Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)

Jumba Minyoso Sandra; Joel Cheruiyot Chelule; Mungatu Joseph

doi:doi:10.11648/j.ajtas.20150406.19

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Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)

Jumba Minyoso Sandra, Joel Cheruiyot Chelule, Mungatu Joseph

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)

Received: 17 September 2015 Accepted: 7 October 2015 Published: 22 October 2015

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Abstract

This study sought to develop consistent estimators for the conditional mean and conditional volatility using exponential smoothing technique and to use the estimators for the conditional mean and conditional volatility to estimate VaR and ES of a financial asset in a given financial portfolio. In particular, we take the Kenyan Matatu business as our financial portfolio and we estimate the ES of the daily returns obtained from Matatus travelling the Nairobi –Eldoret highway as provided by CLASSIC SACCO. In estimating the conditional mean and conditional volatility of the returns of our portfolio, the study explored the exponential smoothing technique, whereby exponentially decreasing weights were assigned to the returns. The study proved that the estimators for the conditional mean and conditional volatility are consistent and also that the estimators for the conditional mean and conditional volatility when conditional mean is known, are asymptotically normal. Further the study gives the estimators for the VaR and ES and proves that the VaR estimator is consistent.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.19
Page(s)	484-495
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Expected Shortfall, Exponential Smoothing, Value At Risk, Conditional Mean, Conditional Volatility

References

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APA Style

Jumba Minyoso Sandra, Joel Cheruiyot Chelule, Mungatu Joseph. (2015). Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). American Journal of Theoretical and Applied Statistics, 4(6), 484-495. https://doi.org/10.11648/j.ajtas.20150406.19

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ACS Style

Jumba Minyoso Sandra; Joel Cheruiyot Chelule; Mungatu Joseph. Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). Am. J. Theor. Appl. Stat. 2015, 4(6), 484-495. doi: 10.11648/j.ajtas.20150406.19

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AMA Style

Jumba Minyoso Sandra, Joel Cheruiyot Chelule, Mungatu Joseph. Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). Am J Theor Appl Stat. 2015;4(6):484-495. doi: 10.11648/j.ajtas.20150406.19

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@article{10.11648/j.ajtas.20150406.19,
  author = {Jumba Minyoso Sandra and Joel Cheruiyot Chelule and Mungatu Joseph},
  title = {Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {484-495},
  doi = {10.11648/j.ajtas.20150406.19},
  url = {https://doi.org/10.11648/j.ajtas.20150406.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.19},
  abstract = {This study sought to develop consistent estimators for the conditional mean and conditional volatility using exponential smoothing technique and to use the estimators for the conditional mean and conditional volatility to estimate VaR and ES of a financial asset in a given financial portfolio. In particular, we take the Kenyan Matatu business as our financial portfolio and we estimate the ES of the daily returns obtained from Matatus travelling the Nairobi –Eldoret highway as provided by CLASSIC SACCO. In estimating the conditional mean and conditional volatility of the returns of our portfolio, the study explored the exponential smoothing technique, whereby exponentially decreasing weights were assigned to the returns. The study proved that the estimators for the conditional mean and conditional volatility are consistent and also that the estimators for the conditional mean and conditional volatility when conditional mean is known, are asymptotically normal. Further the study gives the estimators for the VaR and ES and proves that the VaR estimator is consistent.},
 year = {2015}
}

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TY  - JOUR
T1  - Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)
AU  - Jumba Minyoso Sandra
AU  - Joel Cheruiyot Chelule
AU  - Mungatu Joseph
Y1  - 2015/10/22
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.19
DO  - 10.11648/j.ajtas.20150406.19
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 484
EP  - 495
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.19
AB  - This study sought to develop consistent estimators for the conditional mean and conditional volatility using exponential smoothing technique and to use the estimators for the conditional mean and conditional volatility to estimate VaR and ES of a financial asset in a given financial portfolio. In particular, we take the Kenyan Matatu business as our financial portfolio and we estimate the ES of the daily returns obtained from Matatus travelling the Nairobi –Eldoret highway as provided by CLASSIC SACCO. In estimating the conditional mean and conditional volatility of the returns of our portfolio, the study explored the exponential smoothing technique, whereby exponentially decreasing weights were assigned to the returns. The study proved that the estimators for the conditional mean and conditional volatility are consistent and also that the estimators for the conditional mean and conditional volatility when conditional mean is known, are asymptotically normal. Further the study gives the estimators for the VaR and ES and proves that the VaR estimator is consistent.
VL  - 4
IS  - 6
ER  -

