IDEAS home Printed from https://ideas.repec.org/a/wly/jforec/v40y2021i8p1444-1462.html
   My bibliography  Save this article

The reliability of geometric Brownian motion forecasts of S&P500 index values

Author

Listed:
  • Amit K. Sinha

Abstract

This manuscript extends the literature on the application of geometric Brownian motion. Forecasted drift and diffusion terms estimated separately and recursively are plugged into the framework to forecast S&P500 index values. Expected index values are estimated from 100,000 simulated index values and probabilities. The results of comparing expected index values with actual values indicate that although reliable predictions of S&P500 index values can be obtained at monthly, quarterly, and annual frequencies, the reliability may decrease in that order.

Suggested Citation

  • Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
  • Handle: RePEc:wly:jforec:v:40:y:2021:i:8:p:1444-1462
    DOI: 10.1002/for.2775
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/for.2775
    Download Restriction: no

    File URL: https://libkey.io/10.1002/for.2775?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Asgharian, Hossein & Hou, Ai Jun & Javed, Farrukh, 2013. "Importance of the macroeconomic variables for variance prediction A GARCH-MIDAS approach," Knut Wicksell Working Paper Series 2013/4, Lund University, Knut Wicksell Centre for Financial Studies.
    2. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
    3. Opschoor, Anne & van Dijk, Dick & van der Wel, Michel, 2014. "Predicting volatility and correlations with Financial Conditions Indexes," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 435-447.
    4. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2015. "Regression-based estimation of dynamic asset pricing models," Journal of Financial Economics, Elsevier, vol. 118(2), pages 211-244.
    5. Michela Pelizza & Klaus R. Schenk-Hoppé, 2020. "Pricing Defaulted Italian Mortgages," JRFM, MDPI, vol. 13(2), pages 1-14, February.
    6. Harvey, Campbell R., 2001. "The specification of conditional expectations," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 573-637, December.
    7. Ausloos, Marcel, 2016. "Modelling and measuring the irrational behaviour of agents in financial markets: Discovering the psychological solitonAuthor-Name: Dhesi, Gurjeet," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 119-125.
    8. Marquering, Wessel & Verbeek, Marno, 2004. "The Economic Value of Predicting Stock Index Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(2), pages 407-429, June.
    9. Rime, Dagfinn & Sarno, Lucio & Sojli, Elvira, 2010. "Exchange rate forecasting, order flow and macroeconomic information," Journal of International Economics, Elsevier, vol. 80(1), pages 72-88, January.
    10. Lettau, Martin & Pelger, Markus, 2020. "Estimating latent asset-pricing factors," Journal of Econometrics, Elsevier, vol. 218(1), pages 1-31.
    11. Daniël Linders & Ben Stassen, 2016. "The multivariate Variance Gamma model: basket option pricing and calibration," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 555-572, April.
    12. Charlotte Christiansen & Maik Schmeling & Andreas Schrimpf, 2012. "A comprehensive look at financial volatility prediction by economic variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 956-977, September.
    13. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    14. Grinblatt, Mark & Titman, Sheridan, 1992. "The Persistence of Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 47(5), pages 1977-1984, December.
    15. Gurjeet Dhesi & Marcel Ausloos, 2016. "Modelling and Measuring the Irrational behaviour of Agents in Financial Markets: Discovering the Psychological Soliton," Papers 1601.01553, arXiv.org.
    16. Bryan Kelly & Alexander Ljungqvist, 2012. "Testing Asymmetric-Information Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1366-1413.
    17. Anisha Ghosh & Christian Julliard & Alex P. Taylor, 2017. "What Is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 30(2), pages 442-504.
    18. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
    19. Brennan, Michael J. & Xia, Yihong, 2001. "Stock price volatility and equity premium," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 249-283, April.
