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arXiv:2009.10852q-fin.PM

Efficient Portfolios

Keith A. Lewis

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Abstract

Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz and Roy introduced the following criterion for risk vs. return in portfolio selection: if two portfolios have the same expected realized return then prefer the one with smaller variance. An efficient portfolio has the least variance among all portfolios having the same expected realized return. The primary contribution of this short note is observation that the CAPM formula holds for realized returns as random variables, not just their expectations. This follows directly from writing down a mathematical model for one period investments.

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q-fin.PMPortfolio Management

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  1. The Tensor Cookbook (2024) 1 comment

    • The Wikipedia page on this is sufficient. If F:X -> Y is a function between normed linear spaces then DF:X -> L(X,Y), where L(X,Y) is the vector space of linear operators from X to Y, satisfies F(x + h) = F(x) + DF(x)h + o(h). A function is differentiable if it can be locally…

      keithalewisView on HNParent context

  2. Most important papers for quantitative traders 1 comment

    • A big seller? So you are shorting this list? Little know fact: the CAPM is an equality of random variables, not just their expected value. https://arxiv.org/abs/2009.10852

      keithalewisView on HNParent context

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