**Andy Dunn**advises energy companies on risk management, pricing and portfolio optimization issues.

Price forecasting is a significant business process within any energy merchant that trades electricity and natural gas. Business planning, trading, mergers and acquisitions (M&A), even rate-case activities rely upon some type of a price forecast as the foundation to analysis.

The problem with a single forecast is that it never is correct. As soon as the forecast is complete, the world changes and the information becomes dated and often even irrelevant.

This article reviews two common approaches used to forecast prices and introduces the concept of “three-dimensional price forecasting.” Incorporating these other dimensions changes the environment in a structural way.

#### Econometric vs. Fundamental Forecasting Methods

Energy-price forecasting employs two families of analysis. One is grounded in market based econometrics; the other relies on supply-and-demand fundamentals. Each method requires a deep set of experience and knowledge in very different areas.

Proponents of the two methods reveal an interesting lack of overlap. Analysts with a trading background tend to favor the insights derived from analyzing price data, and they migrate toward the econometric method. Those with an operational background like the idea of measuring the intersection between supply and demand, and they predict prices based on marginal costs. This approach is intuitive and maps to how utilities think about their business.

The econometric method presumes that historic sets of market prices describe some structural behavior that will be repeatable in the future. Analysts focus on statistical attributes of prices. Geometric Brownian Motion, mean reversion, and seasonality are intermixed with tools and methods that include regime switching, ARIMA, co-integration, GARCH, and principal component analysis. Sophisticated and rigorous statistical analysis leads to a better view of the future—or so they would like you to believe.

The fundamental forecasting method attempts to use a number of observable supply-and-demand factors to predict the expected price of electricity over both short- and long-term time periods. Factors include:

• Current generation units within a specific region stack from the lowest to highest marginal costs. These costs are driven primarily by a fuel cost, but they also include operating costs, start-up costs, and operational constraints;

• Generation outages;

• Transmission congestion;

• Customer demand estimated seasonally across the year; and

• Plant additions and retirements.

Experienced forecast managers realize that both approaches fail to predict the future. Markets are simply too dynamic. If the manager is operationally rigorous, he or she should create a quantitative function that includes two equally weighted analyst groups that use these methods competitively. Then the manager can let his or her analysts duke it out for supremacy. Competition is the best way to bring out innovation and creative thought.

#### Volatility and Correlation

All of the hard work described above simply gives you the “expectation”— the first dimension of the three-dimensional price process. But it is incomplete and inadequate if you fail to add the other two dimensions of “uncertainty” and “interrelationship” into the analysis. Statisticians refer to these attributes as volatility and correlation. These are the second and third dimensions of the price-forecasting process.

Analysts must feel free to rely upon fundamentalists or econometricians to generate the expected forecast as always. But beyond that, they should demand a reflection of uncertainty around that number. In addition, there is no market more interrelated than the natural-gas and power markets. Therefore, correlation is equally important. In fact, most gas trading activity is quoted and transacted in a “basis” context rather than “flat price.” This means that one must fully understand the relationship between whatever location he or she are trading in and the flat price location (Henry Hub in many cases). Similarly, in power, we often have liquid traded regional locations and many less liquid, nodal locations where differentials to that liquid market are the only trades available.

Three-dimensional pricing incorporates explicit point forecasts with measures of uncertainty and correlation.

Consider an example. Path-dependent Monte Carlo simulations can incorporate the expected forecasts for each market and build a distribution around them that reflects each market’s volatility and the correlation between each market. Imagine creating a thousand unique price paths for all of the markets relevant to your business. What does this look like?

Suppose forecasting groups apply their fundamental and econometric methods to come up with a consensus six-month forecast of PJM on peak prices. Table 1 summarizes this forecast at the monthly level.

A number of analytic methods are available to generate distributions around this forecast at an hourly, daily, or monthly level. These distributions describe the level of uncertainty the organization has on its forecast. Table 2 illustrates the set of data that would be generated using a path-dependent Monte Carlo price simulator that generates 1,000 price paths of PJM on-peak prices beginning Jan. 1 and moving through June 30, 2007.

One can see that on any day, across the 1,000 iterations, the simulated price varies. Some prices are much higher than the forecast while others are much lower. This information can be summarized and the distribution described simply as a range of prices given some probability. Table 3 summarizes the distribution of prices for May 2007.

By incorporating this uncertainty around the forecast, the analyst now can wrap a range of values around the forecast. Instead of simply indicating that the PJM on-peak spot price is expected to be $61.76/MWh, the analyst also can indicate that he or she is 95 percent certain that the actual number will be above $40.91/MWh. The analyst also can indicate that he or she is 95 percent certain that the actual price will be below $90.30/MWh. This range of value is invaluable for trade pricing, risk measurement, and portfolio optimization.

However, we have not yet identified the third dimension. Correlation between market factors is as important as volatility when dealing with issues that are dependent on more than one market factor.

Suppose the organization wishes to value a 6-month natural-gas-fired tolling contract in PJM. This contract is priced on PJM on- and off-peak prices plus natural-gas prices at Henry Hub. The extent to which these three market factors move together has a significant impact on the overall value of such a contract. If correlation is low, the spread will increase and decrease more than if the markets were highly correlated and this would elevate the value of the contract. Therefore, three-dimensional price forecasting must incorporate the level of correlation among all relevant markets. Instead of examining the distribution of a single market factor, all three markets must be examined simultaneously, as in Table 4.

Basically, it is a three-dimensional price cube. The dimensions: 1) tenor of future time; 2) number of markets; and 3) number of scenarios.

Imagine if you had this information. Not only would you be able to see what your “forecasters” thought about prices over the next year, but you also would be able to apply a distribution around this forecast *and* examine the simultaneous set of prices from other markets.

Why is this a benefit?

Of course, energy merchant have assets, load commitments, and trades in many locations across the regions they serve. Therefore, this set of three prices becomes a much larger set of market factors. Table 5 illustrates the three-dimensional data cube concepts for a multi-regional utility. In this case, powers and fuels must be simulated simultaneously for a large number of regions.

Now that this concept is defined, the data cube concept can be generalized to describe any number of markets, any number of simulations across any time period. The problem is now one of size rather than complexity.

The three-dimensional data cube incorporates expectation, uncertainty, and the interrelationships between markets that enables the analyst to run a wide range of extended analysis in the areas of valuations, risk measurement and portfolio optimization.

• Traders would be able to assess whether or not their view of the market “tradeably” differs from the current, executable forward markets.

• Business-development managers would be able to measure the extrinsic option value embedded in the contracts they were bidding on.

• Asset managers would be able to value and measure the risk on their generation assets and tolling contracts as well as pipelines and transportation contracts.

• With the addition of optimization tools, analysts would be able to value gas storage.

• Senior executives would be able to look across their entire business and understand both the expected value and the corresponding risk of each component, as well as the entire risk-return profile of the entire portfolio.

Every firm with these types of exposures should develop some form of three-dimensional pricing to augment the existing point forecasts. Only with this information can a firm fully understand the risk and opportunities embedded in its business.