Economics as Classical Mechanics: Modeling share prices: TECO Energy to hold

In this article, we revise our original pricing model for TECO Energy (NYSE: TE) estimated in November 2012, when we predicted a period of no change. Here we demonstrate that there was no significant change in TE price since 2012 and our prediction was correct.

TE is one of many energy related companies in the S&P 500 list but its model reveals very specific features. Our approach to pricing modeling is based on the link between stocks and consumer price indices. The intuition is simple and clear, the evolution of a share price is inherently related some goods and services (at least to goods and services the company provides) and thus the evolution of their relative prices. For example, it is not easy to ignore the intuition that there exists a statistically reliable link between oil price and share prices of oil companies. We have reported that such a link exists for ConocoPhillips and formulated an empirical model. On the other hand, the oil price is not the only changing price and other goods and services should obviously affect share prices of oil companies. Thus one needs also some reference price, which best expresses the overall price evolution.

We are testing various pairs of different CPI components from a large number of pre-selected ones. The best fit pair has to minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and February 2014. For TE, we use 92 individual consumer price indices to select the best two (defining) CPIs (i.e. two-component model) in order to describe the evolution of the share price. Our two-component model also includes a free term (constant), which compensates the difference in initial values of the defining CPIs, and a linear time term, which compensates well know linear (time) trends between various CPI components. We allow the modeled share price to lead and lag behind one or both defining CPIs. When the price is lagged, the model is deterministic one and foresees at the horizon of the smallest lag. When the price leads both CPIs, one cannot predict the future of the price but get some information on the future CPIs.

In November 2012, both defining CPIs were contemporary to the share price and the best-fit model was as follows:

TE(t)= -1.43R(t-0) + 0.05E(t-0) + 1.49(t-2000) + 150.92, October 2012 (1)

where R(t) in the index recreation at time t, E is the index of energy also contemporary to the price, (t-2000) is the elapsed time. In February 2014, the model was practically identical:

TE(t)= -1.31(t-0) + 0.047E(t-0) + 1.35 (t-2000) + 137.81, February 2014 (2)

Moreover, the same model is defining for each month between December 2011 and February 2014: the model is valid 27 months in a row.

Figure 1 depicts the evolution of both CPIs. The index of recreation evolves slowly and the energy index has been actually driving the TE price since 2003. Figure 2 depicts the observed and predicted (monthly closing) prices together with the monthly high/low prices, which are natural limits of the intermonth price uncertainty. Our model correctly predicted the price since 2003. The model residual error is shown in Figure 3. It has standard deviation of $0.78 for the period between July 2003 and February 2014.

The energy coefficient in (2) is small but one can see that the evolution of TE is almost fully related to this price index. Our model of oil price evolution implies a significant fall by 2016. This may induce a fall in energy prices in the long run and the TE price will be on a down ward trend as well. On this long term trend, there should be periods of high fluctuations associated with elevated market volatility. When the actual price is far below the predicted price (October 2011), one may consider a profitable (in the short run) share purchase. When the actual price is far above the predicted price (e.g. April 2013), it is the best time to sell. Currently, the predicted and observed prices are almost equal. No action is needed.