#cite_ref-38)** Focardi, Sergio; Fabozzi, Frank J.; Mazza, Davide (31 August 2020). ["Quantum Option Pricing and Quantum Finance"](http://pm-research.com/lookup/doi/10.3905/jod.2020.1.111). *The Journal of Derivatives*. **28** (1): 79–98. [doi](/source/Doi_(identifier)):[10.3905/jod.2020.1.111](https://doi.org/10.3905%2Fjod.2020.1.111). [ISSN](/source/ISSN_(identifier)) [1074-1240](https://search.worldcat.org/issn/1074-1240).

1. **[^](#cite_ref-39)** Ristic, Kristijan (2–3 December 2021). ["New Financial Future: Digital Finance As a key Aspect of Financial Innovation"](https://www.proquest.com/docview/2616890742). *75th International Scientific Conference on Economic and Social Development*: 283–288. [ProQuest](/source/ProQuest) [2616890742](https://www.proquest.com/docview/2616890742).

1. **[^](#cite_ref-40)** Fergusson, Nial. *The Ascent of Money*. United States: Penguin Books.

1. **[^](#cite_ref-41)** ["babylon-coins.com"](http://babylon-coins.com/tast1.html). *babylon-coins.com*. [Archived](https://web.archive.org/web/20210615134016/http://babylon-coins.com/tast1.html) from the original on 15 June 2021. Retrieved 13 May 2021.

1. **[^](#cite_ref-42)** ["Herodotus on Lydia"](https://www.worldhistory.org/article/81/herodotus-on-lydia/). *World History Encyclopedia*. [Archived](https://web.archive.org/web/20210513152131/https://www.worldhistory.org/article/81/herodotus-on-lydia/) from the original on 13 May 2021. Retrieved 13 May 2021.

1. **[^](#cite_ref-43)** ["History of Usury Prohibition – IslamiCity"](https://www.islamicity.org/2773/history-of-usury-prohibition/). *islamicity.org*. 22 December 2005. [Archived](https://web.archive.org/web/20230409014040/https://www.islamicity.org/2773/history-of-usury-prohibition/) from the original on 9 April 2023. Retrieved 9 April 2023.

1. **[^](#cite_ref-44)** ["Handelsbeurs"](https://visit.antwerpen.be/info/handelsbeurs) [Trade fair]. *Visit Antwerp* (in Dutch). Retrieved 2 September 2022. The 'Nieuwe Beurs' was built in 1531 because the 'Old Beurs' in Hofstraat had become too small. It was the first stock exchange ever built specifically for that purpose and later became the example for all stock exchange buildings in the world.

1. **[^](#cite_ref-45)** ["Our History"](https://www.londonstockexchange.com/discover/lseg/our-history). *London Stock Exchange*. [Archived](https://web.archive.org/web/20220902213413/https://www.londonstockexchange.com/discover/lseg/our-history) from the original on 2 September 2022. Retrieved 2 September 2022.

1. **[^](#cite_ref-46)** ["Research Guides: Wall Street and the Stock Exchanges: Historical Resources: Stock Exchanges"](https://guides.loc.gov/wall-street-history/exchanges). *Library of Congress*. [Archived](https://web.archive.org/web/20220804230415/https://guides.loc.gov/wall-street-history/exchanges) from the original on 4 August 2022. Retrieved 2 September 2022.

## Further reading

- [Graham, Benjamin](/source/Benjamin_Graham); [Jason Zweig](/source/Jason_Zweig) (8 July 2003) [1949]. [*The Intelligent Investor*](https://archive.org/details/harrypotterhalfb00rowl_0). Warren E. Buffett (collaborator) (2003 ed.). [HarperCollins](/source/HarperCollins). front cover. [ISBN](/source/ISBN_(identifier)) [0-06-055566-1](https://en.wikipedia.org/wiki/Special:BookSources/0-06-055566-1).

- Graham, Benjamin; [Dodd, David LeFevre](/source/David_Dodd) (1996) [1934]. [*Security Analysis: The Classic 1934 Edition*](https://books.google.com/books?id=wXlrnZ1uqK0C). [McGraw-Hill Education](/source/McGraw-Hill_Education). [ISBN](/source/ISBN_(identifier)) [978-0-070-24496-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-070-24496-2). [LCCN](/source/LCCN_(identifier)) [34023635](https://lccn.loc.gov/34023635).

- [Bogle, John Bogle](/source/John_C._Bogle) (2007). [*The Little Book of Common Sense Investing: The Only Way to Guarantee Your Fair Share of Stock Market Returns*](https://archive.org/details/littlebookofcomm00bogl). John Wiley and Sons. pp. [216](https://archive.org/details/littlebookofcomm00bogl/page/216). [ISBN](/source/ISBN_(identifier)) [978-0-470-10210-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-10210-7).

