Financial Applications of the Mahalanobis Distance

Sebastian Stöckl, Michael Hanke


We describe existing and potential financial applications of the Mahalanobis distance. After a short motivation and a discussion of important properties of this multivariate distance measure, we classify its applications in finance according to the source and nature of its input parameters. Examples illustrate the usefulness of these applications of the Mahalanobis distance for financial market participants.

Full Text:



Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal 48, 28–43.

Bodnar, O. (2009). Sequential surveillance of the tangency portfolio weights. International Journal of Theoretical and Applied Finance 12, 797–810.

Cambanis, S., Huang, S., & Simons, G. (1981). On the theory of elliptically contoured distributions. Journal of Multivariate Analysis 11, 368–385.

Chow, G., Jacquier, E., Kritzman, M., & Lowry, K. (1999). Optimal portfolios in good times and bad. Financial Analysts Journal 55, 65–73.

Geyer, A., Hanke, M., & Weissensteiner, A. (2014). No-arbitrage bounds for financial scenarios. European Journal of Operational Research 236, 657–663.

Golosnoy, V. (2007). Sequential monitoring of minimum variance portfolio. Advances in Statistical Analysis 91, 39–55.

Jones, D. A. (1983). Statistical analysis of empirical models fitted by optimization. Biometrika 70, 67–88.

Jordà, Ò., & Marcellino, M. (2010). Path forecast evaluation. Journal of Applied Econometrics 25, 635–662.

Kaiser, L., Menichetti, M. J., & Veress, A. (2014). Enhanced Mean-Variance Portfolios - A Controlled Integration of Quantitative Predictors. Journal of Portfolio Management 40(4), 28-41.

Kritzman, M., & Li, Y. (2010). Skulls, financial turbulence, and risk management. Financial Analysts Journal 66, 30-41.

Lütkepohl, H. (2006). New introduction to multiple time series analysis. Berlin: Springer.

Mahalanobis, P. C. (1927). Analysis of race-mixture in Bengal. Journal of the Asiatic Society of Bengal 23, 301-333.

Mardia, K. V., Kent, J. T., & Bibby, J.M. (1979). Multivariate analysis. London: Academic Press.

Mathai, A. M., & Provost, S.B. (1992). Quadratic Forms in Random Variables: Theory and Applications. New York: Marcel Dekker Incorporated.

McLachlan, G. J. (1999). Mahalanobis distance. Resonance 4, 20–26.

Meucci, A. (2009). Risk and Asset Allocation (1st ed.). New York: Springer.

Mitchell, A.F., & Krzanowski, W.J. (1985). The mahalanobis distance and elliptic distributions. Biometrika 72, 464-467.

Owen, J., & Rabinovitch, R. (1983). On the class of elliptical distributions and their applications to the theory of portfolio choice. The Journal of Finance 38, 745–752.

Rao, C. R. (2009). Linear Statistical Inference and its Applications. New York: Wiley.

Walters, J. (2011). The Black-Litterman Model in Detail. SSRN Scholarly Paper ID 1314585.

Zivot, E., & Wang, J. (2006). Modeling financial time series with S-plus. New York: Springer.



  • There are currently no refbacks.

Paper Submission E-mail:

Applied Economics and Finance    ISSN 2332-7294 (Print)   ISSN 2332-7308 (Online)

Copyright © Redfame Publishing Inc.

To make sure that you can receive messages from us, please add the '' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders. If you have any questions, please contact: