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Quantitative analysis (finance)

2021-07-31T20:37:02Z

Rudyardcrow: Added a citation about the greatest hedge funds that use quant analysis.

{{short description|Use of mathematical and statistical methods in finance}}
'''Quantitative analysis''' is the use of [[Mathematical finance|mathematical]] and statistical methods in [[finance]] and [[investment management]]. Those working in the field are '''quantitative analysts''' ('''quants'''). Quants tend to specialize in specific areas which may include [[Derivative (finance)|derivative]] structuring or pricing, [[risk management]], [[algorithmic trading]] and [[investment management]]. The occupation is similar to those in [[industrial mathematics]] in other industries.<ref>See Definition in the Society for Applied and Industrial Mathematics http://www.siam.org/about/pdf/brochure.pdf {{dead link|date=May 2021}}</ref> The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns ([[trend following]] or [[Mean reversion (finance)|mean reversion]]). The resulting strategies may involve [[high-frequency trading]].

Although the original quantitative analysts were "[[sell side]] quants" from market maker firms, concerned with derivatives pricing and risk management, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematical finance, including the [[buy side]].<ref>Derman, E. (2004). My life as a quant: reflections on physics and finance. John Wiley & Sons.</ref> Applied quantitative analysis is commonly associated with '''quantitative investment management''' which includes a variety of methods such as [[statistical arbitrage]], algorithmic trading and electronic trading.

Some of the larger investment managers using quantitative analysis include [[Renaissance Technologies]], [[D. E. Shaw & Co.]], and [[AQR Capital Management]].<ref>{{cite web |title=Top Quantitative Hedge Funds |url=https://www.streetofwalls.com/finance-training-courses/quantitative-hedge-fund-training/quant-firms/ |website=Street of Walls}}</ref>

==History==
{{See|Mathematical finance#Derivatives pricing: the Q world|Financial economics#Derivative pricing}}
[[Quantitative finance]] started in 1900 with [[Louis Bachelier]]'s doctoral [[thesis]] "Theory of Speculation", which provided a model to price [[Option (finance)|options]] under a [[normal distribution]]. [[Harry Markowitz]]'s 1952 doctoral thesis "Portfolio Selection" and its published version was one of the first efforts in economics journals to formally adapt mathematical concepts to finance (mathematics was until then confined to mathematics, statistics or specialized economics journals).<ref>{{cite journal |last=Markowitz |first=H. |year=1952 |title=Portfolio Selection |journal=[[Journal of Finance]] |volume=7 |issue=1 |pages=77–91 |doi=10.1111/j.1540-6261.1952.tb01525.x }}</ref> Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves [[Itō calculus]], management of risk in a quantifiable manner underlies much of the modern theory. Modern quantitative investment management was first introduced from the research of [[Edward O. Thorp|Edward Thorp]], a mathematics professor at [[New Mexico State University]] (1961–1965) and [[University of California, Irvine]] (1965–1977).<ref name=":1">{{Cite web|last=Lam|first=Leslie P. Norton and Dan|title=Why Edward Thorp Owns Only Berkshire Hathaway|url=https://www.barrons.com/articles/why-edward-thorp-only-owns-berkshire-hathaway-1521547200|access-date=2021-06-06|website=www.barrons.com|language=en-US}}</ref> Considered the "Father of Quantitative Investing",<ref name=":1" /> Throp sought to predict and simulate [[blackjack]], a card-game he played in Las Vegas casinos.<ref name=":0">{{Cite book|last=Patterson|first=Scott|url=https://books.google.com/books?id=-ydNYWGIussC&q=santa+fe|title=The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It|date=2010-02-02|publisher=Crown|isbn=978-0-307-45339-6|language=en}}</ref> He was able to create a system, known broadly as [[card counting]], which used [[probability theory]] and statistical analysis to successfully win blackjack games.<ref name=":0" /> His research was subsequently used during the 1980s and 1990s by investment management firms seeking to generate systematic and consistent returns in the U.S. stock market.<ref name=":0" />

In 1965 [[Paul Samuelson]] introduced [[stochastic calculus]] into the study of finance.<ref>{{cite journal |last=Samuelson |first=P. A. |year=1965 |title=Rational Theory of Warrant Pricing |journal=Industrial Management Review |volume=6 |issue=2 |pages=13–32 }}</ref><ref>[[Henry McKean]] the co-founder of stochastic calculus (along with [[Kiyosi Itô]]) wrote the appendix: see {{cite journal |last=McKean |first=H. P. Jr. |year=1965 |title=Appendix (to Samuelson): a free boundary problem for the heat equation arising from a problem of mathematical economics |journal=Industrial Management Review |volume=6 |issue=2 |pages=32–39 }}</ref> In 1969 [[Robert C. Merton|Robert Merton]] promoted continuous stochastic calculus and [[continuous-time]] processes. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium", and in later papers he used the machinery of stochastic calculus to begin investigation of this issue. At the same time as Merton's work and with Merton's assistance, [[Fischer Black]] and [[Myron Scholes]] developed the [[Black–Scholes model]], which was awarded the 1997 [[Nobel Memorial Prize in Economic Sciences]]. It provided a solution for a practical problem, that of finding a fair price for a [[Option_style#American_and_European_options|European call option]], i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black–Scholes model on a solid theoretical basis, and showed how to price numerous other derivative securities.<ref>{{cite journal |last1=Harrison |first1=J. Michael |last2=Pliska |first2=Stanley R. |title=Martingales and Stochastic Integrals in the Theory of Continuous Trading |journal=Stochastic Processes and Their Applications |volume=11 |issue=3 |pages=215–260 |year=1981 |doi=10.1016/0304-4149(81)90026-0 |doi-access=free }}</ref> The various [[short-rate model]]s (beginning with [[Vasicek model|Vasicek]] in 1977), and the more general [[Heath–Jarrow–Morton_framework|HJM Framework]] (1987), relatedly allowed for an extension to [[fixed income]] and [[interest rate derivatives]]. Similarly, and in parallel, models were developed for various other underpinnings and applications, including [[credit derivatives]], [[exotic derivatives]], [[real options]], and [[employee stock options]]. Quants are thus involved in pricing and hedging a wide range of securities – [[Asset-backed security|asset-backed]], [[Government bond|government]], and [[Capital structure|corporate]] – additional to classic derivatives; see [[contingent claim analysis]].

