Assume DisCo, a power distribution company, has full service requirement contracts with customer(s). The customer is paying fixed-price (tariff) T per MWh, and the customer's weather-sensitive power demand L is approximately linear in temperature (or rather degree days, eg, Diaz and Quayle ), t:
Figures 7 and 8 show the probability density distribution for weather-contingent change in DisCo revenue under the five hedging scenarios. Figure 7 corresponds to an ideal case when hedging can be done for free, while the simulation presented in figure 8 was made with more realistic assumptions re the transaction costs (see the above).
Both figures 7 and 8 demonstrate that the more comprehensive the hedging strategy is, the tighter the probability density function (PDF) - that is, the smaller the uncertainty about the outcome.
However, the important difference is that while in figure 7 the mean of the distribution (or its mode, which is easier to track) remains the same, the introduction of hedging costs in figure 8 pushes it to the left, into the loss area. Therefore, the burden of hedging costs has two effects: (i) it increases the expected (average) weather-related loss, and (ii) dampens the tail risk reduction. Trade-off between the tail risk (VAR) reduction and the cost of hedging determines the optimal strategy under the current market conditions.
VAR reduction is further illustrated in figures 9 and 10 presenting the cumulative density function (CDF), for change in revenue due to weather under the same hedging scenarios.
Each curve in figures 9 and 10 plots the exposure (VAR) versus percentile (confidence level) in the range from 80% to 99.9% for each of the five hedging scenarios. The difference between VAR for each hedging strategy and VAR for 'do nothing' case gives the scenario's hedge efficiency (risk reduction) at each percentile. Table A tabulates VAR reduction at selected percentiles, and lists average hedging costs associated with each strategy.
Table A shows that while applying all hedges is the best strategy as long as hedging can be done for free, under the more realistic assumptions the combination of static position in weather swap and dynamic power hedging performs the best.
|A. VAR reduction at selected percentiles and cost of hedging|
|Zero spread||30 CDD weather / 2% power spread|
|Weather only||Power only||Wthr & power||All hedges||Weather only||Power only||Wthr & power||All hedges|
We proposed a simple and efficient strategy that can help companies - whose portfolios include full service requirement-type contracts for the delivery of energy commodities, the demand for which is temperature-sensitive (power, natural gas and heating oil) - hedge their weather-related risk. Since this strategy employs only standard instruments in weather and power, hedging, costs can be kept to a minimum compared with hedging with quanto tools. We showed how a simple stochastic model that simulates spot temperatures and prices along with temperature forecasts and price forward curves can be used to select the optimal hedging strategy depending on market particulars such as bid-ask spread.
The suggested strategy can also be employed by entities offering quanto swaps indexed on temperature and energy commodity price to hedge their exposure resulting from selling such instruments.
Victor Dvortsov is associate director in the quantitative risk control department at UBS Investment Bank ([email protected]). He would like to thank Dan Diebold, Bob Klein, Jim Ohnemus and the anonymous referee for their helpful comments and suggestions. The views expressed are those of the author and not necessarily those of UBS AG.
1 DisCo is a fictitious entity. All data pertaining to its business used throughout the paper is fabricated.
2 We chose power just to be specific. All the considerations, analyses and results presented in the paper are fully applicable to natural gas and heating oil
3 Sensitivity of customer's energy demand to temperature,, is a key parameter. Historical temperatures at most locations are readily available from the National Climatic Data Center (NCDC). Electric and gas utilities keep records of their customers' energy usage and therefore have no problem estimating (Alpha) for the existing customers. For the new customers, if historical records are not available, (Alpha) can be calculated based on technical specifications of customers' equipment.
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