Hedging Strategy and Electricity Contract Engineering - IFOR

3.4 Traditional risk management models 53
The liquidation time can be substantial for some OTC contracts and very long
for power plants. We will later show that plants actually can be seen as contracts
4 and will have to be incorporated in the portfolio to determine the risk.
The time to liquidate, for example, a nuclear plant, i. e. to sell the whole plant is
difficult to estimate, but it will certainly be months or even years. The price risk
in a plant could be substantially lowered through entering similar but inverse
contracts in the market. Still, a significant open position would remain. A utility
having a portfolio of plants, OTC contracts and standardized contract would
face a difficult problem of choosing a common time horizon. In the traditional
financial markets it is not seldom that different time horizon are chosen for FX,
FI and equity positions. Though in the case of a utility such a differentiation
would heavily penalize the plants with their tremendous liquidation times. It
is questionable if this would give a reasonable risk assessment of the different
positions. Either one would have to assign a very long time horizon to the
illiquid positions, such as the plants or one would have to relax the connection
between liquidation time and time horizon. We have in this thesis chosen to
relax this connection and will work with a common time horizon over all positions.
We are aware that the liquidity risk component will not be captured by
this approach, but it is out of the scope of this work to further exploit liquidity
risk, and we note that it is an area for further research.
3.4.1.2. Variance
Modern forms of risk quantification find their origins in the article by
Markowitz [Mar52], where he published his work on the mean-variance portfolio
problem. The portfolio variance is minimized subject to a constraint on
the expected return
min
x
x T V x
s.t. x T R R p ,
(3.1)
where n` V n is the covariance matrix R n is a vector of mean returns
and x
n is the weight in each position. One can note that V per definition
as a covariance matrix is symmetric and positive definite. Hence x T V x is strict
convex. The linear constraint x T R R p defines a convex set and the problem
4 See Chapter 4.