[[Emanuel Derman]]'s 2004 book ''My Life as a Quant'' helped to both make the role of a quantitative analyst better known outside of finance, and to popularize the abbreviation "quant" for a quantitative analyst.<ref>{{cite book |last=Derman |first=Emanuel |year=2004 |title=My Life as a Quant |publisher=John Wiley and Sons }}</ref>
After the [[financial crisis of 2007–2008]], considerations re [[counterparty credit risk]] were incorporated into the modelling, previously performed in an entirely "[[risk neutral]] world", entailing three major developments:
(i) Option pricing and hedging inhere the relevant [[volatility surface]] (to some extent, equity-option prices have incorporated the [[volatility smile]] since the [[Black Monday (1987)|1987 crash]]) and banks then apply "surface aware" [[local volatility |local-]] or [[stochastic volatility]] models;
(ii) For discounting, the [[overnight indexed swap|OIS]] curve is used for the "risk free rate", as opposed to [[LIBOR]] as previously, and, relatedly, quants must model under a "[[multi-curve framework]]";
(iii) The risk neutral value is adjusted for the impact of counter-party credit risk via a [[credit valuation adjustment]], or CVA, as well as various of the other [[XVA]].
See {{sectionlink|Valuation of options#Post crisis}}.

==Education==
{{See also| Outline of finance#Education| Financial engineering#Education | Financial modeling#Quantitative finance| Financial analyst#Qualification}}
Quantitative analysts often come from [[Mathematical finance|financial mathematics]], [[financial engineering]], [[applied mathematics]], [[physics]] or [[engineering]] backgrounds, and quantitative analysis is a major source of employment for people with mathematics and physics [[PhD|PhD degrees]], or with [[Master of Financial Mathematics|financial mathematics master's degrees]].

Typically, a quantitative analyst will also need extensive skills in computer programming, most commonly [[C (programming language)|C]], [[C++]], [[Java (programming language)|Java]], [[R (programming language)|R]], [[MATLAB]], [[Mathematica]], and [[Python (programming language)|Python]].

[[Data science]] and [[machine learning]] analysis and modelling methods are being increasingly employed in portfolio performance and portfolio risk modelling,<ref>{{cite web|url=http://marketsmedia.com/machine-learning-in-finance-theory-and-applications/|title=Machine Learning in Finance: Theory and Applications|date=22 January 2013|website=marketsmedia.com|access-date=2 April 2018}}</ref><ref>{{cite web|url=http://www.qminitiative.org/UserFiles/files/S_Cl%C3%A9men%C3%A7on_ML.pdf|title=A Machine-Learning View of Quantitative Finance|website=qminitiative.org}}</ref> and as such data science and machine learning Master's graduates are also hired as quantitative analysts.

This demand for quantitative analysts has led to the creation of specialized Masters and PhD courses in financial engineering, mathematical finance, [[computational finance]], and/or [[financial reinsurance]]. In particular, Master's degrees in mathematical finance, financial engineering, [[operations research]], [[computational statistics]], [[applied mathematics]], [[machine Learning|machine learning]], and [[financial analysis]] are becoming more popular with students and with employers. See [[Master of Quantitative Finance]] for general discussion.

This has in parallel led to a resurgence in demand for [[actuarial]] qualifications, as well as commercial certifications such as the [[Certificate in Quantitative Finance|CQF]].
The more general [[Master of Finance]] (and [[Master of Financial Economics]]) increasingly includes a significant technical component.

==Types==
{{Unreferenced section|date=June 2010}}

===Front office quantitative analyst===
In sales and trading, quantitative analysts work to determine prices, manage risk, and identify profitable opportunities. Historically this was a distinct activity from trading but the boundary between a desk quantitative analyst and a quantitative trader is increasingly blurred, and it is now difficult to enter trading as a profession without at least some quantitative analysis education. In the field of [[algorithmic trading]] it has reached the point where there is little meaningful difference. Front office work favours a higher speed to quality ratio, with a greater emphasis on solutions to specific problems than detailed modeling. FOQs typically are significantly better paid than those in back office, risk, and model validation. Although highly skilled analysts, FOQs frequently lack software engineering experience or formal training, and bound by time constraints and business pressures, tactical solutions are often adopted.

===Quantitative investment management===
Quantitative analysis is used extensively by [[investment manager|asset managers]]. Some, such as FQ, AQR or Barclays, rely almost exclusively on [[quantitative investment|quantitative strategies]] while others, such as PIMPCO, Blackrock or Citadel use a mix of quantitative and [[fundamental analysis|fundamental methods]].

