If financial time series exhibits persistence or long-memory, then their unconditional probability distribution may not be normal. This has important implications for many areas in finance, especially asset pricing, option pricing, portfolio allocation and risk management. Furthermore, if the random walk does not apply, a wide range of results obtained by quantitative analysis may be inappropriate. The capital asset pricing model, the Black-Scholes option pricing formula, the concept of risk as standard deviation or volatility, and the use of Sharpe, Treynor, and other performance measures are not consistent with nonnormal distributions. Unfortunately, nonnormality is common among distributions of financial time series according to observations from empirical studies of financial series.