IDEAS home Printed from https://ideas.repec.org/a/blg/journl/v21y2026i1p88-109.html

Sample Size Matters: A Comparative Analysis Of The I.I.D. Assumption And Risk-Return Estimations In Latin American And Us Stock Markets

Author

Listed:
  • María Inés BARBOSA CAMARGO

    (Universidad de La Salle, Bogota, Colombia)

  • José Rodrigo VÉLEZ MOLANO

    (Universidad de La Salle, Bogota, Colombia)

  • Jorge Mario SALCEDO MAYORGA

    (Universidad de La Salle, Bogota, Colombia)

Abstract

This study examines the impact of sample size on the independent and identically distributed (i.i.d.) assumption in financial time series and its subsequent effect on risk-return estimations. Focusing on Latin American and US stock market indices from August 2007 to December 2024, using 4,477 daily log-returns, our methodology employs moment estimations, i.i.d. tests (Ljung-Box and Augmented Dickey-Fuller), and a modified Capital Asset Pricing Model (CAPM) and Download CAPM across four rolling windows (60, 250, 500, and 1,000 days). Our findings show that financial returns consistently exhibit heavy tails and negative skewness, challenging the assumption of normality. Statistical properties and i.i.d. violations vary significantly with sample size, with tests becoming more stringent for larger samples. CAPM alpha and beta coefficients are also sample size dependent, revealing distinct risk-return profiles: the S&P 500 exhibits higher systematic risk (Beta > 1) with performance explained by the model (alpha ≈ 0), while Latin American markets are more defensive (Beta

Suggested Citation

  • María Inés BARBOSA CAMARGO & José Rodrigo VÉLEZ MOLANO & Jorge Mario SALCEDO MAYORGA, 2026. "Sample Size Matters: A Comparative Analysis Of The I.I.D. Assumption And Risk-Return Estimations In Latin American And Us Stock Markets," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 21(1), pages 88-109, April.
    • Handle: RePEc:blg:journl:v:21:y:2026:i:1:p:88-109
    as

