The Effect of Widespread Use of Value-at-Risk on Liquidity and Prices in the Nordic Power Market

Transcription

1 The Effect of Widespread Use of Value-at-Risk on Liquidity and Prices in the Nordic Power Market Cathrine Pihl Næss Adviser, Nord Pool Spot AS Direct phone: Fax: Business Address: P.O Box 373, N-1326 Lysaker, Norway Abstract The use of Value-at-Risk (VaR) as a risk management standard is now widespread in power markets. However, VaR values increase in periods with higher prices and volatility, and can therefore explode and create unstable markets. Homogenisation among market players with respect to risk measures could help drive prices and volatilities up in previously unstable markets. Participants with similar risk models reach their limits simultaneously, have to exit positions, and exhibit herding behaviour. I investigate which impact widespread use of VaR can have on prices and market liquidity, and evaluate whether we would see the same results if all participants used another risk measure. I perform simulations of the interaction between market players with different objectives and strategies, and subsequently change their VaR approaches, positions and other assumptions, in order to reveal under which conditions the use of VaR can contribute to unstable markets situations. One factor that can lead to this, is whether the risk measure is symmetric or asymmetric (for example those based on skewed return distributions). Another important factor is the constellation of short and long hedgers and speculators, since hedgers usually are not constrained by VaR in the same way as speculators are. VaR and other risk measures differ from each other with respect to properties such as symmetry and potential overreaction to market moves. Many VaR approaches are directly related to both volatility and price level, and will therefore explode under a market correction and intensify an initial price increase. This is in contrast to variance, for instance, which captures a volatility change, but is not consistently higher for higher price levels. One could expect that the VaR restrictions become different for short and long speculators if they apply VaR methods such as a historical simulation approach, Monte Carlo, Liquidity-adjusted VaR or other VaR approaches based on skewed return distributions. When the return distribution is skewed, the VaR values of a short and a long speculator holding the same position will not be the same, and consequently, market pricing could become dominated by one of these groups. Closing of positions on only one side can drive prices dramatically in one direction, where one price change leads to further closing of positions. In an extreme case the result is an unstable market where liquidity has vanished. The other important factor is the constellation of short and long speculators. The difference between the sizes of the positions of the two groups depends on the relative positions of short and long hedgers. I show that if the majority of speculators in the market is positioned one way (either short or long) this will amplify an initial price movement as VaR limits for large group of speculators are met. The price moves, volatility is forced further up, and market liquidity vanishes. 1 Introduction The introduction of Value at Risk (VaR), a methodology presented by the risk management group at J.P. Morgan in 1994, represented the start of increasing focus on risk management in financial markets. The use of VaR as a risk management tool is now widespread, as it has become a risk management standard and is the benchmark risk measure of the Basel

