In our previous post we compared share price models for two financial companies from the S&P 500 list - Franklin Resources (BEN) and Apartment Investment and Management Company (AIV). There was a sound reason behind this direct comparison - both companies has similar models, i.e. are defined by the same consumer price indices. Here we extend our analysis by a triplet: Prudential Financial (PRU), Loews corporation (L) and MetLife (MET). All three companies are driven by the change in the index of food and beverages (F) and the index of transportation services (TS). Several days ago we presented models for Prudential and Loews on the Seeking Alpha.
Why do we rely on consumer price indices in our modeling? Many SA readers have reasonable doubts that some consumer price, which is not directly related to goods and services produced by a given company, may affect its price. We allow the economy to be a more complex system than described by a number of simple linear relations between share prices and goods. The connection between a firm and its products may be better expressed by goods and services which the company does not produce or provide. The demand/supply balance is not well understood yet and may evolve along many nonlinear paths. It would be too simplistic to directly define a company price by its products.
So, the intuition behind our pricing model is more insightful - we link a given share to some goods and services (and thus their consumer price indices), which we have to find among various CPIs. 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 a share price model. These CPIs we select from a predetermined set of 92 CPIs by minimizing the residual model error. All in all, we assume 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 current Loews model is driven by the consumer price index of food and beverages, F, leading the price by seven months and the index transportation services, TS, which leads by five months:
L(t) = -2.02F(t-7) - 2.00TS(t-5) + 27.50(t-2000) + 703.00, February 2012
where t is calendar time. The standard error between July 2003 and February 2012 is $2.41.
MetLife's model is driven by the same consumer price indices leading by six and four months, respectively:
MET(t) = -2.83F(t-6) - 2.71TS(t-4) + 34.81(t-2000) + 981.01, February 2012
The standard error between July 2003 and February 2012 is $3.25. It is worth noting that all co-efficients and time leads are close and have the same signs, i.e. their influence of the corresponding prices are similar.
For PRU, the model is as follows:
PRU(t) = -5.15F(t-5) - 3.80TS(t-4) + 56.20(t-2000) + 1005.63, February 2012
with the standard error between July 2003 and February 2012 of $5.58.
Figure 1 displays the evolution of all three prices since 2003. Their shapes are mainly similar but the amplitudes are quite different. Figure 2 depicts the same curves but normalized to their respective peak values between 2003 and 2012. The overall similarity and the presence of a sharp fall in October-November 2008 are obvious. This might be the reason behind the same defining CPIs and close time delays of the share prices behind the CPIs. Apparently, any information about a probable fall in a share price obtained five months in advance could be of importance. That's why we have been reporting on the prediction of our models for selected S&P 500 companies since 2009.
Figure 1. The evolution of PRU, L and MET share prices.
Figure 2. The evolution of PRU, L and MET share prices, all normalized to their peak values between 2003 and 2012.
We have already presented the newly estimated PRU model in our standard way. Figure 3 illustrates the evolution of both defining indices between 2002 and 2012. Figure 4 depicts the observed and predicted monthly closing prices for L and MET since 2003 and also provides an estimate of the models' natural uncertainty as related to the high/low monthly prices. The real time prediction for L (red curve) leads the observed price by 5 month. As for PRU, all major turns in the prices were well foreseen by the models, including those in November 2007, March 2009, and April 2011. These dates are different from the pivot times for BEN and AIV. The respective residual errors are shown in Figure 5.
Figures 4 suggests that L and MET prices will likely slightly rise in Q2 2012.
Figure 3. The evolution of defining CPIs.
Figure 4. Observed and predicted L and MET share prices together with their high/low monthly prices.
Figure 5 . The residual model error.