Finance

Wealth management consultation – here the financial advisor counsels the client on an appropriate investment strategy

Personal finance is defined as "the mindful planning of monetary spending and saving, while also considering the possibility of future risk".[7] Personal finance may involve paying for education, financing durable goods such as real estate and cars, buying insurance, investing, and saving for retirement.[8] 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.[9] The following steps, as outlined by the Financial Planning Standards Board,[10] 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 and/or a savings account;
• Preparing for retirement or other long term expenses.[11]

Founded in 1602, the Dutch East India Company (VOC), started off as a spice trader, "going public" in the same year, with the world's first IPO.

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 of corporations, and the tools and analysis used to allocate financial resources. While corporate finance is in principle different from managerial finance, which studies the financial management of all firms rather than corporations alone, the concepts are applicable to the financial problems of all firms,[12] 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, its stock, and its return to shareholders, while also balancing risk and profitability. This entails [13] three primary areas:

1. Capital budgeting: selecting which projects to invest in – here, accurately determining value is crucial, as judgements about asset values can be "make or break" [14]
2. Dividend policy: the use of "excess" funds – are these to be reinvested in the business or returned to shareholders
3. Capital structure: deciding on the mix of funding to be used – here attempting to find the optimal capital mix re debt-commitments vs cost of capital

The latter creates the link with investment banking and securities trading, as above, in that the capital raised will generically comprise debt, i.e. corporate bonds, and equity, often listed shares. Re risk management within corporates, see below.

Financial managers – i.e. as opposed to corporate financiers – focus more on the short term elements of profitability, cash flow, and "working capital management" (inventory, credit and debtors), ensuring that the firm can safely and profitably 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. See Financial management § Role and Financial analyst § Corporate and other.

President George W. Bush, speaking on the Federal Budget in 2007, here requesting additional funds from Congress

2020 US Federal Revenues and Outlays

Public finance describes finance as related to sovereign states, sub-national entities, and related public entities or agencies. It generally encompasses a long-term strategic perspective regarding investment decisions that affect public entities.[15] These long-term strategic periods typically encompass five or more years.[16] Public finance is primarily concerned with: [17]

• Identification of required expenditures of a public sector entity;
• Source(s) of that entity's revenue;
• The budgeting process;
• Sovereign debt issuance, or municipal bonds for public works projects.

Central banks, such as the Federal Reserve System banks in the United States and the Bank of England in the United Kingdom, are strong players in public finance. They act as lenders of last resort as well as strong influences on monetary and credit conditions in the economy.[18]

Development finance, which is related, concerns investment in economic development projects provided by a (quasi) governmental institution on a non-commercial basis; these projects would otherwise not be able to get financing. See Public utility § Finance. A public–private partnership is primarily used for infrastructure projects: a private sector corporate provides the financing up-front, and then draws profits from taxpayers and/or users.

Share prices listed in a Korean Newspaper

"The excitement before the bubble burst" – viewing prices via ticker tape, shortly before the Wall Street Crash of 1929

Modern price-ticker. This infrastructure underpins contemporary exchanges, and allows, ultimately, for individual day trading, as well as wholesale computer-executed program trading and high-frequency trading.

Investment management [19][20][12] is the professional asset management of various securities – typically shares and bonds, but also other assets, such as real estate, commodities and alternative investments – 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, or REITs.

At the heart of investment management[12] is asset allocation – diversifying the exposure among these asset classes, and among individual securities within each asset class – as appropriate to the client's investment policy, in turn, a function of risk profile, investment goals, and investment horizon (see Investor profile). Here:

• Portfolio optimization is the process of selecting the best portfolio given the client's objectives and constraints.
• Fundamental analysis is the approach typically applied in valuing and evaluating the individual securities.

Overlaid is the portfolio manager's investment style – broadly, active vs passive , value vs growth, and small cap vs. large cap – and investment strategy.

In a well-diversified portfolio, achieved 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.

