Editing Financial economics (section)

===Portfolio theory===
{{See also|Post-modern portfolio theory|Mathematical finance#Risk and portfolio management: the P world}}
<!-- [[File:Asset Allocation.pdf|thumb|right|250px|[[Modern portfolio theory]] suggests a diversified portfolio of [[shares]] and other [[asset classes]] (such as debt in [[corporate bonds]], [[treasury bond]]s, or [[money market funds]]) will realise more predictable returns if there is prudent market regulation.]] -->
[[Image:Pareto Efficient Frontier for the Markowitz Portfolio selection problem..png|thumb|right|200px|Plot of two criteria when maximizing return and minimizing risk in financial portfolios (Pareto-optimal points in red)]]
[[File:Four_Correlations.svg|thumb|right|alt=Examples of bivariate copulæ used in finance.|Examples of bivariate copulæ used in finance.]]
The majority of developments here relate to required return, i.e. pricing, extending the basic CAPM. Multi-factor models such as the [[Fama–French three-factor model]] and the [[Carhart four-factor model]], propose factors other than market return as relevant in pricing. The [[intertemporal CAPM]] and [[Consumption-based capital asset pricing model|consumption-based CAPM]] similarly extend the model. With [[intertemporal portfolio choice]], the investor now repeatedly optimizes her portfolio; while the inclusion of [[Consumption (economics)|consumption (in the economic sense)]] then incorporates all sources of wealth, and not just market-based investments, into the investor's calculation of required return.

Whereas the above extend the CAPM, the [[single-index model]] is a more simple model. It assumes, only, a correlation between security and market returns, without (numerous) other economic assumptions. It is useful in that it simplifies the estimation of correlation between securities, significantly reducing the inputs for building the correlation matrix required for portfolio optimization. The [[arbitrage pricing theory]] (APT)  similarly differs as regards its assumptions. APT "gives up the notion that there is one right portfolio for everyone in the world, and ...replaces it with an explanatory model of what drives asset returns."<ref>''The Arbitrage Pricing Theory,'' Chapter VI in Goetzmann, under External links.</ref> It returns the required (expected) return of a financial asset as a linear function of various macro-economic factors, and assumes that arbitrage should bring incorrectly priced assets back into line.{{NoteTag|The single-index model was developed by William Sharpe in 1963.
<ref>{{cite journal |author=Sharpe, William F. |s2cid=55778045|title=A Simplified Model for Portfolio Analysis|journal=Management Science|year=1963 |volume=9|issue=2 |pages=277–93 |doi=10.1287/mnsc.9.2.277}}</ref>
APT was developed by [[Stephen Ross (economist)|Stephen Ross]] in 1976.
<ref>{{Cite journal|last=Ross|first=Stephen A|date=1976-12-01|title=The arbitrage theory of capital asset pricing|journal=Journal of Economic Theory|language=en|volume=13|issue=3|pages=341–360|doi=10.1016/0022-0531(76)90046-6|issn=0022-0531}}
</ref>}}
The linear factor model structure of the APT is used as the basis for many of the commercial risk systems employed by asset managers.

As regards [[portfolio optimization]], the [[Black–Litterman model]]<ref>Black F. and Litterman R. (1991). [http://www.iijournals.com/doi/abs/10.3905/jfi.1991.408013 "Asset Allocation Combining Investor Views with Market Equilibrium"]. ''[[Journal of Fixed Income]]''. September 1991, Vol. 1, No. 2: pp.&nbsp;7-18</ref> 
departs from the original [[Markowitz model]] approach to constructing [[efficient frontier|efficient portfolios]]. Black–Litterman starts with an equilibrium assumption, as for the latter, but this is then modified to take into account the "views" (i.e., the specific opinions about asset returns) of the investor in question to arrive at a bespoke <ref>Guangliang He and Robert Litterman (1999). [https://people.duke.edu/~charvey/Teaching/BA453_2004/GS_The_intuition_behind.pdf "The Intuition Behind Black-Litterman Model Portfolios"]. [[Goldman Sachs]] Quantitative Resources Group</ref> asset allocation. Where factors additional to volatility are considered (kurtosis, skew...) then [[multiple-criteria decision analysis]] can be applied; here deriving a [[Pareto efficient]] portfolio. The [[universal portfolio algorithm]] applies [[information theory]] to asset selection, learning adaptively from historical data. [[Behavioral portfolio theory]] recognizes that investors have varied aims and create an investment portfolio that meets a broad range of goals.  Copulas have [[Copula (probability theory)#Quantitative finance|lately been applied here]]; recently this is the case also [[List of genetic algorithm applications#Finance and Economics|for genetic algorithms]] and [[Machine learning#Applications|Machine learning, more generally]] <ref name="Bagnara">Bagnara, Matteo (2021). "Asset Pricing and Machine Learning: A Critical Review". {{SSRN|3950568}}</ref> (see [[#Financial_markets|below]]).