We have presented quite a few pricing models for energy companies (ConocoPhillips, Exxon Mobil, Devon Energy, Chevron, and Chesapeake among many others) because of their clear relation to consumer and producer indices of energy. For different S&P 500 sectors, our pricing models often include indices not related at first glance. Here we present a new pricing model for a company from Utilities category – Northeast Utilities (NYSE: NU), a public utility holding company, which provides electric and natural gas energy delivery services to residential, commercial, and industrial customers in Connecticut, New Hampshire, and western Massachusetts. In part, NU is also linked to energy. But any company, small or big, has a link and is affected by energy prices. The opposite statement is likely wrong – not every company can affect the overall price of energy.

Before presenting the best fit deterministic pricing model for NU we would like to brief on the underlying pricing concept. Our approach consists in decomposition of a share price into a weighted sum of two consumer (or producer) price indices. One may test quantitatively our simple assumption that the growth in some specific CPI related to NU (e.g. housekeeping supplies, the BLS name is CUUR0000SEHN and we abbreviate it to HOS) relative to some independent but dynamic reference (e.g. food away from home, CUUS0000SEF or SEFV) should be seen in a higher pricing power for the studied company. In essence, our stock price model tries to find one defining CPI and the best reference.

In order to find the best pair of CPIs we calculate the RMS residual errors using all permutations from a set of 92 different (not seasonally adjusted) CPIs. In addition we allow for time lag (fixed between 0 and 12 months) between the studied price and both indices, and introduce a linear trend and intercept terms. The best model has the smallest RMS error between July 2003 and February 2012. The complete set includes the headline and core CPI, all major categories from food to other goods and services, and many minor subcategories with long enough history (i.e. continuous estimates should be available since 2001).

We have borrowed the time series of monthly closing prices of NU from Yahoo.com (March 2012 is included) and the CPI estimates through February 2012 are published by the BLS. (The CPI estimates for March 2012 will be reported by the BLS in the middle of April and we will revise all models accordingly). The best-fit model for

*NU(t)*is as follows:*NU(t) =*-2.57SEVF

*(t-6) + 0.97HOS(t-7) +*15.18

*(t-*2000

*) +*267.79, March 2012

where

*NU(t)*is the NU share price in U.S. dollars,*t*is calendar time. Figure 1 displays the evolution of both defining indices since 2002. The housekeeping supplies index has a positive influece on the price, i.e. the growth in HOS results in a higher NU price. Apparently, the negative slope of SEFV implies that higher food prices reduce the NU return. This is not against common sense.Figure 2 depicts the high and low monthly prices for a NU share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the limits of the share price uncertainty. The model residual error is shown in Figure 3 with the standard error between July 2003 and January 2012 of $1.23. All in all, the model is very accurate and all deviations are promptly annihilated, i.e. the measured curve returns to the predicted one, which leads by six months. One can foresee the share price behaviour six months ahead.

Considering Figures 2 and 3, one can conclude that the price should rise in the second quarter of 2012 to the level of $37 per share. Since the current level is also $37, one may expect no big change in Q2.

Figure 1. The evolution of defining indices.

Figure 2. Observed and predicted monthly closing prices for a NU share.

Figure 3. The model residual error: sterr=$1.23.

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