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Author Information

Jumba Minyoso Sandra

Department of Statistics and Actuarial Studies, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Joel Cheruiyot Chelule

Department of Statistics and Actuarial Studies, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Mungatu Joseph

Department of Statistics and Actuarial Studies, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

Jumba Minyoso Sandra, Joel Cheruiyot Chelule, Mungatu Joseph. (2015). Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). American Journal of Theoretical and Applied Statistics, 4(6), 484-495. https://doi.org/10.11648/j.ajtas.20150406.19

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ACS Style

Jumba Minyoso Sandra; Joel Cheruiyot Chelule; Mungatu Joseph. Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). Am. J. Theor. Appl. Stat. 2015, 4(6), 484-495. doi: 10.11648/j.ajtas.20150406.19

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AMA Style

Jumba Minyoso Sandra, Joel Cheruiyot Chelule, Mungatu Joseph. Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya). Am J Theor Appl Stat. 2015;4(6):484-495. doi: 10.11648/j.ajtas.20150406.19

Copy | Download

@article{10.11648/j.ajtas.20150406.19,
  author = {Jumba Minyoso Sandra and Joel Cheruiyot Chelule and Mungatu Joseph},
  title = {Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {484-495},
  doi = {10.11648/j.ajtas.20150406.19},
  url = {https://doi.org/10.11648/j.ajtas.20150406.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.19},
  abstract = {This study sought to develop consistent estimators for the conditional mean and conditional volatility using exponential smoothing technique and to use the estimators for the conditional mean and conditional volatility to estimate VaR and ES of a financial asset in a given financial portfolio. In particular, we take the Kenyan Matatu business as our financial portfolio and we estimate the ES of the daily returns obtained from Matatus travelling the Nairobi –Eldoret highway as provided by CLASSIC SACCO. In estimating the conditional mean and conditional volatility of the returns of our portfolio, the study explored the exponential smoothing technique, whereby exponentially decreasing weights were assigned to the returns. The study proved that the estimators for the conditional mean and conditional volatility are consistent and also that the estimators for the conditional mean and conditional volatility when conditional mean is known, are asymptotically normal. Further the study gives the estimators for the VaR and ES and proves that the VaR estimator is consistent.},
 year = {2015}
}

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TY  - JOUR
T1  - Use of Exponential Smoothing Technique in Estimation of Returns in a Financial Portfolio (A Case of the Matatu Public Transport Business in Kenya)
AU  - Jumba Minyoso Sandra
AU  - Joel Cheruiyot Chelule
AU  - Mungatu Joseph
Y1  - 2015/10/22
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.19
DO  - 10.11648/j.ajtas.20150406.19
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 484
EP  - 495
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.19
AB  - This study sought to develop consistent estimators for the conditional mean and conditional volatility using exponential smoothing technique and to use the estimators for the conditional mean and conditional volatility to estimate VaR and ES of a financial asset in a given financial portfolio. In particular, we take the Kenyan Matatu business as our financial portfolio and we estimate the ES of the daily returns obtained from Matatus travelling the Nairobi –Eldoret highway as provided by CLASSIC SACCO. In estimating the conditional mean and conditional volatility of the returns of our portfolio, the study explored the exponential smoothing technique, whereby exponentially decreasing weights were assigned to the returns. The study proved that the estimators for the conditional mean and conditional volatility are consistent and also that the estimators for the conditional mean and conditional volatility when conditional mean is known, are asymptotically normal. Further the study gives the estimators for the VaR and ES and proves that the VaR estimator is consistent.
VL  - 4
IS  - 6
ER  -

Copy | Download