One of the first quantitative investment funds to launch was based in [[Santa Fe, New Mexico]] and began trading in 1991 under the name [[Prediction Company]].<ref name=":0" /><ref>{{Cite web|last=Rothschild|first=John|date=November 7, 1999|title=The Gnomes of Santa Fe|url=https://archive.nytimes.com/www.nytimes.com/books/99/11/07/reviews/991107.07rothcht.html|url-status=live|access-date=May 6, 2021|website=archive.nytimes.com}}</ref> By the late-1990s, Prediction Company began using [[statistical arbitrage]] to secure investment returns, along with three other funds at the time, [[Renaissance Technologies]] and [[D. E. Shaw & Co.|D. E. Shaw & Co]], both based in New York.<ref name=":0" /> Prediction hired scientists and computer programmers from the neighboring [[Los Alamos National Laboratory]] to create sophisticated statistical models using "industrial-strength computers" in order to "[build] the [[Particle accelerator|Supercollider]] of Finance".<ref>{{Cite news|last=Kelly|first=Kevin|date=July 1, 1994|title=Cracking Wall Street|language=en-US|work=Wired|url=https://www.wired.com/1994/07/wall-st/|access-date=May 6, 2021|issn=1059-1028}}</ref><ref>{{Cite web|last=Beilselki|first=Vincent|date=September 6, 2018|title=Millennium Shuts Down Pioneering Quant Hedge Fund|url=https://www.bloomberg.com/news/articles/2018-09-06/millennium-is-said-to-shut-down-pioneering-quant-hedge-fund-firm|url-status=live|access-date=May 6, 2021|website=www.bloomberg.com}}</ref>

===Library quantitative analysis===
Major firms invest large sums in an attempt to produce standard methods of evaluating prices and risk. These differ from front office tools in that Excel is very rare, with most development being in C++, though Java, C# and Python are sometimes used in non-performance critical tasks. LQs spend more time modeling ensuring the analytics are both efficient and correct, though there is tension between LQs and FOQs on the validity of their results. LQs are required to understand techniques such as [[Monte Carlo methods]] and [[finite difference methods]], as well as the nature of the products being modeled.

===Algorithmic trading quantitative analyst===
Often the highest paid form of Quant, ATQs make use of methods taken from [[signal processing]], [[game theory]], gambling [[Kelly criterion]], [[market microstructure]], [[econometrics]], and [[time series]] analysis. [[Algorithmic trading]] includes [[statistical arbitrage]], but includes techniques largely based upon speed of response, to the extent that some ATQs modify hardware and Linux kernels to achieve ultra low [[Latency (engineering)|latency]].

===Risk management===
This has grown in importance in recent years, as the credit crisis exposed holes in the mechanisms used to ensure that positions were correctly hedged, though in no bank does the pay in risk approach that in front office. A core technique is [[value at risk]], and this is backed up with various forms of [[stress test (financial)]], [[economic capital]] analysis and direct analysis of the positions and models used by various bank's divisions.

===Innovation===
In the aftermath of the financial crisis[which one?], there surfaced the recognition that quantitative valuation methods were generally too narrow in their approach. An agreed upon fix adopted by numerous financial institutions has been to improve collaboration.

===Model validation===
Model validation (MV) takes the models and methods developed by front office, library, and modeling quantitative analysts and determines their validity and correctness. The MV group might well be seen as a superset of the quantitative operations in a financial institution, since it must deal with new and advanced models and trading techniques from across the firm. Before the crisis however, the pay structure in all firms was such that MV groups struggle to attract and retain adequate staff, often with talented quantitative analysts leaving at the first opportunity. This gravely impacted corporate ability to manage model risk, or to ensure that the positions being held were correctly valued. An MV quantitative analyst would typically earn a fraction of quantitative analysts in other groups with similar length of experience. In the years following the crisis, this has changed. Regulators now typically talk directly to the quants in the middle office such as the model validators, and since profits highly depend on the regulatory infrastructure, model validation has gained in weight and importance with respect to the quants in the front office.

===Quantitative developer===
Quantitative developers, sometimes called quantitative software engineers, or quantitative engineers, are computer specialists that assist, implement and maintain the quantitative models. They tend to be highly specialised language technicians that bridge the gap between [[software engineers]] and quantitative analysts. The term is also sometimes used outside the finance industry to refer to those working at the intersection of [[software engineering]] and [[quantitative research]].

==Mathematical and statistical approaches==
{{see|Mathematical finance|Financial modeling#Quantitative finance|Outline of finance#Mathematical tools|Financial economics#Derivative pricing}}
Because of their backgrounds, quantitative analysts draw from various forms of mathematics: [[statistics]] and [[probability]], [[calculus]] centered around [[partial differential equation]]s, [[linear algebra]], [[discrete mathematics]], and [[econometrics]]. Some on the buy side may use [[machine learning]]. The
majority of quantitative analysts have received little formal education in mainstream economics, and often apply a mindset drawn from the physical sciences. Quants use mathematical skills learned from diverse fields such as computer science, physics and engineering. These skills include (but are not limited to) advanced statistics, linear algebra and partial differential equations as well as solutions to these based upon [[numerical analysis]].

Commonly used numerical methods are:
* [[Finite difference method]] – used to solve [[partial differential equation]]s;
* [[Monte Carlo method]] – Also used to solve [[partial differential equation]]s, but [[Monte Carlo simulation]] is also common in risk management;
* [[Ordinary least squares]] – used to estimate parameters in [[regression analysis|statistical regression analysis]];
* [[Spline interpolation]] – used to interpolate values from [[yield curve|spot and forward interest rates curves]], and [[volatility smile]]s;
* [[Bisection method|Bisection]], [[Newton method|Newton]], and [[Secant method]]s – used to find the [[root of a function|roots]], [[maxima and minima]] of functions (e.g. [[internal rate of return]], [[multi-curve framework|interest rate curve-building]].)

