A bell curve — formally known as a normal distribution or Gaussian distribution — is a symmetric, bell-shaped probability distribution where data points are most densely concentrated around the mean, with progressively fewer observations occurring as values move further from the centre in either direction. The distribution is completely characterised by two parameters: the mean (centre of the bell) and the standard deviation (width of the bell). In a normal distribution, approximately 68% of observations fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In financial risk management, the bell curve underpins many standard models — including Black-Scholes option pricing and Value at Risk (VaR) calculations — which assume that asset returns are normally distributed. However, real-world financial returns — including Nifty 50 daily returns — exhibit fat tails and negative skewness, meaning extreme negative events occur far more frequently than a normal distribution predicts. This 'fat tail' or leptokurtic behaviour means that standard bell-curve-based risk models systematically underestimate the probability of severe market crashes, making them inadequate for comprehensive risk management in Indian and global equity markets.
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