2 Committee on Banking Supervision and other regulators in the European Union (Jorion, 2001). The concept of VaR has also reached the power markets, and VaR is now the main risk measure within the financial markets, at least by the larger participants. Smaller market players that can not afford to develop or handle their own VaR models, buy entire risk management systems, usually based on VaR, from specialized companies (Participant information, 2003/2004). One of the dangers of the wide use of VaR is the homogenisation of risk-behaviour across market participants. Persaud (2002) presents the paradox that when investors use same portfolio optimisation and risk management systems they end up herding, and with that influence market properties. It is not clear if this herding is due to the fact that all speculators in the market use VaR, or if we would see the same results if they all used another risk measure. For instance, the risk measure variance will not be directly affected by the price level, since it is only a measure of volatility itself. VaR, on the other hand, is directly related to both volatility and price level, and will therefore increase more than the variance does after a price increase. VaR explodes under a market correction, and will therefore intensify big price moves (Erzegovesi, 2002). In a situation with increasing prices and volatility speculators with short positions collectively exit their positions due to VaR limits. Hence prices increase, volatility is forced further up and market liquidity vanishes. During the winter of the Nordic electricity market experienced extreme volatility, high spot and forward prices and low liquidity. One could ask if the large price moves and fall in volumes might have been influenced by market players wide use of VaR. Since the market consists of as well hedging as speculation portfolios, the group of speculators can in total be either net short or net long. In a situation where speculators are short, they are forced to exit positions as prices increased and VaR limits are hit, and prices are driven even higher. The purpose of this paper is to investigate what impact the wide use of VaR can have on prices and market liquidity. I will briefly describe the Nordic power market and present some theory on risk, risk measures and the theories about herding among participants. Is it a general homogenisation among market players or the widespread use of VaR, that leads to herding and overreactions to initial market moves? I will investigate this problem through a simulation of the interaction between market players with different objectives and strategies, and evaluate how the choice of risk measure can affect the market situation. 2 The Nordic Power Market The Nordic power exchange, Nord Pool, was the world s first multinational commodity exchange for electric power. It started as a Norwegian power exchange in 1993 and now covers all the Nordic countries, except Iceland. In 2002 Nord Pool ASA was licensed as an exchange and clearing house for power derivatives. Listed products at Nord Pool are options, futures and forwards, with the system spot price as underlying. The derivatives market is financial settled. The system spot price is set daily by Nord Pool Spot AS, a partly owned daughter company of Nord Pool ASA. The spot market has physical delivery. 2.1 Properties of electricity prices Electricity markets differ from both other commodity forward markets and pure financial markets. Because of the non-storability property of electricity no-arbitrage restrictions based on storage costs and convenience yield only can not be applied for valuing forward contracts (Lucia & Schwartz, 2000). Curves for spot prices, forward prices and option pricing for financial power contracts are more complicated to develop than in pure financial markets, mostly due to the special characteristics of the electricity spot price. The electricity price can be described by mean

3 reversion, jumps, spikes, stochastic volatility, and a deterministic component (due to intra-day, intra-week, seasonal patterns) (Lucia & Schwartz, 2000). The return distribution tends to be fat tailed (Clewlow & Strickland, 2000). Since hydropower is the main energy source in the Nord Pool area (46% in 2003 (Nordel, 2004)) the spot prices are highly dependent on weather conditions and the hydrological balance. This makes the spot price volatile. Even though the spot price shows mean reversion, prices on forward contracts can react significantly to changes in spot prices. The forward price reflects expected future spot price, adjusted for a significant risk premium. A producer commented in November 2003 (DN, 2003) that on a certain day the price for the 2004 winter 1 contract lay about 20 NOK (3 USD) above the fundamental price, due to this risk premium. This perception is supported by various empirical analyses (Mork 2004, Longstaff and Wang 2002) This risk premium is the source of speculation possibilities in the market, and can be seen as the price the hedgers are willing to pay for transferring risk to the speculators. 2.2 Participants in the financial market The forward market is used for both risk management and speculation purposes. Physical participants like power producers, power-intensive industry and retailers use the derivatives for hedging purposes as well as for speculation. As there is usually a risk premium paid by the hedgers, there are possibilities for speculators to earn money on buying risk from those who need to hedge. International hedge funds, banks and other financial speculators are among this speculation group. The focus in this paper lies on the speculators strategies. It is important to keep in mind that both hedgers and speculators trade in this market, and that participants in these two groups differ from each other in terms of position sizes, risk limits and strategies. The total net position among all exchange participants is of course zero, but the net position of speculation portfolios does not need to be zero. Since there are usually quite different strategies for hedging and speculation portfolios, this composition is essential for the market s reaction to any price changes. 2.3 Trading and hedging strategies Speculators would, to a larger extent than hedgers, change their positions due to changes in spot prices and close contracts. Hedging portfolios, on the other hand, do usually have a longer perspective, and do therefore tend to be more static. Continuous closing and entering of hedging positions would imply taking risk, while the objective of a hedging portfolio is to minimise risk. When speculators are net short, they will need to close positions when prices increase too much. Oppositely, speculators with long positions will hit their risk limits after a price decrease. This is what could have been one of the reasons for the extreme market situation we experienced during the winter of 2002/2003. Spot prices rose due to little rain and cold weather, long hedging positions increased as retailers and industrial users wanted to hedge their future demand, and prices of the financial contracts also rose to extremely high levels. One factor that could have contributed to this price explosion is that when high volatility made many financial traders hit their risk limits, short speculators where forced to close positions due to high prices, and prices were forced further up. Hedgers' net positions vary over the year, and for example in the spring flood producers go short in order to hedge their future production. 2.4 Market liquidity Pilipovic (1998) lists many aspects of energy markets that are quite different from money markets, among them that they are usually young and suffer from low liquidity and market activity. This is to a certain extent true for the Nordic power market as well, even though it is one of the oldest deregulated markets in the world.

