The Central Limit Theorem (CLT) is a foundational theorem in probability and statistics that states: regardless of the underlying distribution of a population (which may be skewed, bimodal, or non-normal), the distribution of the sample mean — calculated from sufficiently large random samples drawn from that population — will approximate a normal (bell-curve) distribution as the sample size increases, typically becoming reliably normal for sample sizes of 30 or more. The CLT is one of the most powerful results in statistics because it justifies the widespread use of normal distribution-based statistical methods (such as confidence intervals, hypothesis testing, and z-scores) across virtually all fields, even when the underlying data is not normally distributed. In finance, the CLT underpins portfolio theory, risk modelling (VaR calculations), options pricing, and sampling-based market research. For quantitative investors, algo traders, and risk managers on Ventura Securities, the CLT is a critical theoretical foundation — but its limitations must also be respected, as financial returns often exhibit fat tails and extreme events (black swans) that the normal distribution significantly underestimates.
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