Here, we revise our pricing model for Franklin Resources (NYSE: BEN) presented on March 18, 2012. According to Yahoo.com “The firm provides its services to individuals, institutions, pension plans, trusts, and partnerships. It manages, through its subsidiary, separate client-focused equity, fixed income, and balanced portfolios.” BEN is a financial company and we analyzed it three years ago as a candidate for bankruptcy.
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. Our model also includes a linear time trend and an intercept in order to remove mean and trend components from all involved time series. The intuition behind our pricing model is obvious – we link a given share to those goods and services which are produced/provided by the company. In order to provide a dynamic reference we also introduce in the model some relative and independent level of prices (also expressed by CPIs). Hence, one needs two different CPIs to define the model. These CPIs we select from a big set of 92 CPIs by minimizing the residual model error.
In March 2012, the tentative model was driven by the consumer price index of food at home, FH, leading the price by five months and the index of other goods and services, O, which led by nine months. In the 2012 revised model, the former index is replaced by the index of food without beverages, FB, which leads the share price by four months. Both indices are shown in Figure. The tentative and revised pricing models are as follows:
BEN(t) = -5.47FH(t-5) – 1.81O(t-9) – 59.55(t-2000) + 1327.36, February 2012
BEN(t) = -7.33FB(t-4) – 1.52O(t-9) – 69.58(t-2000) + 1536.22, October 2012
BEN(t) = -2.39FB(t-4) – 0.50O(t-9) + 22.75(t-2000) + 504.08, March 2014
where t is calendar time. The standard error between July 2003 and March 2014 is $2.50 ($7.55 in March 2012). Figure 3 shows the model residual.
Figure 2 depicts the observed and predicted monthly closing prices since 2003 and also provides the high/low monthly prices, which may serve as the estimates of uncertainty in the monthly price. (One can model the monthly high or low price instead of the closing one.) At a four month horizon, the price is expected to grow to the final level of $60.
Figure 1. The evolution of defining CPIs.
Figure 2. Observed and predicted BEN share prices together with the high/low monthly prices.
Figure 3 . The standard model error.