A quantitative fund is managed using computer-based techniques (increasingly, machine learning) instead of human judgment. The actual trading also, is typically automated via sophisticated algorithms.

Crowds gathering outside the New York Stock Exchange after the Wall Street Crash of 1929

Customers queuing outside a Northern Rock branch in the United Kingdom to withdraw their savings during the financial crisis of 2007–2008

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 [21][22] is the practice of protecting corporate value by using financial instruments to manage exposure to risk, here called "hedging"; the focus is particularly on credit and market risk, and in banks, through regulatory capital, includes operational risk.

• Credit risk is risk of default on a debt that may arise from a borrower failing to make required payments;
• Market risk relates to losses arising from movements in market variables such as prices and exchange rates;
• Operational risk relates to failures in internal processes, people, and systems, or to external events.

Financial risk management is related to corporate finance[12] 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 and provisioning. Secondly, both disciplines share the goal of enhancing or at least preserving, the firm's economic value, and in this context[23] overlaps also enterprise risk management, typically the domain of strategic management. Here, businesses devote much time and effort to forecasting, analytics and performance monitoring. See also "ALM" and treasury management.

For banks and other wholesale institutions,[24] risk management focuses on managing, and as necessary hedging, the various positions held by the institution – both trading positions and long term exposures – and on calculating and monitoring the resultant economic capital, and regulatory capital under Basel III. The calculations here are mathematically sophisticated, and within the domain of quantitative finance as below. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed to counterparty credit risk. Banks typically employ Middle office "Risk Groups" here, whereas front office risk teams provide risk "services" / "solutions" to customers.

Additional to diversification – the fundamental risk mitigant here – investment managers will apply various risk management techniques to their portfolios as appropriate:[12] these may relate to the portfolio as a whole or to individual stocks; bond portfolios are typically managed via cash flow matching or immunization. Re derivative portfolios (and positions), "the Greeks" is a vital risk management tool – it measures sensitivity to a small change in a given underlying parameter so that the portfolio can be rebalanced accordingly by including additional derivatives with offsetting characteristics.

Quantitative finance – also referred to as "mathematical finance" – includes those finance activities where a sophisticated mathematical model is required,[25] 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 in the next section:

1. Quantitative finance is often synonymous with financial engineering. This area generally underpins a bank's customer-driven derivatives business – delivering bespoke OTC-contracts and "exotics", and designing the various structured products and solutions mentioned – and encompasses modeling and programming in support of the initial trade, and its subsequent hedging and management.
2. Quantitative finance also significantly overlaps financial risk management in banking, as mentioned, both as regards this hedging, and as regards economic capital as well as compliance with regulations and the Basel capital / liquidity requirements.
3. "Quants" are also responsible for building and deploying the investment strategies at the quantitative funds mentioned; they are also involved in quantitative investing more generally, in areas such as trading strategy formulation, and in automated trading, high-frequency trading, algorithmic trading, and program trading.

Decision trees, a more sophisticated valuation-approach, sometimes applied to corporate "project" valuations (and a standard [29] in business school curricula); various scenarios are considered, and their discounted cash flows are probability weighted.

Managerial finance is the branch of management that concerns itself with the managerial application of finance techniques and theory, emphasizing the financial aspects of managerial decisions; the assessment is per the managerial perspectives of planning, directing, and controlling. The techniques addressed and developed relate in the main to managerial accounting and corporate finance: the former allow management to better understand, and hence act on, financial information relating to profitability and performance; the latter, as above, are about optimizing the overall financial structure, including its impact on working capital. The implementation of these techniques – i.e. financial management – is outlined above. Academics working in this area are typically based in business school finance departments, in accounting, or in management science.

The "efficient frontier", a prototypical concept in portfolio optimization. Introduced in 1952, it remains "a mainstay of investing and finance".[30]

Modigliani–Miller theorem, a foundational element of finance theory, introduced in 1958; it forms the basis for modern thinking on capital structure. Even if leverage (D/E) increases, the WACC (k0) stays constant.

