## 4/28/11

### Abercrombie & Fitch between 2009 and 2011

Abercrombie and Fitch (ANF) was one of the first companies with a stable and deterministic share price model estimated in September 2009.  This is a company from Services subcategory of the S&P 500 list specialized in apparel stores. We have revisited this model several times since 2009 and always found the same defining variables. The model is based on the decomposition of a share price into a sum of two selected consumer price indices. All models are defined by the (not seasonally adjusted) index of pets, pet products and services (PETS) and the price index of transportation services (TS), as reported by the US BLS. The former CPI component leads the share price by 1 month and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011.
In this post, we compare the 2009 and 2011 share price models for ANF. For the 2009 model we use the most recent defining CPIs as available in April 2011 and the measured monthly closing prices through March 2011. This allows validating the initial model and demonstrating its reliability.  These models are  as follows:
ANF(t) =  -4.56PETS(t-1) – 2.96TS(t-4)  + 47.09(t-1990) + 544.90 (September 2009)   (1)
ANF(t) =  -4.74PETS(t-1) – 2.45TS(t-4)  + 44.47(t-1990) + 494.79 (March 2011)   (2)
where t is calendar time. All coefficients are very close with just minor variations related to the updated share prices. Therefore, the model is effectively the same between January 2009 and March 2011. In other word, we obtained a deterministic (leading by one month) model which was valid during 27(!) months.   Figure 2 illustrates the difference between the original and current models.
The residual error is \$5.88 for the period between June 2003 and March 2011. One can expect a fall in the share price. Otherwise, the model will fail in the near future after 2 successful years.

Figure 1. Evolution of the price of PETS and TS.

Figure 2. Observed ANF share prices and that predicted in 2009 and 2011.