===Techniques===
A typical problem for a mathematically oriented quantitative analyst would be to develop a model for pricing, hedging, and risk-managing a complex derivative product. These quantitative analysts tend to rely more on numerical analysis than statistics and econometrics. One of the principal mathematical tools of quantitative finance is [[stochastic calculus]]. The mindset, however, is to prefer a deterministically "correct" answer, as once there is agreement on input values and market variable dynamics, there is only [[law of one price|one correct price]] for any given security (which can be demonstrated, albeit often inefficiently, through a large volume of Monte Carlo simulations).

A typical problem for a statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap. The model might include a company's book value to price ratio, its trailing earnings to price ratio, and other accounting factors. An investment manager might implement this analysis by buying the underpriced stocks, selling the overpriced stocks, or both. Statistically oriented quantitative analysts tend to have more of a reliance on statistics and econometrics, and less of a reliance on sophisticated numerical techniques and object-oriented programming. These quantitative analysts tend to be of the psychology that enjoys trying to find the best approach to modeling data, and can accept that there is no "right answer" until time has passed and we can retrospectively see how the model performed. Both types of quantitative analysts demand a strong knowledge of sophisticated mathematics and computer programming proficiency.

==Academic and technical field journals==
* [[Society for Industrial and Applied Mathematics]] (SIAM) ''Journal on Financial Mathematics''
* ''[[The Journal of Portfolio Management]]''<ref>{{Cite web|url=https://jpm.iijournals.com/|title=The Journal of Portfolio Management|website=jpm.iijournals.com|access-date=2019-02-02}}</ref>
* ''Quantitative Finance''<ref>http://www.tandfonline.com/toc/rquf20/current|</ref>
* ''Risk Magazine''
* ''Wilmott Magazine''
* ''Finance and Stochastics''<ref>{{Cite web | url=https://www.springer.com/mathematics/quantitative+finance/journal/780 | title=Finance and Stochastics – incl. Option to publish open access}}</ref>
* ''Mathematical Finance''

== Areas of work ==
* [[Trading strategy]] development
* [[Portfolio manager|Portfolio management]] and [[Portfolio optimization]]
* [[Derivatives pricing]] and hedging: involves software development, advanced numerical techniques, and stochastic calculus.
* [[Risk management]]: involves a lot of time series analysis, calibration, and [[backtesting]].
* [[Credit analysis]]
* [[Asset and liability management]]
* [[Structured finance]] and [[securitization]]
* [[Asset pricing]]

== Seminal publications ==
* 1900 – [[Louis Bachelier]], ''Théorie de la spéculation''
* 1938 – [[Frederick Macaulay]], ''The Movements of Interest Rates. Bond Yields and Stock Prices in the United States since 1856'', pp. 44–53, [[Bond duration]]
* 1944 – [[Kiyosi Itô]], "Stochastic Integral", Proceedings of the Imperial Academy, 20(8), pp. 519–524
* 1952 – [[Harry Markowitz]], ''Portfolio Selection'', [[Modern portfolio theory]]
* 1956 – [[John Larry Kelly Jr.|John Kelly]], ''A New Interpretation of Information Rate''
* 1958 – [[Franco Modigliani]] and [[Merton Miller]], ''The Cost of Capital, Corporation Finance and the Theory of Investment'', [[Modigliani–Miller theorem]] and [[Corporate finance]]
* 1964 – [[William F. Sharpe]], ''Capital asset prices: A theory of market equilibrium under conditions of risk'', [[Capital asset pricing model]]
* 1965 – [[John Lintner]], ''The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets'', [[Capital asset pricing model]]
* 1967 – [[Edward O. Thorp]] and Sheen Kassouf, ''Beat the Market''
* 1972 – [[Eugene Fama]] and [[Merton Miller]], ''Theory of Finance''
* 1972 – [[Martin L. Leibowitz]] and Sydney Homer, ''[[Inside the Yield Book]]'', [[Fixed income analysis]]
* 1973 – [[Fischer Black]] and [[Myron Scholes]], ''The Pricing of Options and Corporate Liabilities'' and [[Robert C. Merton]], ''Theory of Rational Option Pricing'', [[Black–Scholes]]
* 1976 – [[Fischer Black]], ''The pricing of commodity contracts'', [[Black model]]
* 1977 – [[Phelim Boyle]], ''Options: A Monte Carlo Approach'', [[Monte Carlo methods for option pricing]]
* 1977 – [[Oldřich Vašíček]], ''An equilibrium characterisation of the term structure'', [[Vasicek model]]
* 1979 – [[John Carrington Cox]]; [[Stephen Ross (economist)|Stephen Ross]]; [[Mark Rubinstein]], ''Option pricing: A simplified approach'', [[Binomial options pricing model]] and [[Lattice model (finance)|Lattice model]]
* 1980 – Lawrence G. McMillan, ''Options as a Strategic Investment''
* 1982 – Barr Rosenberg and Andrew Rudd, ''Factor-Related and Specific Returns of Common Stocks: Serial Correlation and Market Inefficiency'', Journal of Finance, May 1982 V. 37: #2
* 1982 – [[Robert F. Engle|Robert Engle]], ''Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of U.K. Inflation,'' Seminal paper in ARCH family of models [[GARCH]]
* 1985 – [[John Carrington Cox|John C. Cox]], [[Jonathan E. Ingersoll]] and [[Stephen Ross (economist)|Stephen Ross]], ''A theory of the term structure of interest rates'', [[Cox–Ingersoll–Ross model]]
* 1987 – Giovanni Barone-Adesi and [[Robert Whaley]], ''Efficient analytic approximation of American option values''. Journal of Finance. 42 (2): 301–20. [[Barone-Adesi and Whaley]] method for pricing [[American options]].
* 1987 – [[David Heath (probabilist)|David Heath]], [[Robert A. Jarrow]], and Andrew Morton ''Bond pricing and the term structure of interest rates: a new methodology'' (1987), [[Heath–Jarrow–Morton framework]] for interest rates
* 1990 – [[Fischer Black]], [[Emanuel Derman]] and William Toy, ''A One-Factor Model of Interest Rates and Its Application to Treasury Bond'', [[Black–Derman–Toy model]]
* 1990 – [[John C. Hull|John Hull]] and [[Alan White (economist)|Alan White]], "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) [[Hull-White model]]
* 1991 – Ioannis Karatzas & [[Steven E. Shreve]]. ''Brownian motion and stochastic calculus''.
* 1992 – [[Fischer Black]] and Robert Litterman: Global Portfolio Optimization, Financial Analysts Journal, September 1992, pp. 28–43 {{JSTOR|4479577}} [[Black–Litterman model]]
* 1994 – [[J. P. Morgan|J.P. Morgan]] [[RiskMetrics]] Group, [https://www.msci.com/documents/10199/5915b101-4206-4ba0-aee2-3449d5c7e95al RiskMetrics Technical Document], 1996, RiskMetrics model and framework
* 2002 – Patrick Hagan, Deep Kumar, Andrew Lesniewski, Diana Woodward, ''Managing Smile Risk'', Wilmott Magazine, January 2002, [[SABR volatility model]].
* 2004 – [[Emanuel Derman]], ''My Life as a Quant: Reflections on Physics and Finance''