- [Buffett, W.](/source/Warren_Buffett); Cunningham, L.A. (2009). [*The Essays of Warren Buffett: Lessons for Investors and Managers*](https://books.google.com/books?id=njy3PQAACAAJ). [John Wiley & Sons (Asia) Pte Limited](/source/Wiley_(publisher)). [ISBN](/source/ISBN_(identifier)) [978-0-470-82441-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-82441-2).

- [Kiyosaki, Robert](/source/Robert_Kiyosaki) and [Sharon Lechter](/source/Sharon_Lechter) (2000). *[Rich Dad Poor Dad](/source/Rich_Dad_Poor_Dad): What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!* [Warner Business Books](/source/Warner_Business_Books). [ISBN](/source/ISBN_(identifier)) [0-446-67745-0](https://en.wikipedia.org/wiki/Special:BookSources/0-446-67745-0)

- [Stanley, Thomas J.](/source/Thomas_J._Stanley); Danko, W.D. (1998). [*The Millionaire Next Door*](https://books.google.com/books?id=ldpaww5kkmoC). [Gallery Books](/source/Gallery_Books). [ISBN](/source/ISBN_(identifier)) [978-0-671-01520-6](https://en.wikipedia.org/wiki/Special:BookSources/978-0-671-01520-6). [LCCN](/source/LCCN_(identifier)) [98046515](https://lccn.loc.gov/98046515).

- [Soros, George](/source/George_Soros) (1988). [*The Alchemy of Finance: Reading the Mind of the Market*](https://books.google.com/books?id=JDSii-QgejoC). A Touchstone book. [Simon & Schuster](/source/Simon_%26_Schuster). [ISBN](/source/ISBN_(identifier)) [978-0-671-66238-7](https://en.wikipedia.org/wiki/Special:BookSources/978-0-671-66238-7). [LCCN](/source/LCCN_(identifier)) [87004745](https://lccn.loc.gov/87004745).

- [Fisher, Philip Arthur](/source/Philip_Arthur_Fisher) (1996). [*Common Stocks and Uncommon Profits and Other Writings*](https://books.google.com/books?id=UES-QgAACAAJ). Wiley Investment Classics. [Wiley](/source/Wiley_(publisher)). [ISBN](/source/ISBN_(identifier)) [978-0-471-11927-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-471-11927-2). [LCCN](/source/LCCN_(identifier)) [95051449](https://lccn.loc.gov/95051449).

## External links

**Finance**  at Wikipedia's [sister projects](https://en.wikipedia.org/wiki/Wikipedia:Wikimedia_sister_projects)

- [Definitions](https://en.wiktionary.org/wiki/Special:Search/Finance) from Wiktionary
- [Media](https://commons.wikimedia.org/wiki/Category:Finance) from Commons
- [Quotations](https://en.wikiquote.org/wiki/Finance) from Wikiquote
- [Texts](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Finance) from Wikisource
- [Textbooks](https://en.wikibooks.org/wiki/Special:Search/Finance) from Wikibooks
- [Resources](https://en.wikiversity.org/wiki/Special:Search/Finance) from Wikiversity

- [Hypertextual Finance Glossary](https://people.duke.edu/~charvey/Classes/wpg/glossary.htm) ([Campbell Harvey](/source/Campbell_Harvey))

- [Finance Glossary](http://www.vernimmen.com/Practice/Glossary.php) ([Pierre Vernimmen](/source/Pierre_Vernimmen))

- [Glossary of financial risk management terms](https://www.risk.net/glossary) ([Risk.net](/source/Risk_(magazine)))

- [Glossary of Key Investment Terms](https://www.pimco.com/us/en/resources/glossary) ([PIMCO](/source/PIMCO))

- [Corporate finance resources](http://pages.stern.nyu.edu/~adamodar/) ([Aswath Damodaran](/source/Aswath_Damodaran))

- [Financial management resources](https://web.utk.edu/~jwachowi/wacho_world.html) ([James Van Horne](/source/James_Van_Horne))

- [Personal finance resources](https://www.mymoney.gov/mymoneyfive) ([Financial Literacy and Education Commission](/source/Financial_Literacy_and_Education_Commission), mymoney.gov)

- [Public finance resources](https://gsdrc.org/professional-dev/public-financial-management/) (Governance and Social Development Resource Centre, gsdrc.org) [[Archived](https://web.archive.org/web/20230602184354/https://gsdrc.org/professional-dev/public-financial-management/) 2023-06-02 at the [Wayback Machine](/source/Wayback_Machine)]

- [Risk management resources](https://globalriskinstitute.org/resources/) ([Global Risk Institute](/source/Global_Risk_Institute))

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