■ The Economic Implications of Volatility Scaling by the Square-Root-of-Time Rule

One common application of volatility scaling laws in financial economics is the estimation of long-horizon volatility in models such as the capital asset pricing model (CAPM) and the Black-Scholes option pricing model, both of which are typically estimated on the basis of annual equivalent measures of asset return and volatility. Investors wishing to price positions based on a target level of volatility and preferred investment horizon also typically assume a Gaussian random walk when scaling shorthorizon volatility to estimate long-horizon volatility (Celati, 2004).