Financial economics [31] is the branch of economics that studies the interrelation of financial variables, such as prices, interest rates and shares, as opposed to real economic variables, i.e. goods and services. It thus centers on pricing, decision making, and risk management in the financial markets, [31] [26] and produces many of the commonly employed financial models. (Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize the relationships suggested.)

The discipline has two main areas of focus: [26] 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:

• Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the portfolio- and investment theory applied in asset management. The analysis essentially explores how rational investors would apply risk and return to the problem of investment under uncertainty; producing the key "Fundamental theorem of asset pricing". Here, the twin assumptions of rationality and market efficiency lead to modern portfolio theory (the CAPM), and to the Black–Scholes theory for option valuation. At more advanced levels – and often in response to financial crises – the study then extends these "Neoclassical" models to incorporate phenomena where their assumptions do not hold, or to more general settings.
• Much of corporate finance theory, by contrast, considers investment under "certainty" (Fisher separation theorem, "theory of investment value", Modigliani–Miller theorem). Here theory and methods are developed for the decisioning about funding, dividends, and capital structure discussed above. A recent development is to incorporate uncertainty and contingency – and thus various elements of asset pricing – into these decisions, employing for example real options analysis.

"Trees" are widely applied in mathematical finance; here used in calculating an OAS. Other common pricing-methods are simulation and PDEs. These are used for settings beyond those envisaged by Black-Scholes. Post crisis, even in those settings, banks use local and stochastic volatility models to incorporate the volatility surface.

Financial mathematics [33] is the field of applied mathematics concerned with financial markets; Louis Bachelier's doctoral thesis, defended in 1900, is considered to be the first scholarly work in this area.  As above, in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed.

The field is largely focused on the modeling of derivatives – with much emphasis on interest rate- and credit risk modeling – while other important areas include insurance mathematics and quantitative portfolio management. Relatedly, the techniques developed are applied to pricing and hedging a wide range of asset-backed, government, and corporate-securities. The main mathematical tools and techniques are:

• for derivatives,[34] Itô's stochastic calculus, simulation, and partial differential equations; see aside boxed discussion re the prototypical Black-Scholes and the various numeric techniques now applied
• for risk management,[24] value at risk, stress testing, "sensitivities" analysis (applying the "greeks"), and xVA; the underlying mathematics comprises mixture models, PCA, volatility clustering and copulas.[35]
• in both of these areas, and particularly for portfolio problems, quants employ sophisticated optimization techniques

Mathematically, these separate into two analytic branches: derivatives pricing uses risk-neutral probability (or arbitrage-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".

The subject has a close relationship with financial economics, which, as above, is concerned with much of the underlying theory that is involved in financial mathematics: generally, financial mathematics will derive and extend the mathematical models suggested. Computational finance is the branch of (applied) computer science that deals with problems of practical interest in finance, and especially [33] emphasizes the numerical methods applied here.

Experimental finance[36] 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 can study to what extent existing financial economics theory makes valid predictions and therefore prove them, as well as attempt to discover new principles on which such theory can be extended and be applied to future financial decisions. Research may proceed by conducting trading simulations or by establishing and studying the behavior of people in artificial, competitive, market-like settings.

Behavioral finance studies how the psychology of investors or managers affects financial decisions and markets[37] 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.[38] Behavioral finance has grown over the last few decades to become an integral aspect of finance.[39]

Behavioral finance includes such topics as:

1. Empirical studies that demonstrate significant deviations from classical theories;
2. Models of how psychology affects and impacts trading and prices;
3. Forecasting based on these methods;
4. Studies of experimental asset markets and the use of models to forecast experiments.

A strand of behavioral finance has been dubbed quantitative behavioral finance, which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation.

Quantum finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a branch of econophysics. Finance theory is heavily based on financial instrument pricing such as 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. 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.