Creating an Index to Measure Financial Uncertainty Using the Fama-French Five-factor Model in State Space by the Kalman Filter Algorithm

Document Type : Research Paper


1 MSc. Student, Department of Financial Management, Faculty of Economic and Management, University of Urmia, Urmia, Iran.

2 Associate Prof., Department of Financial Management, Faculty of Economic and Management, University of Urmia, Urmia, Iran.


Objective: The primary purpose of this study is to quantify uncertainty and consequently develop an indicator of financial uncertainty for the Tehran Stock Exchange (TSE). Since paying attention to uncertainty is of importance in the development of economics and management, it is worth acquiring a deep and accurate understanding of it. Financial market participants are always faced with uncertainties about the future; therefore, getting familiar with the concept and understanding it is necessary for all market participants.
Methods: In the present study, conditional fluctuations were filtered from the series of efficiency fluctuations in order to obtain a more appropriate criterion for expressing uncertainty. According to recent studies, the Fama-French five-factor model can explain 69 to 93% of cross-sectional changes in expected returns. Accordingly, in this study, the estimation of this model was initially compared with two methods of ordinary least squares and state space by the filter-Kalman algorithm to obtain a suitable model for filtering conditional fluctuations. In this study, state space by  Kalman filter algorithm and ordinary least squares method for selecting the appropriate model for filtering conditional fluctuations from the series of efficiency fluctuations was compared in the first step to quantify the uncertainty from the fitting of the 5-factor model of Fama and French in two ways.
Results: Information criteria along with Debold and Mariano approaches for comparing the fit of the 5-factor model of Fama and French with two methods of state space by Kalman filter algorithm and ordinary least squares were used. The results indicated the superiority of state space estimation by Kalman filter algorithm. After selecting the appropriate model, the conditional performance fluctuations of each portfolio were filtered from the series of yield fluctuations to obtain a more appropriate measure of uncertainty. In this regard, the returns of 18 portfolios were used based on the classifications of variables; size factor, book value to market value factor, profitability factor, and investment factor.
Conclusion: Finally, the extracted uncertainty components were averaged monthly to obtain our index. This index clearly showed the conditions under uncertainty that occurred continuously in the past.
Practicability: To prevent the reduction of investment and the outflow of capital, as well as the loss of shareholders, government, and governmental institutions, including the stock exchange can use this index in times of uncertainty by increasing the use of financial instruments, proper pricing of securities, as well as other methods that control uncertainty to reduce investment. Researchers who study the relationship between economic and financial variables with uncertainty are advised instead of using different criteria to express uncertainty, they should use the approach used in this research, which shows uncertainty better, in order to reach better results.
Limitations: The index in this study was obtained based on the observance of the data frequency on a monthly basis, so this index is weak in explaining the uncertainties that have a short-term impact on the market. Since in creating the index, the average components of uncertainty were used and they showed the general uncertainty of the market, comparing the results with the uncertainty of companies individually may provide different results.


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