Editing Modern portfolio theory (section)

==Criticisms==
Despite its theoretical importance, critics of MPT question whether it is an ideal investment tool, because its model of financial markets does not match the real world in many ways.<ref name=":0" />

The risk, return, and correlation measures used by MPT are based on [[expected value]]s, which means that they are statistical statements about the future (the expected value of returns is explicit in the above equations, and implicit in the definitions of [[variance]] and [[covariance]]). Such measures often cannot capture the true statistical features of the risk and return which often follow highly skewed distributions (e.g. the [[log-normal distribution]]) and can give rise to, besides reduced [[volatility (finance)|volatility]], also inflated growth of return.<ref name="pnas.org">{{cite journal|last1=Hui|first1=C.|last2=Fox|first2=G.A.|last3=Gurevitch|first3=J.|title=Scale-dependent portfolio effects explain growth inflation and volatility reduction in landscape demography|journal=Proceedings of the National Academy of Sciences of the USA|volume=114|issue=47|pages=12507–12511|date=2017|doi=10.1073/pnas.1704213114|pmid=29109261|pmc=5703273|bibcode=2017PNAS..11412507H |doi-access=free}}</ref> In practice, investors must substitute predictions based on historical measurements of asset return and volatility for these values in the equations. Very often such expected values fail to take account of new circumstances that did not exist when the historical data was generated.<ref name="sciencedirect.com">{{cite journal|last1=Low|first1=R.K.Y.|last2=Faff|first2=R.|last3=Aas|first3=K.|title=Enhancing mean–variance portfolio selection by modeling distributional asymmetries|journal=Journal of Economics and Business|volume=85|pages=49–72|date=2016|doi=10.1016/j.jeconbus.2016.01.003|url=http://espace.library.uq.edu.au/view/UQ:377912/UQ377912_OA.pdf}}</ref> An optimal approach to capturing trends, which differs from Markowitz optimization by utilizing invariance properties, is also derived from physics. Instead of transforming the normalized expectations using the inverse of the correlation matrix, the invariant portfolio employs the inverse of the square root of the correlation matrix.<ref name="Benichou">{{cite journal|last1=Benichou|first1=R. |last2=Lemperiere|first2=Y. |last3=Serie|first3=E.|last4=Kockelkoren|first4=J. |last5=Seager|first5=P. |last6=Bouchaud|first6= J.-P. |last7=Potters|first7= M.| year=2017|title= Agnostic Risk Parity: Taming Known and Unknown-Unknowns |journal= Journal of Investment Strategies |volume=6|issue=3 |pages=1–12 |doi=10.21314/JOIS.2017.083 |arxiv=1610.08818 }}</ref> The optimization problem is solved under the assumption that expected values are uncertain and correlated.<ref name="Valeyre">{{cite journal|last1=Valeyre|first1=S.|year=2024|title= Optimal trend-following portfolios |journal= Journal of Investment Strategies |volume=12|doi=10.21314/JOIS.2023.008 |arxiv=2201.06635 }}</ref> The Markowitz solution corresponds only to the case where the correlation between expected returns is similar to the correlation between returns.

More fundamentally, investors are stuck with estimating key parameters from past market data because MPT attempts to model risk in terms of the likelihood of losses, but says nothing about why those losses might occur. The risk measurements used are [[probability|probabilistic]] in nature, not structural.  This is a major difference as compared to many engineering approaches to [[risk management]].

{{blockquote|
[[Option (finance)|Options]] theory and MPT have at least one important conceptual difference from the [[probabilistic risk assessment]] done by nuclear power [plants]. A PRA is what economists would call a ''structural model''. The components of a system and their relationships are modeled in [[Monte Carlo simulations]]. If valve X fails, it causes a loss of back pressure on pump Y, causing a drop in flow to vessel Z, and so on.

But in the [[Black–Scholes]] equation and MPT, there is no attempt to explain an underlying structure to price changes. Various outcomes are simply given probabilities. And, unlike the PRA, if there is no history of a particular system-level event like a [[liquidity crisis]], there is no way to compute the odds of it. If nuclear engineers ran risk management this way, they would never be able to compute the odds of a meltdown at a particular plant until several similar events occurred in the same reactor design.
|[[Douglas W. Hubbard]], ''The Failure of Risk Management'', p. 67, John Wiley & Sons, 2009. {{ISBN|978-0-470-38795-5}}|source=}}

Mathematical risk measurements are also useful only to the degree that they reflect investors' true concerns—there is no point minimizing a variable that nobody cares about in practice.  In particular, [[variance]] is a symmetric measure that counts abnormally high returns as just as risky as abnormally low returns. The psychological phenomenon of [[loss aversion]] is the idea that investors are more concerned about losses than gains, meaning that our intuitive concept of risk is fundamentally asymmetric in nature. There many other risk measures (like [[coherent risk measure]]s) might better reflect investors' true preferences.