4 After the extreme winter of 2002/2003, with high prices and volatility, participants complained about low market liquidity. Trading volumes went down, as illustrated by the graph of Figure 2-1, which shows Nord Pool s weekly financial market traded volumes (given in TWh), (Nord Pool, 2003). The graph shows that trading volumes have fluctuated over the years, but decreased significantly after However, trading activity has now increased, and turnover has reached the levels from before the extreme winter. Figure 2-1 Financial market turnover The risk exposure that a participant can have in the electricity market depends on more than prices and volatility, but in extreme market situations these factors can affect significantly the particpants positions sizes. Nord Pool s annual report of 2003 tells that participants tend to reduce trading volumes when prices and market volatility rise. Hence the market situation in 2003 with high prices and high volatility led to decline in trading volume. Liquidity of year contracts suffered most as participants switched from long term contracts to week-, monthand season contracts. 3 Risk Management and Value-at-Risk 3.1 Value-at-Risk Jorion (2001) defines risk as volatility of unexpected outcomes, and risk can also be understood as unpredictability. Participants in the financial power market are exposed to various types of risk. Value-at-Risk (VaR), presented by the risk management group at J.P. Morgan in 1994, is one of the most used measures for quantifying the price risk connected to holding a position. VaR summarises the worst loss over a target horizon with a given level of confidence (Jorion, 2001). For example, a one-day 95% VaR of means that, statistically, five out of hundred days the holder should expect a loss of or more. The confidence level, α, is usually set between 90 and 99%. The time period refers to the expected liquidation time for the position, and can vary from 1 day to 1 year.

5 Figure 3-1 Value-at-Risk The VaR-number for a position or a portfolio is found by constructing a probability distribution of returns, and then finding the return associated to the given confidence level. Hence the VaR number does not describe the worst loss that can actually occur, but is says that with a certain probability you will not experience a larger loss than the VaR number. It should be stressed that VaR is only valid under normal market situations. In extreme periods a stress test should be applied. VaR is usually given as relative, but can also be absolute. Absolute VaR is the loss (in currency units) relative to zero or without reference to expected value, while relative VaR is related to the expected return. 3.2 Methodologies There are innumerable methods that can be applied to calculate VaR for a portfolio, and choice of method depends on the composition of the portfolio, underlying assumptions on returns, and the degree of expertise within the areas of speculation and risk management. In general the methods can be divided into three groups; parametric, historical simulation and Monte Carlo simulation. Implementation, advantages and problems of these methods are briefly described in the next sections Parametric approach The parametric delta-var method, also called variance covariance, was popularised by J.P. Morgan s RiskMetrics and is simple to understand and implement. Change in portfolio value is calculated by multiplying possible changes in market variables by the deltas (representing the partial derivative of portfolio value with respect to underlying market variables.) However, it is not suitable for portfolios including options because it assumes that derivative values are linearly dependent on changes in market variables. The simple deltanormal approach assumes that market variable returns are normally distributed; hence it is a bad approximation for common portfolios in power markets. The strength of this method is that it is simple, in particular for calculating VaR for a single instrument (Clewlow & Strickland, 2000). Delta VaR for a single-instrument portfolio with standard normal distributed returns is straightforward calculated by the formula VaR = Value* σ * NSD * t = p * V * h* σ * NSD * t (3.1) Value is the current instrument value. For a power contract the value is calculated as current price (NOK/MWh) * contract size (MWh)

