Here we present a tentative model for the evolution of FedEx (NYSE: FDX) stock price. FDX is a company from Services sector of the S&P 500 index which “provides transportation, e-commerce, and business services in the United States and internationally”. We decompose a FDX share price into a weighted sum of two consumer price indices, one has to be related to the overall FDX activity and one index is independent on FDX services. We assume that all goods and services produced (provided) by FDX should define the share price evolution relative to other companies. In other words, the FDX relative pricing power is defined by the pricing power of its G&S. Since other companies are also driven by prices for their goods and services, which compete with FDX, one need two defining sets of G&S to estimate the relative pricing power. It is not excluded that the studied share price can be accurately defined by two CPIs. There are some measurement errors in all CPIs which are directly mapped into the model errors. Since we model the monthly closing prices (CPIs are reported at a monthly rate) the intermonth variations (high/low prices) can be treated as natural uncertainty of the monthly closing prices. Therefore our pricing model has two sources of uncertainty.
The best CPIs are selected from a set of 92 CPIs with estimates available from 2000 (one may extend this set). The best fit (in the LSQ sense) consumer price indices are that of food and beverages (F - CUUS0000SAF) and the index of communication (CO - CUUR0000SAE2). The latter index is directly related to FedEx and the former one seems to be mainly independent and evolving according to own forces. The defining time lags are as follows: the food index leads the share price by 3 months and the CO index leads by 5 months:
FDX(t) = -4.87F(t-3) – 5.09CO(t-5) + 26.50(t-1990) + 1039.05, February 2012
where FDX(t) is the FDX share price in U.S. dollars, t is calendar time. Figure 1 displays the evolution of both defining indices since 2002. Figure 2 depicts the high and low monthly prices for a share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are mainly within the bounds of the share price uncertainty and lead by 3 months. Since the measured price volatility is much higher than the predicted one there are some large deviations from the predicted level. In any case, such fluctuations have always ended on the predicted curve. One can use this observation for a qualitative forecast of the future price movements.
It should be noted that here we present a tentative model which is fresh and needs to be validated by new data (new CPI estimates will be published tomorrow).
The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $6.33. It is not excluded that the share will have a negative correction in April/May.
Figure 1. The evolution of F and CO indices
Figure 2. Observed and predicted FDX share prices.
Figure 3. The model residual error: sterr=$6.33.
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