Introduction of New Risk Metric using Kernel Density Estimation Via Linear Diffusion

محورهای موضوعی : Risk Management

Ahmad Darestani Farahani ¹ , Mohammadreza Miri Lavasani ² , Hamidreza Kordlouie ³ , Ghodratallah Talebnia ⁴

1 - Department of Finance, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of HSE, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Financial Management, Eslamshahr Branch, Islamic Azad University, Tehran, Iran
4 - Department of Accounting, Science and Research Branch, Islamic Azad University, Tehran, Iran.

تاریخ دریافت : 1399/01/06 تاریخ پذیرش : 1399/05/30 تاریخ انتشار : 1401/01/12

کلید واژه: Stock market, Generalized Co-Lower Partial Moment, Nonparametric estimation, Portfolio optimization, Risk measurement,

چکیده مقاله :

Any investor in stock markets around the world has a deep concern about the shortfalls of allocation wealth to any stock without accurate estimation of related risks. As we review the literature of risk management methods, one of the main pillars for the risk management framework in defining risk measurement approach using historical data is the estimation of the probability distribution function. In this paper, we propose a new measure by using kernel density estimation via diffusion as a nonparametric approach in probability distribution estimation to enhance the accuracy of estimation and consider some distribution characteristics, investor risk aversion and target return which will make it more accurate, compre-hensive and consistent with stock historical performance and investor concerns.

منابع و مأخذ:

References

 

[1] Markowitz, H.M., Portfolio selection, Journal of Finance, 1952, 7, P. 77–91. Doi: 10.2307/2975974.

[2] Lien, D., and Tse, Y K., Hedging downside risk with futures contracts, Applied Financial Economics, 2000, 10(2), P. 163–170. Doi: 10.1080/096031000331798.

[3] Miryekemami, S.A., Sadeh, E., and Amini Sabegh, Z., Using Genetic Algorithm in Solving Stochastic Programming for Multi-Objective Portfolio Selection in Tehran Stock Exchange, Advances in Mathematical Finance and Applications, 2017, 2(4), P. 107-120. Doi: 10.22034/AMFA.2017.536271.

 

[4] Navidi, S., Rostamy-Malkhalifeh, M., and Banihashemi, S., Using MODEA and MODM with Different Risk Measures for Portfolio Optimization, Advances in Mathematical Finance and Applications, 2020, 5(1), P. 29-51. Doi: 10.22034/AMFA.2019.1864620.1200.

 

[5] Rahmani, M., Khalili Eraqi, M., and Nikoomaram, H., Portfolio Optimization by Means of Meta Heuristic Algorithms, Advances in Mathematical Finance and Applications, 2019, 4(4), P.83-97.

 Doi: 10.22034/AMFA.2019.579510.1144.

 

[6] Fix, E., and Hodges, J.L., Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties, International Statistical Review, 1989, 57(1), P.238-247. Doi: 10.2307/1403797.

 

[7] Silverman, B.W., Jones M.C., E. Fix and J.L. Hodges (1951) An Important Contribution to Nonparametric Discriminant analysis and Density Estimation, International Statistical Review, 1989, 57(3). P. 233-247. Doi: 10.2307/1403796.

 

[8] Gyorfi, L., Kohler, M., Krzyzak, A., and Walk, H., A Distribution-Free Theory of Nonparametric Regression, Springer Series in Statistics, 2002, P. 9-12. Doi: 10.1007/b97848.

 

[9] Roy, A.D., Safety first and the holding of assets, Econometrica, 1952, 20, P. 431- 449. Doi: 10.2307/1907413.

 

[10] Rom, B.M. and Ferguson, K., Post-Modern Portfolio Theory Comes of Age, Journal of Investing, 1993, 2(4), P. 27-33. Doi: 10.3905/joi.2.4.27.

 

[11] Adams, J. and Montesi, C. J., Major Issues Related to Hedge Accounting, Financial Accounting Standard Board, 1995, Newark, Connecticut. Bib ID: 1091732.

 

[12] Lien, D., Tse, Y.K., Hedging time-varying downside risk, Journal of Futures Markets, 1998, 18, P. 705–722. Doi: 10.1002/(SICI)1096-9934(199809)18.

