The most likely explanation for “fat tails” is that the second moment or volatility is time-varying. For example, volatility changes in interest rates are observed prior to much anticipated Federal Reserve announcements. Examining a data sample at different points of time from the full sample could generate fat tails in the unconditional distribution even if the conditional distributions are normally distributed. The conditional mean is not expected to deviate over time. The first two moments (mean and variance) of the distributions are similar for the fat-tailed and normal distribution. However, fat-tailed distributions typically have less probability mass in the intermediate range, around +/-1 standard deviation, compared to the normal distribution. Fat-tailed distributions have greater mass in the tails and a greater probability mass around the mean than the normal distribution. |
