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1/ In honor of Monday: A review of key academic research relating to modern portfolio mgmt—the foundation of everything we do—in tweet.
In the beginning there was darkness, Harry Markowitz speaks: Portfolio Selection (1952). https://www.math.ust.hk/~maykwok/courses/ma362/07F/markowitz_JF.pdf
In the beginning there was darkness, Harry Markowitz speaks: Portfolio Selection (1952). https://www.math.ust.hk/~maykwok/courses/ma362/07F/markowitz_JF.pdf
2/ Markowitz (1952, 1959), father of modern portfolio theory (MPT), expresses behavior w/in portfolio context, establishing the use of mean-variance assumption (MVA) and st. dev as the definition of risk
Many people respond (Roy, Porter, &etc); we rarely cite their names.
Many people respond (Roy, Porter, &etc); we rarely cite their names.
3/James Tobin (1958) adds risk free rate and derives the efficient frontier and capital markets line based on the works of Markowitz.
He is also rarely mentioned.
He is also rarely mentioned.
4/ Sharpe, Lintner, and Mossin (1964) provide the next step…the Capital Assets Pricing Model (CAPM), based on Markowitz’s papers.
Sharpe (1966) introduces Sharpe ratio, measuring reward to variability...it remains the gold standard in obnoxious portfolio mgmt debates
Sharpe (1966) introduces Sharpe ratio, measuring reward to variability...it remains the gold standard in obnoxious portfolio mgmt debates
5/ BUT WE WERE ALL WRONG. Issues with MPT: normally distributed returns (Gaussian), st. dev. treats both (+) and (-) returns identically (no one complains about upside), and quadratic utility framework claims absolute risk aversion inc with wealth (Pratt (1964) disproves?)
6/Markowitz concedes in 1959 that we should all probably use semi-variance, but computers can’t do this yet so like *shrug*
Roy (1952), which creates the foundation for Mean-Value at Risk (mVaR), gets a second look
Roy (1952), which creates the foundation for Mean-Value at Risk (mVaR), gets a second look
7/MORE RESEARCH SAYS THAT WE’RE ALL WRONG: Brown (1976), et. al all highlight that MVA optimization also incorrectly treats input parameters as certain…in reality, input parameters are prone to sampling and error estimation (oops.). 1970s-80s: "Bayesian methods are better."
8/BUT WAIT, THERE’S MORE. The optimal MVA portfolio implicitly assumes asset class returns are linear. Now, insert a body of research proving that returns may be non-linear in univariate (and even bivariate) frameworks.
Does your head hurt yet?
Does your head hurt yet?
9/STILL WRONG. Bc we use serial corr of asset returns. Fisher (1966), Dimson (1979) and Scholes and Williams (1977) all say stock returns priced at different times probably exhibit spurious serial correlations.
10/ Sidebar: @CliffordAsness , Krail and Liew (2001) show the similar effects with hedge funds; serial correlation exists due to illiquidity and smoothed return factors.
P.s. also tail risk. Oh and all of this suggests your portfolio is still sub-optimal.
P.s. also tail risk. Oh and all of this suggests your portfolio is still sub-optimal.
11/ Fama French (1993) note CAPM only uses ONE variable to describe returns. Why use ONE when you can use THREE. 3 factor model: 1) market risk, (2) outperf of small v. large, (3) outperf of high book/mkt vs. small (#3 still debated)…model now has *like* 1M factors
12/ Other notable research
Efficient market hypothesis…Fama (1965) thesis argues for the random walk, as does Samuelson (also warns “from a non-empirical base of axioms, you never get empirical results” and then claims EMH is better suited for single stocks vs. mkts in agg)
Efficient market hypothesis…Fama (1965) thesis argues for the random walk, as does Samuelson (also warns “from a non-empirical base of axioms, you never get empirical results” and then claims EMH is better suited for single stocks vs. mkts in agg)
13/ Mandelbrot and Fama also hate on Gassian distribution in the 60s. There's a ton of research that suggests hedge funds returns are linear, no non-linear, no linear....There are 100+ branches of asset class specific research that often conflict with each other.
14/ I didn't start this with any grand point in mind, except to say that st dev has become the conventional risk measure, inc Mossin (1966), Sharpe (1964), Lintner (1965), and Black Scholes (1973) despite issues of upside penalty and normality assumptions
15/ Oh and if you rely solely on Markowitz's MVA model, you're understating risk (hashtag everyone who disproved the normal distribution of mkt returns), AND if the relationship bt asset class returns is non-linear then your covariance matrix is kinda worthless
