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

Author

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  • 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
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