6 p is the current forward price (in NOK/MWh V is position size (in MW) h is number of hours in the delivery period of the contract σ is volatility NSD is the number of standard deviations corresponding to the wanted confidence level x t is the chosen time period (If σ is given as annual standard deviation, t is given as fraction of a year. If σ is given as daily standard deviation, t is given as number of days.) In this case VaR is given in NOK. As we see, VaR is positively dependent on both current price and volatility The delta-normal VaR is a symmetric risk measure in the sense that it will always be the same for the long holder of a forward contract as for the short holder assuming that position size and other assumptions behind the VaR calculation are equal. This VaR becomes symmetric because the normal distribution is not skewed. A method that considers both linear and nonlinear dependence of derivative value on underlying market variables, is the delta-gamma method, which also considers gamma; the sensibility of delta to changes in the underlying asset. This method can be applied on portfolios that include options, but is more complicated than the delta method. 3.3 Simulation approaches The historical simulation approach is based on historical data. Historical time series of market variables (like price and volatility) are used to obtain a joint distribution of hypothetical historical portfolio returns. VaR is then calculated at the chosen confidence level (Jorion, 2001). The underlying assumption of this approach is that the past is a good representation of what might happen in the future. This approach is called a simulation approach because what you actually do is to simulate what how well your portfolio would have done in the past. Since returns in the Nordic power market do not fit well to a normal distribution, but has shown skew, a historical simulation would usually give a quite different VaR number than a will a calculation based on the normal distribution function. Monte Carlo simulation is based on assuming return distributions for the relevant market variables. The simulation approach assumes a model for joint behaviour of these variables, and uses this to simulate possible portfolio values. It could assume a certain distribution function of returns, like for example the normal distribution, but it also allows for incorporation of price jumps, stochastic volatility and other price characteristics. Since returns on power contracts often exhibit kurtosis and skew, a simulation approach will usually be a better approximation to the development of market returns than the delta-var. Methods based on asymmetric return distributions parametric or simulation based give different VaR numbers for short and long position on a forward or future contract, and also different sensitivity of price change on VaR for short and long participants. Hence short and long speculators will probably react differently to a market move. 3.4 Properties of VaR as a risk measure Main advantages and disadvantages of VaR as a risk measure VaR might sound like an ideal risk measure. However, it has its disadvantages. First of all, it does not say anything about how large losses you can actually experience, as the distribution of outcomes that are worse than the VaR number are not taken into account. Two distributions with the same 99% VaR can actually differ considerably from each other if the 1% worst returns are differently distributed. Many approaches assume that returns follow a normal distribution function, which historically has not been a good representation of returns on power derivatives. Hence the historical approach could predict the risk better. However, the historical approach is usually

