During the past two days, we re-estimated share price models for a few companies from the S&P 500 list and found them reliable and accurate for a year and even longer. Forest Laboratories (NYSE: FRX) is one of the first companies with a stable and deterministic share price modelestimated in September 2009 (this early model tracks back into November 2008). This is a company from Healthcare subcategory specialized in drugs manufacturing. We revisited this model in September 2010, December 2010, and March 2011 and always found the same defining variables with almost the same time lags.
Our approach to deterministic share pricing is based on the decomposition of a share price into a weighted sum of two selected consumer price indices. For FRX, all models between 2009 and 2011 are defined by the (not seasonally adjusted) index of dairy and related products (DAIRY) and the price index of other household equipment and furnishing (OHEF), as reported by the US BLS. In the September 2011 model, the former CPI component leads the share price by 4 month and the latter is 5 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through August 2011.
Thus, three models mentioned above are as follows:
FRX(t) = -0.53DAIRY(t-3) – 4.18OHEF(t-5) - 13.41(t-1990) + 706.57 (September 2009)
FRX(t) = -0.61DAIRY(t-3) – 3.89OHEF(t-4) - 11.65(t-1990) + 668.75 (March 2011)
FRX(t) = -0.66DAIRY(t-4) – 3.45OHEF(t-5) - 9.78(t-1990) + 613.99 (September 2011)
where t is calendar time. All coefficients have been slightly drifting due to then trade-off between the linear time trend and the trend in the difference between the CPIs and due to new data. Therefore, the model is effectively the same between November 2008 and September 2011. In other words, we obtained a deterministic (leading by three months) model which was valid during 36(!) months. Figure 2 depicts the predicted and observed prices together with the relevant monthly highs and lows. The residual error is $4.75 (see Figure 3) for the period between June 2003 and September 2011 ($4.40min March 2011). From the most recent model in Figure 2, we expect a fall to the level of $20 per share in the fourth quarter of 2011.
Figure 1. Evolution of the price of DAIRY and OHEF.
Figure 2. Observed and predicted FRX share prices.
Figure 3. The model residual.