    20. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    21. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    22. Kim, Soohun & Skoulakis, Georgios, 2018. "Ex-post risk premia estimation and asset pricing tests using large cross sections: The regression-calibration approach," Journal of Econometrics, Elsevier, vol. 204(2), pages 159-188.
    23. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
    24. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    25. Fama, Eugene F. & French, Kenneth R., 2012. "Size, value, and momentum in international stock returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 457-472.
    26. Jie Zhu, 2008. "Testing for Expected Return and Market Price of Risk in Chinese A-B Share Market: A Geometric Brownian Motion and Multivariate GARCH Model Approach," CREATES Research Papers 2008-15, Department of Economics and Business Economics, Aarhus University.
    27. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    28. Jeong, Daehee & Kim, Hwagyun & Park, Joon Y., 2015. "Does ambiguity matter? Estimating asset pricing models with a multiple-priors recursive utility," Journal of Financial Economics, Elsevier, vol. 115(2), pages 361-382.
    29. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    30. Eric Djeutcha & Didier Alain Njamen Njomen & Louis-Aimé Fono, 2019. "Solving Arbitrage Problem on the Financial Market Under the Mixed Fractional Brownian Motion With Hurst Parameter H ∈]1/2,3/4[," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(1), pages 76-92, February.
    31. Berk, Jonathan B. & van Binsbergen, Jules H., 2016. "Assessing asset pricing models using revealed preference," Journal of Financial Economics, Elsevier, vol. 119(1), pages 1-23.
    32. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    33. Paye, Bradley S. & Timmermann, Allan, 2006. "Instability of return prediction models," Journal of Empirical Finance, Elsevier, vol. 13(3), pages 274-315, June.
    34. Chuo Chang, 2020. "Dynamic correlations and distributions of stock returns on China's stock markets," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 10(1), pages 1-6.
    35. Pedro P. Mota & Manuel L. Esquível, 2016. "Model selection for stock prices data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2977-2987, December.
    36. Dash, M., 2019. "Testing the Random Walk Hypothesis in the Indian Stock Market Using ARIMA Modelling," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 8(2), pages 71-77, May.
    37. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    38. Mittnik, Stefan & Robinzonov, Nikolay & Spindler, Martin, 2015. "Stock market volatility: Identifying major drivers and the nature of their impact," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 1-14.
    39. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    40. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    41. Lee, Charles & Ng, David & Swaminathan, Bhaskaran, 2009. "Testing International Asset Pricing Models Using Implied Costs of Capital," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(2), pages 307-335, April.
    42. Yi-Cheng Shih & Sheng-Syan Chen & Cheng-Few Lee & Po-Jung Chen, 2014. "The evolution of capital asset pricing models," Review of Quantitative Finance and Accounting, Springer, vol. 42(3), pages 415-448, April.
    43. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    44. Prakasa Rao, B.L.S., 2016. "Pricing geometric Asian power options under mixed fractional Brownian motion environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 92-99.
    45. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    46. Kim, Kyong-Hui & Kim, Nam-Ung & Ju, Dong-Chol & Ri, Ju-Hyang, 2020. "Efficient hedging currency options in fractional Brownian motion model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    47. Siddhartha Chib & Xiaming Zeng & Lingxiao Zhao, 2020. "On Comparing Asset Pricing Models," Journal of Finance, American Finance Association, vol. 75(1), pages 551-577, February.
    48. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    49. Eugene F. Fama, 2014. "Two Pillars of Asset Pricing," American Economic Review, American Economic Association, vol. 104(6), pages 1467-1485, June.
    50. Benninga, Simon, 2014. "Financial Modeling," MIT Press Books, The MIT Press, edition 4, volume 1, number 0262027283, December.
    51. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    52. David E. Rapach & Jack K. Strauss & Guofu Zhou, 2010. "Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy," The Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 821-862, February.