7 more demanding to calculate than the parametric methods. A simulation method would need to be applied when an asymmetric derivative as an option is included in a portfolio. The risk gets asymmetric, and more complex risk methods need to be applied VaR sensitivity with respect to composition of the portfolio For simple portfolios parametric VaR could be a good representation, while for more complex portfolios a more complex VaR method need to be implemented. Options are not linearly dependent on underlying (spot system price), and therefore give asymmetric VaR results VaR sensitivity with respect to choice of underlying return distribution Calculated risk for a given portfolio could change significantly when VaR methodology and assumptions are changed. One of the most important factors is the choice of distribution for the market variables. Delta-Normal VaR could measure a quite different risk for a position in a forward contract than would a calculation based on historical return distribution with skew and kurtosis. As mentioned, the VaR number for a short participant might be different from VaR for a long holder of the same forward contract if the underlying return distributions are skewed. While the delta-normal VaR would give equal risk for a short and a long participant, the historical VaR would show that the short and the long holder were subject to quite different risk numbers. Positive skew indicates that large positive returns are larger than large negative returns, as illustrated in Figure 3-2. Note that return is related to change in price, and negative return leads to profit for those who are short (S) and loss for those who are long (L). Positive skew should imply that actual VaR for S is higher than delta-normal VaR suggests, and VaR is overestimated for L. Similarly, negative skew leads to a higher VaR for L and lower VaR for S. An interesting implication is that when they possess equal positions of a derivative with positively skewed returns it is expected that VaR turns out to be higher for S than for L. A skewed return distribution involves that even in a market where net position of short and long speculators is zero, VaR can lead to a one-sided market. Probability 95% absolute VaR for Long 0 95% absolute VaR for Short Figure 3-2 Positive skew and VaR Return The choice of underlying return distribution also affects the change in VaR from one market situation to another. An initial upward price move could force short participants to close positions, while long participants would stay within their risk limits. The short participants need for buying could drive prices even higher, and trigger new upward price moves.

8 3.4.4 VaR sensitivity with respect to market moves It is easy to illustrate that VaR calculated by the delta-normal approach is equally dependent on changes in price and volatility. VaR for both short and long positions are positively correlated to both price and volatility, and VaR will therefore change more after an upward market move than after a price decrease. I compare maximum position of a contract that a participant can hold at two different market situations, assuming that VaR is calculated by the delta-normal approach and VaR limits are the same at time 1 and time 2. Maximum position can be expressed by VaR limit, confidence level (expressed by NSD), time horizon and daily standard deviation. The relationship between maximum positions in the two situations can be found by setting VaR limits for the two situations (see eq.3.1) equal to each other and solve for Max position 2 on Max position 1. Time horizon and confidence level are equal at time 1 and 2. VaR limit = VaR limit 1 2 Max position 1 NSD t σ1 price 1 = Max position 2 NSD t σ2 price2 Max position σ price = Max position σ price (3.2) We see that if volatility remains constant maximum position will decrease as the price increases. If volatility increases too, max position will be even lower. As an example, max position will decrease by 9,3% if price increases by 5% (ex. from 200 to 210 NOK/MWh) and daily volatility increases by 5% (from 2% to 2,1%). It is therefore not surprising that changes in price and/or volatility rapidly leads to less market liquidity as speculation volume is dragged down after a large market move. For many VaR approaches one assumes that volatilities on following days are correlated and consequently a price move in itself lead to new price moves. 3.5 Evaluation of VaR as risk measure Variance (estimated volatility of price returns), is another measure for risk - often used in connection to portfolio optimalization with respect to risk and return. It does not overreact to high price levels in the same manner as VaR does since VaR is positively dependent not only on variance, but also on price. However, it should be commented that since variance is the square of standard deviation, it increases significantly as standard deviation increases. As will be shown later, VaR has the property that it explodes under a market correction. However, it should be commented that risk in terms of money units (for example $) actually increases as the actual value of the contract goes up, and this is not considered when using variance as risk measure. So for a trader VaR might be a good indicator of risk, but the danger lies in the fact that when VaR is widely used the properties of VaR itself will affect the price development. There are different variants of VaR, among them Conditional VaR (C-VaR) and liquidityadjusted VaR (L-VaR). C-VaR takes into account the distribution of the returns in the tail, and is therefore also called tail VaR. It actually gives the expected value of a loss, give that the loss exceeds the VaR number. C-VaR handles portfolios with large numbers of scenarios and instruments (Pflug, 2000). C-VaR is also appropriate for the estimation of risk when return-loss distributions are non-symmetric. Minimisation of C-VaR leads to nearly same results as minimisation of VaR, but is much easier to handle. However, C-VaR will probably still react to market moves in the same way as standard VaR. L-VaR incorporates the risk for not being able to unload a position immediately at the current market price. Since liquidity usually goes down as prices and volatility increase, L-VaR can also lead to an overreaction to market moves.