==See also==
* [[List of quantitative analysts]]
* [[Financial modeling]]
* [[Black–Scholes equation]]
* [[Financial signal processing]]
* [[Financial analyst]]
* [[Technical analysis]]
* [[Fundamental analysis]]
* [[Financial economics]]

==References==
<references />

==Further reading==
* [[Peter L. Bernstein|Bernstein, Peter L.]] (1992) ''Capital Ideas: The Improbable Origins of Modern Wall Street''
* Bernstein, Peter L. (2007) ''Capital Ideas Evolving''
* [[Emanuel Derman|Derman, Emanuel]] (2007) ''My Life as a Quant'' {{ISBN|0-470-19273-9}}
* [[Scott Patterson (author)|Patterson, Scott D.]] (2010). ''[[The Quants]]: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It''. Crown Business, 352 pages. {{ISBN|0-307-45337-5}} {{ISBN|978-0-307-45337-2}}. [https://www.amazon.com/Quants-Whizzes-Conquered-Street-Destroyed/dp/0307453375 Amazon page for book] via [https://www.npr.org/templates/story/story.php?storyId=123209339 Patterson and Thorp interview] on [[Fresh Air]], Feb. 1, 2010, including excerpt "Chapter 2: The Godfather: Ed Thorp". Also, [https://www.wsj.com/articles/SB10001424052748704509704575019032416477138?mod=WSJ_hps_MIDDLEForthNews an excerpt] from "Chapter 10: The August Factor", in the January 23, 2010 ''Wall Street Journal''.
* Read, Colin (2012) ''Rise of the Quants'' (Great Minds in Finance Series) {{ISBN|023027417X}}
* [https://books.google.com/books?hl=en&lr=&id=FV2mBgAAQBAJ&oi=fnd&pg=PT13&dq=%22what+is+Quantitative+analysis%22&ots=LCnNueZDHt&sig=7bbyR8R0p8ojcBCHGNct7MqgnZ8&redir_esc=y#v=onepage&q=%22what%20is%20Quantitative%20analysis%22&f=false Analysing Quantitative Data for Business and Management Students]

== External links ==
* http://sqa-us.org – Society of Quantitative Analysts
* http://www.q-group.org/ — Q-Group Institute for Quantitative Research in Finance
* http://cqa.org – CQA—Chicago Quantitative Alliance
* http://qwafafew.org/ – QWAFAFEW – Quantitative Work Alliance for Finance Education and Wisdom
* http://prmia.org – PRMIA—Professional Risk Managers Industry Association
* http://iaqf.org – International Association of Quantitative Finance
* http://www.lqg.org.uk/ – London Quant Group
* http://quant.stackexchange.com – question and answer site for quantitative finance

{{stock market}}

[[Category:Valuation (finance)]]
[[Category:Mathematical finance]]
[[Category:Financial analysts]]

Queen's Pawn Game

2021-05-16T11:55:02Z

Rudyardcrow: /* 1...e6 */Fixed typo

{{Short description|Chess opening}}
{{Infobox chess opening
|openingname = Queen's Pawn Game
|image = {{Chess diagram||
|rd|nd|bd|qd|kd|bd|nd|rd
|pd|pd|pd|pd|pd|pd|pd|pd
| | | | | | | |
| | | | | | | |
| | | |pl| | | |
| | | | | | | |
|pl|pl|pl| |pl|pl|pl|pl
|rl|nl|bl|ql|kl|bl|nl|rl
}}
|moves = 1.d4
|ECO = A40–A99 D00–D99 E00–E99
|birth =
|nameorigin =
|parentopening = [[Chess opening|Starting position]]
|AKA = d4
|chessgid = 10703&move=1.5&moves=d4
}}