    53. Sharma, Prateek & Vipul,, 2016. "Forecasting stock market volatility using Realized GARCH model: International evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 59(C), pages 222-230.
    54. Frank Kleibergen & Zhaoguo Zhan, 2020. "Robust Inference for Consumption‐Based Asset Pricing," Journal of Finance, American Finance Association, vol. 75(1), pages 507-550, February.
    55. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    56. Parthajit Kayal & Sayanti Mondal, 2020. "Speed of Price Adjustment in Indian Stock Market: A Paradox," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(4), pages 453-476, December.
    57. Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
    58. Kan, Raymond & Robotti, Cesare, 2008. "Specification tests of asset pricing models using excess returns," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 816-838, December.
    59. Jegadeesh, Narasimhan & Noh, Joonki & Pukthuanthong, Kuntara & Roll, Richard & Wang, Junbo, 2019. "Empirical tests of asset pricing models with individual assets: Resolving the errors-in-variables bias in risk premium estimation," Journal of Financial Economics, Elsevier, vol. 133(2), pages 273-298.
    60. Eric Girard & Amit Sinha, 2006. "Does Total Risk Matter? The Case of Emerging Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 10(1-2), pages 117-151, March-Jun.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    2. Nonejad, Nima, 2017. "Forecasting aggregate stock market volatility using financial and macroeconomic predictors: Which models forecast best, when and why?," Journal of Empirical Finance, Elsevier, vol. 42(C), pages 131-154.
    3. Paye, Bradley S., 2012. "‘Déjà vol’: Predictive regressions for aggregate stock market volatility using macroeconomic variables," Journal of Financial Economics, Elsevier, vol. 106(3), pages 527-546.
    4. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    5. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    6. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    8. Brenner, Menachem & Izhakian, Yehuda, 2018. "Asset pricing and ambiguity: Empirical evidence⁎," Journal of Financial Economics, Elsevier, vol. 130(3), pages 503-531.
    9. Jennie Bai & Turan G. Bali & Quan Wen, 2019. "Is There a Risk-Return Tradeoff in the Corporate Bond Market? Time-Series and Cross-Sectional Evidence," NBER Working Papers 25995, National Bureau of Economic Research, Inc.
    10. Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    11. Wang, Yunqi & Zhou, Ti, 2023. "Out-of-sample equity premium prediction: The role of option-implied constraints," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 199-226.
    12. Wang, Cindy S.H. & Chen, Yi-Chi & Lo, Hsin-Yu, 2021. "A fresh look at the risk-return tradeoff," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    13. Yueh-Neng Lin & Ken Hung, 2008. "Is Volatility Priced?," Annals of Economics and Finance, Society for AEF, vol. 9(1), pages 39-75, May.
    14. Çakmaklı, Cem & van Dijk, Dick, 2016. "Getting the most out of macroeconomic information for predicting excess stock returns," International Journal of Forecasting, Elsevier, vol. 32(3), pages 650-668.
    15. Boguth, Oliver & Carlson, Murray & Fisher, Adlai & Simutin, Mikhail, 2011. "Conditional risk and performance evaluation: Volatility timing, overconditioning, and new estimates of momentum alphas," Journal of Financial Economics, Elsevier, vol. 102(2), pages 363-389.
    16. Bai, Jennie & Bali, Turan G. & Wen, Quan, 2021. "Is there a risk-return tradeoff in the corporate bond market? Time-series and cross-sectional evidence," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1017-1037.
    17. Li Liu & Yudong Wang, 2021. "Forecasting aggregate market volatility: The role of good and bad uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(1), pages 40-61, January.
    18. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    19. Michael Scholz & Jens Perch Nielsen & Stefan Sperlich, 2012. "Nonparametric prediction of stock returns guided by prior knowledge," Graz Economics Papers 2012-02, University of Graz, Department of Economics.
    20. Smith, Simon C., 2021. "International stock return predictability," International Review of Financial Analysis, Elsevier, vol. 78(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jforec:v:40:y:2021:i:8:p:1444-1462. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.