9 A stress test is not a risk measure, but a method that is usually used as an addition to VaR or other risk strategies. It simulates a portfolio s performance under various extreme market conditions. However, the selection of scenarios is subjective, and it can be difficult to use the results since there are no probabilities related to these scenarios. So under extreme market conditions, when VaR is not a good risk measure, participants would probably act differently according to their perception of the situation and their stress test results. 4 Herding Result of Wide Use of VaR? Herding has been a discussed subject in various finance markets over the last years. Erzegovesi (2002) and Persaud (2002) support the hypothesis that homogenisation of risk models leads to even higher volatility and less liquidity in already unstable markets. Krapels (2000) explains how other factors, like hedging among producers and consumers, can lead to herding. 4.1 Modern practice of finance contributes to market instability Persaud (2002) presents the paradox that when investors use same portfolio optimalization and risk management systems they end up seeking the same markets, and in that way influence the properties of those markets. An underlying assumption of today s risk management systems, among them VaR, is that returns, volatility and correlations are exogenous factors. However, when a considerable group of investors use the same input variables and same risk management systems, they end up acting homogeneously. Hence returns, volatility and correlations in fact end up being endogenous factors. Assumptions behind their risk management are no longer valid, neither are the risk measures. A portfolio that everyone considered safe and a good investment can suddenly turn risky due to herding. 4.2 Positive and negative feedback traders In order to understand how VaR can contribute to a one-way market Erzegovesi (2002) separates market participants into two groups; negative feedback traders who sell when prices go up and buy when the price falls, and positive feedback traders who buy when prices rise and sell when the price falls. In a liquid market the negative feedback traders outweigh positive feedback traders, market price fluctuations are dampened, and liquidity does not dry up after a stressful shock. A collapse of market liquidity occurs when the market share of positive feedback traders increases enough to outweigh that of negative feedback traders, and market becomes one-sided and market liquidity vanishes. Dominance of positive feedback traders can be related to factors like stop-loss rules and dynamic hedging, but is also connected to properties of risk measures and return distribution for market returns. 4.3 Skewed returns and positive feedback traders An interesting observation related to VaR for positions with positively skewed returns is that VaR turns out to be higher for those who are short than for those who are long. VaR for the positive feedback traders (traders with short positions) is also more sensitive to price changes than VaR for negative feedback traders (long). VaR therefore gives larger incentives for short participants to close their positions (buy) when price goes up than for long participants to close positions (sell) when price goes down. This means that even in a market where net position of short and long speculators is zero an increase in price would lead to a one-sided market dominated by positive feedback traders as short-holders hit their limits. When prices go down VaR does not go up unless volatility increases more than price decreases, and speculators will not hit any VaR limits.

