I am an applied mathematician and recently I have decided to study the portfolio management theory. As a final objective, I want to manage my own portfolio and to try make some money on it using my mathematical background. But at the same time, I would like to have a general understanding of this field to be able to contribute at some stage.

In this connection, I would like to ask for the most significant research articles that are worth reading. I have already started with the great work (Markowitz, 1952) where the foundations of the modern portfolio theory were established and the next article in my list is (Sharpe, 1964) for the foundations of CAPM.

I already have some background in mathematical finance. At the university I had an course on financial mathematics where I had an assignment on pricing and hedging of European rainbow options using discrete-time models. But for me this remained disconnected from the real world.

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    $\begingroup$ Maybe not a perfectly related paper, but Cochrane (2006) The dog that did not bark: A Defense of Return Predictability, is one of the few papers which emphasizes the "econ-" in econometrics the most: The absence of certain effects (dividend predictability) can be exploited to get a more precise estimator for other effects (return predictability). The described approach may be interesting to develop tests for certain strategies. $\endgroup$ Commented Mar 5, 2019 at 9:54
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    $\begingroup$ Cochrane comes at portfolio theory from an economics rather than practical investing perspective, but you may find his notes on portfolio theory a useful resource. $\endgroup$ Commented Mar 8, 2019 at 19:08

3 Answers 3


A lot has happened since Markowitz and Sharpe. While their work is still considered foundational, the empirical/practical relevance of their models has been questioned by later work.

Here are a few more recent articles about portfolio theory, in no particular order (all accessible online):

Jorion: Bayes-Stein Estimation for Portfolio Analysis, JFQA, 1986

Ledoit, Wolf: Honey, I Shrunk the Sample Covariance Matrix, 2003

DeMiguel, Garlappi, Uppal: Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?, RFS, 2009

Fama, French: A Five-Factor Asset Pricing Model, 2014

Maillard, Roncalli, Teiletche: On the properties of equally-weighted risk contributions portfolios, 2009

He, Litterman: The Intuition Behind Black-Litterman Model Portfolios, GS, December 1999

Hurst, Johnson, Ooi: Undertanding Risk Parity, AQR Capital Management, Fall 2010


Below is the list of articles which I find significant based on their number of citations according to Google and on the overall impact according to discussions in Investopedia, Wikipedia and other sources. I will update this list as I come across other articles. To compare (which is just for fun), according to Google Scholar, the most cited A. Einstein's article has 17531 citations.

Foundations of the modern portfolio theory

Markowitz, H.M. (1952). "Portfolio Selection". The Journal of Finance. 7 (1): 77–91. (Cited by 38478)

Capital Asset Pricing Model

Sharpe, William F. (1964). "Capital asset prices: A theory of market equilibrium under conditions of risk". Journal of Finance. 19 (3): 425–442. (Cited by 22321)

Black-Scholes model

Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy. 81 (3): 637–654. (Cited by 36875)

Fama-French three-factor model

Fama, E. F.; French, K. R. (1993). "Common risk factors in the returns on stocks and bonds". Journal of Financial Economics. 33: 3–56. (Cited by 22924)

Arbitrage pricing theory

Ross, Stephen (1976). "The arbitrage theory of capital asset pricing". Journal of Economic Theory. 13 (3): 341–360 (Cited by 8497)

Carhart four-factor model

Carhart, M. M. (1997). "On Persistence in Mutual Fund Performance". The Journal of Finance. 52 (1): 57–82 (Cited by 14334)


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