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
Volume 4, Issue 6, November 2015, Pages: 484-495
Received: Sep. 17, 2015; Accepted: Oct. 7, 2015; Published: Oct. 22, 2015
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Authors
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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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.
Keywords
Expected Shortfall, Exponential Smoothing, Value At Risk, Conditional Mean, Conditional Volatility
To cite this article
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), American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 484-495. doi: 10.11648/j.ajtas.20150406.19
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