'''Queen's Pawn Game''' broadly refers to any [[chess opening]] starting with the move [[b:Chess Opening Theory/1. d4|1.d4]], which is the second most popular opening move after [[1.e4]] ([[King's Pawn Game]]).
{{algebraic notation|pos=toc}}

==Term==
The term "Queen's Pawn Game" is usually used to describe openings beginning with 1.d4 where White does not play the [[Queen's Gambit]]. The most common Queen's Pawn Game openings are:
* The [[London System]], 2.Bf4 or 2.Nf3 and 3.Bf4
* The [[Trompowsky Attack]], 1...Nf6 2.Bg5 and the [[Hodgson Attack|Pseudo-Trompowsky]] 1...d5 2.Bg5
* The [[Torre Attack]], 2.Nf3 and 3.Bg5
* The [[Stonewall Attack]], 2.e3
* The [[Colle System]], 2.Nf3 and 3.e3,
* The [[King's Fianchetto Opening]], 2.Nf3 and 3.g3
* The [[Barry Attack]], 1...Nf6 2.Nf3 g6 3.Nc3 d5 4.Bf4
* The [[Richter–Veresov Attack]], 1...d5 2.Nc3 Nf6 3.Bg5 or 1...Nf6 2.Nc3 d5 3.Bg5
* The [[Blackmar–Diemer Gambit]], 1...d5 2.e4, and the Hübsch Gambit 1...Nf6 2.Nc3 d5 3.e4

In the ''[[Encyclopaedia of Chess Openings]]'' (''ECO''), [[Closed Game]]s (1.d4 d5) are classified under codes D00–D69. Openings where Black does not play 1...d5 are called [[Semi-Closed Game]]s and classified as:
* [[Indian Defence]]s, where Black plays 1...Nf6 (''ECO'' codes A45–A79, D70–D99, E00–E99); for instance the [[Queen's Indian Defence]] (''ECO'' E12–E19);
* other Queen's Pawn Games, where Black plays neither 1...d5 nor 1...Nf6; these include the [[Dutch Defence]] (''ECO'' A40–A44 and A80–A99).

==History==
In the 19th century and early 20th century, [[b:Chess Opening Theory/1. e4|1.e4]] was by far the most common opening move by White {{Harvcol|Watson|2006|p=87}}, while the different openings starting with 1.d4 were considered somewhat unusual and therefore classed together as "Queen's Pawn Game".

As the merits of 1.d4 started to be explored, it was the [[Queen's Gambit]] which was played most often—more popular than all other 1.d4 openings combined. The term "Queen's Pawn Game" was then narrowed down to any opening with 1.d4 which was not a Queen's Gambit. Eventually, through the efforts of the [[hypermodernism (chess)|hypermodernists]], the various Indian Defences (such as the [[King's Indian Defence|King's Indian]], [[Nimzo-Indian Defence|Nimzo-Indian]], and [[Queen's Indian Defense|Queen's Indian]]) became more popular, and as these openings were named, the term "Queen's Pawn Game" narrowed further.

==Continuations==
The Black responses given below are ranked in order of popularity according to ChessBase.

=== 1...Nf6 ===
This move prevents White from establishing a full pawn centre with 2.e4. The opening usually leads to a form of [[Indian Defence]], but can also lead to versions of the Queen's Gambit if Black plays ...d5 at some point. Since 1...Nf6 is a move that is likely to be made anyway, the move is a flexible response to White's first move. White usually plays 2.c4. Then Black usually plays 2...e6 (typically leading to the [[Nimzo-Indian]], [[Queen's Indian]], or [[Queen's Gambit Declined]]), 2...g6 (leading to the [[King's Indian]] or [[Grünfeld Defence]]), or 2...c5 (leading to the [[Benoni Defence]] or [[Benko Gambit]]). Rarer tries include 2...e5 ([[Budapest Gambit]]) and 2...d6 ([[Old Indian Defence]]). Also White can play 2.Nf3 which like Black's move is not specific as to opening. A third alternative is the [[Trompowsky Attack]] with 2.Bg5.

=== 1...d5 ===
1...d5 ([[Closed Game]]) also prevents White from playing 2.e4 unless White wants to venture the dubious [[Blackmar–Diemer Gambit]]. 1...d5 is not any worse than 1...Nf6, but committing the pawn to d5 at once makes it somewhat less flexible since Black can no longer play the Indian Defences, although if Black is aiming for Queen's Gambit positions this may be of minor importance. Also, a move like 2.Bg5 ([[Hodgson Attack]]) is considered relatively harmless compared to 1.d4 Nf6 2.Bg5 since there is no knight on f6 for the bishop to harass. White's more common move is 2.c4 leading to the [[Queen's Gambit]] when Black usually chooses between 2...e6 ([[Queen's Gambit Declined]]), 2...c6 ([[Slav Defence]]) or 2...dxc4 ([[Queen's Gambit Accepted]]). Also White can play 2.Nf3 which again is not specific as to opening. Then Black may play ...Nf6 (same as above) or ...e6. A Queen's Gambit may arise anyway if White plays c4 soon afterward, but lines like the [[Colle System]] and [[Stonewall Attack]] are also possible.

