Here is the problem : we should adopt the point of view of an industrial company which purchases electricity as an input in its production line and which wants to achieve the following two goals : -minimize the variance of its total purchase price on a weekly/monthly/yearly basis depending on the delivery period of the futures used -minimize its purchase price and beats the yearly average spot price

The specific features of the electricity market to take into account are the fact that electricity is a non-storable good which leads to some jumps in the spot prices which are then more volatile than futures prices. Moreover, futures contracts are designed with delivery periods on specific lengthes of time : month, quarter or year depending on the contract. For instance, you fix a certain price today for receiving a fixed volume of electricity everyday for the next month/quarter/year.

Finally, we have two constraints to take into account : -the industrial company wants to buy at list 25% of its electricity on the spot market to manage its volume risk -the company can only be long : we cannot sell electricity on the spot or futures market.

My first idea was to compute the minimum variance portfolio weights to allocate to spot, futures with montly delivery, quarterly delivery and yearly delivery. Though the problem comes from the fact that modern portfolio theory applies to assets' returns assuming that we can either be Long/short an asset whereas here we are only interested in prices since the company can only be long.

Thanks for your help should you have any insight or references.


  • $\begingroup$ I don't think I understand exactly what you're asking. Hypothetically speaking, a natural way to set this problem up is an assumption that the company is implicitly short (by some estimate of their future consumption) the forward curve and is purchasing 100% of their power in the spot market (which according to no-arb converges to spot price as contract goes to delivery). $\endgroup$ Jun 16, 2014 at 20:28
  • $\begingroup$ The last statement about futures prices'convergence towards spot prices is not true I think as first the cash&carry strategy can not be implemented regarding electricity as it is not storable and then electricity is not fully delivered at the maturity date but on a given period (month/quarter/year) from the maturity date on. Actually after some research the two main questions to be solved are : what is the most relevant portofolio risk metrics ? If we should buy a given quantity of electricity forward what quantity and when ? With still the same goals mentioned above : minimize price & risk. $\endgroup$
    – Vincent
    Jun 16, 2014 at 21:01

1 Answer 1


Only certain aspects of the risks that you bear in power markets given exposure to variable quantity swaps can be hedged. To your point, you have to have some expectation of what the load will look like. Even if you immediately go out and buy power against this expected qty you are subject to the risk that the load will deviate from said qty. There is no product except for 'load-following' fixed price contracts sold by power retailers (who charge extremely high margins) that offer protection against this risk.

There is plenty of literature out there on load forecasting models -- no need to overengineer this. Typically simulation of temperatures (via OU process) can be married to a linear/nonlinear historical regression of the load in question to produce some long-term estimate of the load. You should try to capture behavior at an hourly level to best estimate the shape of the load.

As for when to hedge, a model of the forward market price distribution will be your best guide to timing the market. Without going into specific details, this presentation by the guys at Hess's power marketing arm is very good:


  • $\begingroup$ Thanks very much for your answer. Though the volume risk is not the primary issue I think as the industrial company wants to buy at least 25% in the spot market I guess to manage it. Then it is more about the timing as you say and assessing the optimal proportion to buy forward. Do you think then that we should use historical data to empirically determine forward prices distribution and use the VaR as a risk metric rather than variance ? $\endgroup$
    – Vincent
    Jun 17, 2014 at 7:55
  • $\begingroup$ You may not consider it to be the primary risk but your exposure will absolutely depend on your ability to minimize the error in your forecast. I do think that \$ @ risk is better because you can then unitize this and potentially compare against the prices of load-following products that electric retailers offer. $\endgroup$ Jun 17, 2014 at 12:53

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