Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation

Santanu Dutta () and Tushar Kanti Powdel
Additional contact information
Santanu Dutta: Tezpur University
Tushar Kanti Powdel: Tezpur University

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 9, 257-289

Abstract: 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.

Keywords: Long term asset return model; normal and bootstrap approximation of return distribution; value-at-risk; median-shortfall; back-testing.; Primary 62G05; Secondary 91B28 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13571-023-00303-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-023-00303-x

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13571

DOI: 10.1007/s13571-023-00303-x

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().