Here we present a simple two-component share price model for Apartment Investment and Management Company (AIV)]. We presume that any share price can be represented as a weighted sum of two consumer price indices (not seasonally adjusted in our model) which may be leading the share price by several months. The model also includes a linear time trend and an intercept in order to remove mean and trend components from the time series. AIV is a financial company listed in the S&P 500 market index. It "engages in the acquisition, ownership, management, and redevelopment of apartment properties."
We have been following the evolution of AIV share price since 2008 and a preliminary model was presented in 2009. It was based on a selection from a smaller set of CPIs and thus subject to further improvement. The current model is based on the index of food and beverages (F) and the index of other (O); the former is five months and the latter is six months ahead of the price. Figure 1 shows both CPIs since 2002. This set of CPIs has been determining the best-fit model during the past 24 months. The best-fit two-component model for AIV(t) is as follows:
AIV(t)= -2.57F(t-5) -0.41O(t-6) +20.51(t-1990) + 520.76, February 2012
where AIV(t) is the AIV share price in U.S. dollars, t is calendar time. The standard error of the model is $2.15 for the period between July 2003 and February 2012.
Figure 2 depicts the observed and predicted monthly closing prices since 2003 and also provides an estimate of the model natural uncertainty as related to the high/low monthly prices. Actually, the predicted curve leads the observed price by 5 months and is shifted back for better visual comparison. In that sense all major turn in the price were well foreseen by the model, including those in April 2007, May 2009, and May 2011. In other words, AIV share price is completely defined by the behaviour of these two CPI components. The residual error is also shown in Figure 3 with standard deviation of $2.15 for the period between July 2003 and February 2012.
Figure 3 shows that the price is likely overvalued by about $5. From Figure 2, one can conclude that AIV share will likely to fall slightly in the first quarter of 2012 and then will go up. It could be a new turn up in the price evolution.
Figure 1. The evolution of defining CPIs.
Figure 2. Observed and predicted AIV share prices together with the high/low monthly prices.
Figure 3 . The residual model error.