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.