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Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation

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  • Santanu Dutta

    (Tezpur University)

  • Tushar Kanti Powdel

    (Tezpur University)

Abstract

The log-return of an asset is the change in the asset price, measured in natural logarithmic scale, over a certain time period. We introduce a mathematical model for long term asset return. This model is a generalization of the well known random walk model and provides the mathematical basis for normal approximation and i.i.d. bootstrap approximation of the long-term return distribution and its quantiles. Our results yield estimators of long term value at risk (VaR) and median shortfall (MS) which are well known measures of market risk. Extensive simulations suggest that the proposed estimators outperform a number of existing estimators of VaR and MS especially over a time horizon of at least one year. Unconditional backtest by Kupiec (J. Derivat. 3, 73–84 1995) based on the annual returns of the Nifty 50 index of the national stock exchange in India, crude oil and gold prices suggests that the proposed model yields reliable estimates of the one-year Value-at-Risk and Median-Shortfall for these assets.

Suggested Citation

  • Santanu Dutta & Tushar Kanti Powdel, 2023. "Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 257-289, May.
    • Handle: RePEc:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-023-00303-x
    DOI: 10.1007/s13571-023-00303-x
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    1. Stijn De Backer & Luis E. C. Rocha & Jan Ryckebusch & Koen Schoors, 2025. "Characterizing asymmetric and bimodal long-term financial return distributions through quantum walks," Papers 2505.13019, arXiv.org.

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