[13] Lien, D., and Tse, Y. K., Hedging downside risk with futures contracts, Applied Financial Economics, 2000, 10(2), P. 163–170. Doi: 10.1080/096031000331798.

[14] Chen, S.S., Lee, C.F., and Shrestha, K., Empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short- and long-run hedge ratios, Journal of Futures Markets, 2004, 24, P. 359–386. Doi: 10.1002/fut.10121.

[15] Bond, S.A., and Satchell, S. E., Statistical properties of the sample semi-variance, Applied Mathematical Finance, 2002, 9(4), P. 219-239. Doi: 10.1080/1350486022000015850.

[16] Fishburn, P.C., Mean-risk analysis with risk associated with below target returns, American Economic Review, 1977, 67(2), P.116–126. Doi: 10.2307/1807225.

 

[17] Harlow, W.V., and Rao, R.K.S., Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence, Journal of Financial and Quantitative Analysis, 1989, 24, P. 285–311. Doi: 10.2307/2330813.

 

[18] Huang, X.X., Mean-semi variance models for fuzzy portfolio selection, Journal of Computational and Applied Mathematics, 2008, 217(1), P. 1-8. Doi: 10.1016/j.cam.2007.06.009.

 

[19] Porter, R.B., and Gaumnitz, J.E., Stochastic dominance vs. mean-variance portfolio analysis: An empirical evaluation, American Economic Review, 1972, 62(3), P. 438-446.

 

[20] Leibowitz, M.L. and Langetieg, T.C., Shortfall risk and the asset allocation decision: A simulation analysis of stock and bond risk profiles, Journal of Portfolio Management, 1989, P. 61-68. Doi: 10.3905/jpm.1989.409236

 

[21] Sortino, F. and Forsey, H., On the Use and Misuse of Downside Risk, The Journal of Portfolio Management, 1996, P. 381-408. Doi: 10.3905/jpm.1996.35.

 

[22] Rosenblatt, M., Remarks on some nonparametric estimates of a density function, Annals of Mathematical Statistics, 1956, 27, P. 832–837. Doi: 10.1214/aoms/1177728190.

 

[23] Silverman, B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, 1986, London. ISBN-13: 978-0412246203.

 

[24] Foster, D.P., and Nelson, D.B., Continuous Record Asymptotics for Rolling Sample Variance Estimators, Econometrica, 1996, 64(1), P. 139-174. Doi: 10.2307/2171927.

 

[25] Botev, Z.I., Grotowski, J.F., and Kroese, D.P., Kernel Density Estimation via Diffusion, The Annals of Statistics, 2010, 38(5), P.2916–2957. Doi: 10.1214/10-AOS799.

 

[26] Devroye, D., Beirlant, J., Fraiman, R., Hall, P., Jones, M. C., Logosi, G., Mammen, E., Marron, J.S., Sanchez-Sellero, C., de Una, J., Udina, F. and Devroye, L., Universal smoothing factor selection in density estimation: Theory and practice, Test, 1997, 6, P. 223–320. Doi: 10.1007/BF02564701.

 

[27] Jones, M.C., Marron, J.S., Sheather, S.J., A brief survey of bandwidth selection for density estimation, Journal of the American Statistical Association, 1996, 91, P. 401–407. Doi: 10.2307/2291420.

 

[28] Figueroa-Lópeza, J.E., and Li, C. Optimal kernel estimation of spot volatility of stochastic differential equations, Stochastic Processes and their Applications, 2020, 130(8), P. 4693-4720. Doi: 10.1016/j.spa.2020.01.013.

 

[29] Hogan, W.W. and Warren J.M., Computation of the Efficient Boundary in the E-S Portfolio Selection Model, Journal of Financial and Quantitative Analysis, 1972, 7(4), P. 1881-1896. Doi: 10.2307/2329623.

 

[30] Bawa. V.S., and Lienderberg E.B., Capital Market Equilibrium in a Mean-Lower Partial Moment Framework, Journal of Financial Economics, 1977, 5(2), P.189-200. Doi: 10.1016/0304-405X(77)90017-4.