=== 1...e6 ===
The [[Horwitz Defense]] is a chess opening characterized by the moves: 1.d4 e6. This play allows White to play 2.e4, entering the [[French Defence]]. If White wants to continue with a Queen's Pawn Game however, 2.c4 and 2.Nf3 usually [[Transposition (chess)|transpose]] to a familiar opening such as the [[Queen's Gambit Declined]], [[Nimzo-Indian]] or [[Queen's Indian]]. A line that is unique to the 1...e6 move order is the [[Keres Defence]], 1.d4 e6 2.c4 Bb4+.

=== 1...d6 ===
This move also allows 2.e4 entering the [[Pirc Defence]]. If White avoids this, 2.Nf3 or 2.c4 may lead to a [[King's Indian]] or [[Old Indian Defence]], or Black may play 2...Bg4, sometimes called the [[Wade Defence]] (A41, see [[b:Chess Opening Theory/1. d4/1...d6/2. Nf3/2...Bg4|1.d4 d6 2.Nf3 Bg4]]). 2.c4 e5 is the [[Rat Defense]] or English Rat.

=== 1...f5 ===
1...f5 is the [[Dutch Defence]]. Common White moves are 2.g3, 2.Nf3, and 2.c4.

=== 1...g6 ===
1...g6 is sometimes called the [[Modern Defence]] line.
White can play 2.e4 to enter the Modern Defence.
More commonly, White plays 2.c4. Black may play 2...Nf6 for the [[King's Indian Defence]] (same as 1.d4 Nf6 2.c4 g6). More commonly, Black plays 2...Bg7. Then White's moves include 3.Nc3, 3.e4, and 3.Nf3. 3.Nc3 often leads to the Modern Defence, Averbakh System, and 3.e4 usually leads to the Modern Defence, Averbakh System. 2...d6 often leads to the Modern Defence, Averbakh System.
Also, White can play 2.Nf3. Black may play 2...Nf6 for the King's Indian. More commonly, Black plays 2...Bg7. Common White moves are 3.e4, 3.c4, and 3.g3.

=== 1...c5 ===
1...c5 is the [[Benoni Defense#Old Benoni|Old Benoni Defence]]: this is a form of the [[Benoni Defence]] seldom used; however, it is not a bad move. If White captures 2.dxc5, then Black plays 2...e5 and has a good game.

=== 1...Nc6 ===
1...Nc6 is the [[Queen's Knight Defense]] (or [[Vladas Mikėnas|Mikenas]] Defense): this can usually transpose to the [[Chigorin Defense]] or the [[Nimzowitsch Defense]].

=== 1...c6 ===
This move allows White to play 2.e4, entering the [[Caro–Kann Defence]]. If, however, White wants to continue with a Queen's Pawn Game, 2.c4 and 2.Nf3 usually transpose to a familiar opening such as the [[Slav Defence]], [[London System]], or [[Dutch Defence]].

=== 1...b6 ===
1...b6 is the [[English Defence]]. Common White moves are 2.e4, 2.Nf3, and 2.c4.

=== 1...b5 ===
1...b5 is the [[Polish Defence]]: this is risky and should be played with care. It is better to delay ...b5 until the 2nd move.

=== 1...a6 ===
1...a6 can quickly transpose to the [[St. George Defence]].

=== 1...e5 ===
1...e5 is the [[Englund Gambit]]: this gives up a pawn for questionable [[Compensation (chess)|compensation]].

=== 1...g5 ===
1...g5{{chesspunc|?}} is the [[Borg Defense]], Borg Gambit: this simply loses a pawn to 2.Bxg5.

=== 1...Na6 ===
1...Na6 is the [[Australian Defence]].<ref>https://www.chess.com/openings/Queens-Pawn-Opening-Australian-Defense</ref>

==See also==
* [[List of chess openings]]

==References==
{{wikibooks|Chess Opening Theory|1. d4|Queen's Pawn Opening}}
{{Reflist}}
* {{Citation
|last=Watson|first=John|author-link=John L. Watson
|title=Mastering the Chess Openings, vol 1
|year=2006
|publisher=Gambit
|isbn= 978-1-904600-60-2}}

{{White's twenty opening moves in chess}}
{{chess}}
{{Authority control}}

[[Category:Chess openings]]

Talk:Fisher equation

2018-04-18T19:16:41Z

Rudyardcrow: /* Cost–benefit analysis conclusion is wrong */

{{WikiProject Economics|class=Start|importance=Mid}}

== Example doesn't make any sense ==

The example doesn't make any sense to me - can somebody fix it? Why is the return at 3.775% HIGHER than at 3.81%? What do you mean by "third term"? Third term of what? Why is the focus on the different paybacks when it should illustrate the fisher equation? —Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/92.117.27.227|92.117.27.227]] ([[User talk:92.117.27.227|talk]]) 07:25, 29 September 2008 (UTC) 
Third term is actually clear -- it is product of two rates (interest and inflation) -- what is really not clear is how the author arrived at values of 107.84 and 108.50 (how these specific values were calculated?) pounds with bond having higher-yielding rate being valued at lower price.

