Crisis hits financial markets at regular intervals but the market participants keep assuming that they “understand the behavior” of markets and are in “total control” of the situation until the day things crash. There is an army of portfolio managers, equity research analysts, macro analysts, low frequency quants,derivative modeling quants, high frequency quants etc., all trying to understand the markets and trying to make money out of it. Do their gut /intuitive/quant models come close to how the market behaves ?

This paper is just 8 pages long but conveys an important point about random walk tests. The paper analyzes the use of variance and absolute variation as measures of volatility while testing a series for random walk. The paper suggest the following plot : for different values of zeta. For zeta=1 ,one ends up using absolute variation and for zeta=2, one ends up using variance. If the time series has fat tails, it might happen that variance ratio plots do not show anything fishy.

This paper by Lo and MacKinlay analyze the effects of non synchronous trading on stochastic properties. The transaction data of any asset traded in an exchange is irregularly spaced. Homogeneous time series is an artifact. Non Homogeneous time series is the reality. For example, the daily prices of securities quoted in the news papers as “closing prices” are not the prices that are exactly traded at the very last second of the market close.

This paper by Anderson, Bollerslev, Diebold and Labys documents an empirical finding about standardized returns. If one needs to obtain standardized returns, the usual way is to divide the returns by volatility estimated by ARCH, GARCH type of models. This does not eliminate fat tails though. This paper studies 10 years of high frequency returns for USD-Yen. It begins by showing that the unstandardized returns are fat tailed(obvious to everyone in today’s world).

Let’s say you want to compute the annualized monthly volatility of your portfolio. There are two ways to go about doing it : Compute the monthly volatility of each month for your portfolio, average it and multiply by sqrt(12) Create a moving window to capture monthly volatility, average it, and then multiply by sqrt(12). In this case, there will many more data points that give you an estimate of monthly volatility as compared to the first case.