Characteristics of volatile return series

1. Characteristics of volatile return series

In the previous chapter, you have seen compelling evidence that financial returns are often heavier tailed than normal, particularly for daily, weekly and monthly data.

2. Log-returns compared with iid data

In this chapter, you are going to investigate whether financial returns can be modeled as independent and identically distributed or iid. This is sometimes known as the random walk model, a model whose merits and validity have long been debated in the financial economics literature. If log-returns are iid, then the log of the price series follows a random walk. This would effectively mean that it would be impossible to use past prices to predict future market behavior. Of course, it is always possible to make some statements about the typical distribution of price changes, but the best guess of tomorrow's price would simply be today's price. In the first exercise of this chapter, you are going to compare a real financial time series - the log-returns of the Dow Jones index - with iid data from both the normal and the Student t distributions. To make the pictures comparable, you will fit the normal and Student t distributions to the data, using the techniques from the previous chapter, and then randomly generate data from the fitted models. What you are going to observe is that there is a clear difference between the real log-return series and the simulated iid series. The real data show a phenomenon that econometricians often describe as volatility clustering - periods in which there are many large returns with differing signs interspersed with periods when the returns are of smaller magnitude. Why is this important in quantitative risk management? If you know that volatility clustering is present, you can use this information to make more risk-sensitive estimates of the future behavior of financial portfolios. You can, to an extent, predict their future volatility.

3. Let's practice!

So why don't you go ahead and try the exercise, and I'll discuss the implications in the next video.

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