== revision to notation and addition of time dependence ==

I have made two major changes. First, I have updated the notation to the more traditional r, i, and pi notation which is the same as that used in [[interest]]. This is what I see in most modern texts. Second I have added a time dimension to help the intuition on this and to again, bring this aspect of the content up to par with economics texts. The subscripts of the previous notation would also have conflicted -- another motivation for the updated more standard notation. I realize these changes may be controversial, so Ive started this talk section. Please bear with me if I cannot answer immediately, but I will definitely get back here as I can. ([[User:Econotechie|Econotechie]] ([[User talk:Econotechie|talk]]) 00:27, 5 July 2008 (UTC))

:To make it easier for the less economically-inclined, maybe explicitly state that Pi is being used to represent a variable rather than the constant 3.14159... that most people associate with Pi. Upon first read I thought you were assuming the inflation rate to be 3.14% --[[User:Stable attractor|Stable attractor]] ([[User talk:Stable attractor|talk]]) 12:25, 27 August 2008 (UTC)

::Good point. I looked around a couple books to see what else might be used, but I things like dotted p might be confusing also. If I run across anything else, Ill come back and change it. For now Ive added a note. ([[User:Econotechie|Econotechie]] ([[User talk:Econotechie|talk]]) 19:53, 19 September 2008 (UTC))

: Does <math>e</math> stand for 2.71828... or is that also a variable? The standard notation here is unfortunate IMHO... [[Special:Contributions/76.174.15.250|76.174.15.250]] ([[User talk:76.174.15.250|talk]]) —Preceding [[Wikipedia:Signatures|undated]] comment added 07:38, 5 December 2010 (UTC). 

== Cost–benefit analysis conclusion is wrong ==

These math steps are wrong, it is using the fisher equation two times and concluding that inflation doesn't change the net present value. When i try to acess the referred article at the beginning of the section it leads to a paywall and i couldn't see the original. My suggestion is to delete the algebra part leaving only the first and the second paragraphs which are good.
[[User:Rudyardcrow|Rudyardcrow]] ([[User talk:Rudyardcrow|talk]]) 19:16, 18 April 2018 (UTC)

Talk:Fisher equation

2018-04-17T19:35:23Z

Rudyardcrow: /* Cost–benefit analysis conclusion is wrong */ new section

Jagannatakam

2014-12-29T01:40:08Z

Rudyardcrow:

{{multiple issues|
{{copy edit|for=grammar|date=December 2014}}
{{overlinked|date=December 2014}}
{{refimprove|date=December 2014}}
}}

{{New unreviewed article|date=December 2014}}
{{Infobox film
| name = Jagannatakam
| image =
| caption =
| writer = [[Paruchuri Brothers]] {{small|(story / dialogues)}}
| screenplay = A. Mohan Gandhi
| producer = Radha Krishna Chalapathi Rao [[Sharada (actress)|Sharada]] {{small|(presents)}}
| director = A. Mohan Gandhi
| starring = [[Jagapathi Babu]] [[Meena (actress)|Meena]] [[Sharada (actress)|Sharada]]
| music = [[Vidyasagar (Composer)|Vidyasagar]]
| cinematography = D. Prasad Babu
| editing = Vemuri Ravi
| studio = R. C. Creations
| released = {{Film date|df=y|1991|7|3}}
| runtime = 2:16:03
| country = {{flagicon|IND}} India
| language = Telugu
| budget =
| preceded_by =
| followed_by =
}}

'''''Jagannatakam''''' is a 1991 [[Telugu cinema|Telugu]], a [[drama film]] directed by A. Mohan Gandhi and produced by Radha Krishna and Chalapathi Rao under R. C. Creations banner. Starring [[Jagapathi Babu]], [[Meena (actress)|Meena]], [[Sharada (actress)|Sharada]] on lead roles and music composed by [[Vidyasagar (Composer)|Vidyasagar]].

==Cast==
{{colbegin}}
*[[Jagapathi Babu]] as Jagam
*[[Meena (actress)|Meena]] as Jhansi
*[[Sharada (actress)|Sharada]] as Manikyamma
*[[Kaikala Satyanarayana|Satyanarayana]] as Balakotaiah
*[[Anand (actor)|Anand]] as Prabhakar
*[[Narra Venkateswara Rao]] as Parameswara Rao
*[[Chalapathi Rao]] as Yerra Subbaiah
*[[Prasad Babu]] as Krishna Rao
*[[P. Ravi Shankar|Ravi Shankar]] as Chakarvathy
*Rajeevi as Madhavi
*[[Easwari Rao]] as Neela
*[[Jayalalitha]] as Lanka Papa
*Varalakshmi as Sarada
*Tatineni Rajeswari as Parameswara Rao's wife
*Anitha as Krishna's Rao's sister
{{colend}}

==Soundtrack==
{{Infobox album
| Name = Jagannatakam
| Tagline =
| Type = film
| Artist = [[Vidyasagar (Composer)|Vidyasagar]]
| Cover =
| Released = 1991
| Recorded =
| Genre = Soundtrack
| Length = 20:47
| Label = LEO Audio
| Producer = [[Vidyasagar (Composer)|Vidyasagar]]
| Reviews =
| Last album =
| This album =
| Next album =
}}

Music composed by [[Vidyasagar (Composer)|Vidyasagar]]. Lyrics written by [[Veturi Sundararama Murthy]]. Music released on LEO Audio Company.
{|class="wikitable"
|-
!S.No!!Song Title !!Singers !!length
|-
|1
|All Rounder Hero
|[[S. P. Balasubrahmanyam|SP Balu]], [[K. S. Chithra|Chitra]]
|4:06
|-
|2
|Khaleja
|SP Balu,Chitra
|3:59
|-
|3
|Chuduitaga Sukumarudaa
|Chitra
|4:23
|-
|4
|Dash Dash
|SP Balu,Chitra
|3:24
|-
|5
|Jungle Jagguki
|SP Balu
|4:55
|}
<ref name="Songs">{{cite web|url=http://www.song.cineradham.com/song.php?movieid=2764&moviename=Jagannatakam(1992)# |title=Songs |publisher=Cineradham}}</ref>

==References==
{{reflist}}

*
*
*
*