Modern financial markets are overflowing with information, and multitudes of number crunchers constantly parse and probe the growing stream of data to find quantitative relationships that can help improve the performance of portfolios. During this process, many analysts use obscure statistical terms derived from ancient Greek that seem more designed to intimidate outsiders than to illuminate the concepts they are covering. Thus, with the belief that even a strained everyday analogy can help improve understanding, we will make a brief attempt to explain a couple of the most formidable phrases analysts use by looking at a very common activity — lawncare.
Many homeowners will use a fertilizer spreader at least once a year to help maintain their lawn. Now as they apply the fertilizer, they don’t need to know with absolute certainty where each individual pellet will fall, they
just need the spreader to generate a consistent scattering in order to produce a future healthy lawn. If for some reason we wanted to use a term from ancient Greece to describe this desirable property, we would say that the spreader is homoskedastic ( homo– meaning “similar” and –skedastic from the Greek word for “scattering”, skedasis). If some variable of the fertilizer application began to change, like the pace of the person pushing the spreader or a clog forming in one of the spreader’s ports, then the scattering would start to become uneven, or heteroskedastic if we must insist on Greek terminology. This inconsistent scattering could lead to poor future results like a lawn with weedy patches or fertilizer burn.
Back to financial market analysis, there is considerable effort spent trying to derive equations that predict useful variables like domestic GDP, corporate earnings, or equity index returns through a process called multiple linear regression. These equations are never exact, but as long their variance or scattering is consistent, then there can be useful predictions gleaned from these relationships. However, most equations that try to explain connections in the global economy are more fragile than the most cheaply made fertilizer spreader. Thus, both lawn care enthusiasts and quantitative financial analysts should always be concerned about heteroskedasticity.