Modeling share prices of financial companies: AIV

The model for Apartment Investment and Management Company (AIV) has both defining CPIs leading the share price: the index of other food at home (OFH) and the index of prescribed drugs (PDRUG) are both five months ahead of the price. At first glance, this set of defining CPIs does not look convincing. This might be an effect of the changing trend in the CPI. Before November 2009, the best-fit model included the index of food and beverages (F) and the PDRUG, both leading by 8 months. This set determined the best-fit model during the 12 months previous to November 2009 (Kitov, 2010).

In a smaller set of 34 CPI components used by Kitov (2010), the index of food and beverages and that of medical care (M) were the driving ones between November 2008 and October 2009 and provided the standard error of $2.058, but for a shorter period. With the PDRUG, the standard error for the same period between July 2003 and October 2009 is $2.055, i.e. only marginally better. This fact demonstrates how sensitive the model is to the defining CPIs. When more components are included, one could expect changes in the previously obtained models and lower standard errors.

So, the best-fit 2-C model for AIV(t) is as follows:

AIV(t)= -1.25OFH(t-4) + 1.23PDRUG(t-4) - 7.83(t-2000) – 151.7

The predicted curve should lead the observed price by 4 months with the residual error of $2.19. In other words, the price of an AIV share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted four months back for synchronization. The residual error is also shown.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In March, April and May 2010, the price is expected at $19.5, $18.9 and $21.8, respectively. On 26th of March, the price was at $18.66.

Figure 1. Observed and predicted AIV share prices, and the residual error.

ReferencesKitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.