    Download full text from publisher

    File URL: http://magazines.ulbsibiu.ro/eccsf/RePEc/blg/journl/21105barbosa.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rui Ding, 2023. "f-Betas and portfolio optimization with f-divergence induced risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 23(10), pages 1483-1496, October.
    2. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    3. Vassalou, Maria, 2000. "Exchange Rate And Foreign Inflation Risk Premiums In Global Equity Returns," CEPR Discussion Papers 2448, Centre for Economic Policy Research.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    5. Rui Ding, 2023. "f-Betas and Portfolio Optimization with f-Divergence induced Risk Measures," Papers 2302.00452, arXiv.org, revised May 2023.
    6. Clark, Ephraim & Kassimatis, Konstantinos, 2011. "An alternative measure of the "world market portfolio": Determinants, efficiency, and information content," Journal of International Money and Finance, Elsevier, vol. 30(5), pages 724-748, September.
    7. Bao, Yong & Ullah, Aman, 2006. "Moments of the estimated Sharpe ratio when the observations are not IID," Finance Research Letters, Elsevier, vol. 3(1), pages 49-56, March.
    8. Ahmed, Shamim & Bu, Ziwen & Symeonidis, Lazaros & Tsvetanov, Daniel, 2023. "Which factor model? A systematic return covariation perspective," Journal of International Money and Finance, Elsevier, vol. 136(C).
    9. Vassalou, Maria, 2000. "Exchange rate and foreign inflation risk premiums in global equity returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 433-470, June.
    10. N. Muriel, 2025. "Weighted portmanteau statistics for testing for zero autocorrelation in dependent data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 52(10), pages 1950-1967, July.
    11. Schuster, Martin & Auer, Benjamin R., 2012. "A note on empirical Sharpe ratio dynamics," Economics Letters, Elsevier, vol. 116(1), pages 124-128.
    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. Ding Du, 2018. "The pricing of common exchange rate factors in the U.S. equity market," Review of Quantitative Finance and Accounting, Springer, vol. 50(3), pages 775-798, April.
    2. Boons, Martijn & Duarte, Fernando & de Roon, Frans & Szymanowska, Marta, 2020. "Time-varying inflation risk and stock returns," Journal of Financial Economics, Elsevier, vol. 136(2), pages 444-470.
    3. Qiao, Tongshuai & Ding, Wenjie & Han, Liyan & Li, Donghui, 2024. "RMB exchange rate volatility and the cross-section of Chinese A-share returns," Journal of International Money and Finance, Elsevier, vol. 142(C).
    4. Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    5. Huang, Lin & Wu, Jia & Zhang, Rui, 2014. "Exchange risk and asset returns: A theoretical and empirical study of an open economy asset pricing model," Emerging Markets Review, Elsevier, vol. 21(C), pages 96-116.
    6. Gerard Hoberg & S. Katie Moon, 2019. "The Offshoring Return Premium," Management Science, INFORMS, vol. 67(6), pages 2876-2899, June.
    7. Chung, Hyunchul & Majerbi, Basma & Rizeanu, Sorin, 2015. "Exchange risk premia and firm characteristics," Emerging Markets Review, Elsevier, vol. 22(C), pages 96-125.
    8. Adam Karp & Gary Van Vuuren, 2019. "Investment Implications Of The Fractal Market Hypothesis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-27, March.
    9. Paul Handro & Bogdan Dima, 2024. "Analyzing Financial Markets Efficiency: Insights from a Bibliometric and Content Review," Journal of Financial Studies, Institute of Financial Studies, vol. 16(9), pages 119-175, May.
    10. Bonga-Bonga, Lumengo & Gnagne, Pascal Xavier, 2017. "The impact of exchange rate volatility on capital flows in BRICS economies," MPRA Paper 84773, University Library of Munich, Germany.
    11. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    12. Barron, John M. & Ni, Jinlan, 2008. "Endogenous asymmetric information and international equity home bias: The effects of portfolio size and information costs," Journal of International Money and Finance, Elsevier, vol. 27(4), pages 617-635, June.
    13. Moerman, Gerard A. & van Dijk, Mathijs A., 2010. "Inflation risk and international asset returns," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 840-855, April.
    14. Du, Ding & Hu, Ou & Wu, Hong, 2014. "Emerging market currency exposure: Taiwan," Journal of Multinational Financial Management, Elsevier, vol. 28(C), pages 47-61.
    15. Kodongo, Odongo & Ojah, Kalu, 2011. "Foreign exchange risk pricing and equity market segmentation in Africa," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2295-2310, September.
    16. Stübinger, Johannes & Endres, Sylvia, 2017. "Pairs trading with a mean-reverting jump-diffusion model on high-frequency data," FAU Discussion Papers in Economics 10/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    17. David G. Kenchington, 2019. "Does a change in dividend tax rates in the U.S. affect equity prices of non-U.S. stocks?," Review of Accounting Studies, Springer, vol. 24(2), pages 593-628, June.
    18. Mika Vaihekoski, 2007. "Global Market and Currency Risk in Finnish Stock Market," Finnish Economic Papers, Finnish Economic Association, vol. 20(1), pages 72-88, Spring.
    19. Tashreef Muhammad, 2026. "Temporal Coverage Bias in Financial Panel Data: A Coverage-Aware Structuring Framework with Evidence from the Dhaka Stock Exchange," Papers 2603.20237, arXiv.org, revised Mar 2026.
    20. Begoña Font Belaire, 2012. "Can the exchange rate, inflation and domestic risk factors be overlooked in international asset pricing?," Working Papers. Serie EC 2012-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:blg:journl:v:21:y:2026:i:1:p:88-109. 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: Mihaela Herciu (email available below). General contact details of provider: https://edirc.repec.org/data/feulbro.html .

    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.