What this chapter is about

The previous chapter analyzed "one shot" risks. In real life risk plays out over time. Analyzing risk in a dynamic context is complicated. This chapter introduces two classic dynamic models of risk over time.

One is the random walk model – also known as geometric Brownian motion. This is the standard introductory model employed to analyze risk for stocks and other financial assets. It is also the model that underpins the famous Black-Scholes option pricing formula. The other is a mean reverting model. This is often employed to analyze the risk of interest rate, commodity prices and other underlying risk factors.

These two models have very different risk properties. We use the contrast between the two to exercise the student’s mind about the different properties one might encounter when evaluating different risk factors.

Finally, we finish with a glance at the wide range of other possible dynamic models available. The universe of models is large because the universe of real world risk properties exhibited by different risk factors is large.

Current events and hot topics

Is GDP a Random Walk or Mean Reverting?

Earlier in the Great Recession, in 2009, there was an exchanges between Harvard economist Greg Mankiw, who criticized the Obama administration’s economic growth forecasts as too optimistic, and Princeton’s Paul Krugman and Berkeley’s Brad De Long, who defended the forecast. The debate turned out to be all about whether GDP is a random walk or a mean reverting process. If it is a random walk, then a recession means a permanent drop in income going forward. A recover means that growth will return to its old RATE, but the growth in the level of GDP will be from a lower starting point. If it is a mean reverting process, then GDP will bounce back up to its old level.

The debate starts with Mankiw, here:

Here are De Long and Krugman:

And Mankiw a couple of more times: