Markowitz Variance May Vastly Undervalue or Overestimate Portfolio Variance and Risks

Olkhov, Victor (2025): Markowitz Variance May Vastly Undervalue or Overestimate Portfolio Variance and Risks.

Abstract

We consider the investor who doesn’t trade shares of his portfolio. The investor only observes the current trades made in the market with his securities to estimate the current return, variance, and risks of his unchanged portfolio. We show how the time series of consecutive trades made in the market with the securities of the portfolio can determine the time series that model the trades with the portfolio as with a single security. That establishes the equal description of the market-based variance of the securities and of the portfolio composed of these securities that account for the fluctuations of the volumes of the consecutive trades. We show that Markowitz’s (1952) variance describes only the approximation when all volumes of the consecutive trades with securities are assumed constant. The market-based variance depends on the coefficient of variation of fluctuations of volumes of trades. To emphasize this dependence and to estimate possible deviation from Markowitz variance, we derive the Taylor series of the market-based variance up to the 2nd term by the coefficient of variation, taking Markowitz variance as a zero approximation. We consider three limiting cases with low and high fluctuations of the portfolio returns, and with a zero covariance of trade values and volumes and show that the impact of the coefficient of variation of trade volume fluctuations can cause Markowitz’s assessment to highly undervalue or overestimate the market-based variance of the portfolio. Incorrect assessments of the variances of securities and of the portfolio cause wrong risk estimates, disturb optimal portfolio selection, and result in unexpected losses. The major investors, portfolio managers, and developers of macroeconomic models like BlackRock, JP Morgan, and the U.S. Fed should use market-based variance to adjust their predictions to the randomness of market trades.

• Item Type: MPRA Paper
• Language: English
• Keywords: portfolio variance; portfolio theory; random market trades
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation; G - Financial Economics > G2 - Financial Institutions and Services > G23 - Non-bank Financial Institutions ; Financial Instruments ; Institutional Investors; G - Financial Economics > G2 - Financial Institutions and Services > G24 - Investment Banking ; Venture Capital ; Brokerage ; Ratings and Ratings Agencies

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