Modern portfolio theory has also been criticized because it assumes that returns follow a [[Normal distribution|Gaussian distribution]]. Already in the 1960s, [[Benoit Mandelbrot]] and [[Eugene Fama]] showed the inadequacy of this assumption and proposed the use of more general [[stable distributions]] instead. [[Stefan Mittnik]] and [[Svetlozar Rachev]] presented strategies for deriving optimal portfolios in such settings.<ref>Rachev, Svetlozar T. and Stefan Mittnik (2000), Stable Paretian Models in Finance, Wiley, {{ISBN|978-0-471-95314-2}}.</ref><ref>Risk Manager Journal (2006), {{cite web |title=New Approaches for Portfolio Optimization: Parting with the Bell Curve — Interview with Prof. Svetlozar Rachev and Prof.Stefan Mittnik |url=https://statistik.econ.kit.edu/download/doc_secure1/RM-Interview-Rachev-Mittnik-EnglishTranslation.pdf}}</ref><ref>{{cite journal |last=Doganoglu |first=Toker |author2=Hartz, Christoph|author3=Mittnik, Stefan |year=2007 |title=Portfolio Optimization When Risk Factors Are Conditionally Varying and Heavy Tailed |journal=Computational Economics |volume=29 |issue= 3–4|pages=333–354 |doi=10.1007/s10614-006-9071-1 |s2cid=8280640 |url=http://publikationen.ub.uni-frankfurt.de/files/2101/06_24.pdf}}</ref> More recently, [[Nassim Nicholas Taleb]] has also criticized modern portfolio theory on this ground, writing:{{blockquote|After the stock market crash (in 1987), they rewarded two theoreticians, Harry Markowitz and William Sharpe, who built beautifully Platonic models on a Gaussian base, contributing to what is called Modern Portfolio Theory. Simply, if you remove their Gaussian assumptions and treat prices as scalable, you are left with hot air. The Nobel Committee could have tested the Sharpe and Markowitz models—they work like quack remedies sold on the Internet—but nobody in Stockholm seems to have thought about it.
|Nassim N. Taleb, ''The Black Swan: The Impact of the Highly Improbable'', p. 277, Random House, 2007. {{ISBN|978-1-4000-6351-2}}|source=}}

[[Contrarian investing|Contrarian investors]] and [[Value investing|value investors]] typically do not subscribe to Modern Portfolio Theory.<ref>[[Seth Klarman]] (1991). Margin of Safety: Risk-averse Value Investing Strategies for the Thoughtful Investor. HarperCollins, {{ISBN|978-0887305108}}, pp. 97-102</ref> One objection is that the MPT relies on the [[efficient-market hypothesis]] and uses fluctuations in share price as a substitute for risk. [[Sir John Templeton]] believed in diversification as a concept, but also felt the theoretical foundations of MPT were questionable, and concluded (as described by a biographer): "the notion that building portfolios on the basis of unreliable and irrelevant statistical inputs, such as historical volatility, was doomed to failure."<ref>Alasdair Nairn (2005). "Templeton's Way With Money: Strategies and Philosophy of a Legendary Investor." Wiley, ISBN 1118149610, p. 262</ref>

A few studies have argued that "naive diversification", splitting capital equally among available investment options, might have advantages over MPT in some situations.<ref>{{Cite journal|doi=10.3905/JPM.2009.35.2.071|title=Markowitz Versus the Talmudic Portfolio Diversification Strategies|year=2009|last1=Duchin|first1=Ran|last2=Levy|first2=Haim|journal=The Journal of Portfolio Management|volume=35|issue=2|pages=71–74|s2cid=154865200}}</ref>

When applied to certain universes of assets, the Markowitz model has been identified by academics to be inadequate due to its susceptibility to model instability which may arise, for example, among a universe of highly correlated assets.<ref>{{Cite journal |last=Henide |first=Karim |date=2023 |title=Sherman ratio optimization: constructing alternative ultrashort sovereign bond portfolios |url=https://www.risk.net/journal-of-investment-strategies/7957165/sherman-ratio-optimization-constructing-alternative-ultrashort-sovereign-bond-portfolios |journal=Journal of Investment Strategies |doi=10.21314/JOIS.2023.001|url-access=subscription }}</ref>