10 4.4 VaR explodes under market correction If a substantial share of market participants adopts VaR models they will move in herds in response to shocks in the market. One could comment that a group of investors holding the same instruments is likely to have the same perception of risk and therefore would herd if risk increased, independently of risk management system. However, Erzegovesi (2002) points at the fact that VaR explodes under an upward market correction since it increases for higher prices, and will therefore intensify big price moves more than if the investors used risk measures that were not directly dependent on price. Investors with more or less similar portfolios hit their VaR limits together, unload their undesired positions at the same time, and liquidity goes down. The volatility of the certain market increases, which in turn feeds back into risk management systems and leads to further sales. Thus the cycle becomes self-feeding (Erzegovesi, 2002). Furthermore, a comment in The Economist (1999) claims that the more the VaR models are used, the more likely it is that markets will suffer the way that they did in It points at the fact that VaR models are profoundly affected by rises and falls in volatility. Less volatile markets mean a lower VaR. When volatility rises, VaR rises. It is suggested that it might be better to use a consistently higher, but stable, level of volatility in the risk models. 5 Modelling interaction between participants As we have seen, herding among market participants can have various reasons. I will now, by modelling the interaction between market players in the Nordic power market, investigate to what extent the wide use of VaR can affect prices and liquidity. I intent to reveal under what conditions the use of VaR can indeed contribute to unstable market situations. The main idea behind the market simulation is the following: o I assume a certain market situation (price level, volatility, participants positions, risk limit) o I model a change in market variables o Each speculator s risk exposure changes o Speculators need to trade if their risk limits are hit o Price changes due to the trade (for example increased buying-side drives prices up) o Risk exposure changes again o Speculators need to trade o Trade goes on until an equilibrium is obtained after a number of iterations o The new price level, volatility and open interest are compared to those at the start of the simulations o I do NOT consider any other strategies like stop loss, take profit or volume limits 5.1 The real market As explained earlier, the financial market is made up by market participants of different types (producers, industrial participant, retailers and speculators). According to what groups a participant belongs to he has a certain strategy on his portfolio mix (options/forwards/futures, position sizes, time to maturity etc.) and trading limits (stop loss, volume limit, VaR limit etc.). Many participants trade both in the physical and the financial market, and strategies within these two areas are closely related. 5.2 My market model o I model a market consisting of ten participants and one market maker. In the first simulations all participants are speculators, and I do not consider hedging positions (I assume that they are kept constant.) The market maker is obliged to quote prices with minimum volumes. o The traded product is the forward contract FWSO-05, which is settled against the system spot price during the summer season of 2005 (June-October). This delivery consists of

11 3672 hours, so the price per MWh should be multiplied by 3672 to obtain the real value of the contract. o Some participants are short the contract, while others are long. From simulation to simulation I change the initial volumes that each participant holds. o Various approaches of VaR are evaluated, and I will test for different input variables and assumptions. o Initial volatility and forward price are fictive, but based on market data observed during winter At the start time price is set at 250NOK/MWh and daily standard deviation at 2,65% (42% annual), o I start with modelling an initial price move, and let the speculator trade if he hits his VaR limit. I assume that hedgers do not change their positions. o The price changes on the forward contract are set by the market maker. He adjusts his bid and ask prices as the buying- and selling willingness in the market change. Participants then again adjust their position sizes in order to lie within their risk limits. Speculators continuously control their risk exposure and trade if VaR lies above the limit. o VaR is calculated by using certain approaches that are described for each simulation o Change in volatility is calculated by the EWMA-method (Equally Weighted Mean Average) and assuming normally distributed returns. o Open interest is used as indicator for market liquidity A simple example of how the simulation works follows: o Participant A is short 100MW of the contract, and participant B is long 70MW. Both positions are within the participants risk limits o I model an increase in price and volatility o Both participants need to close positions in order to stay below the VaR limits: A need to buy 6 MW while B sells 2 MW net demand is 4 MW o A has to buy those 4 MW from the market maker o Market maker quotes higher prices as a result of the changed demand situation o VaR for both participants increase, and they need to trade with MM o MM changes prices again Here I assume that traders are net short. This is the case when hedgers are net long, which in theory is when the demand side of electricity is more risk averse than are the producers, for example when prices are high and the market expects (or fears) high prices in the future. 5.3 Simulations: Assumptions and Results From simulation to simulation I change initial positions of the ten market participants so that net position of speculators is either short, long or zero. I will use VaR as risk measure calculated by the delta-normal approach and by the historical simulation approach Simulation 1: Net position zero. Initial price increase Assumptions I assume that price initially increases with 5 NOK/MWh from the day before. The market consists of ten speculators, where five are short and five are long. They apply exactly the same VaR approach: Delta-Normal-VaR with variables chosen as in Table 5-1: Table 5-1: Participant data simulation 1 Participant Confidence level Days Initial position (MW) VaR limit % 1-10 NOK % 1 10 NOK Net position 0 Open interest 50

12 Results All participants need to trade 1 MW in the first iteration, in order to get below their VaR limits. However, since the short and the long participants need to trade exactly the same volumes, market maker does not change his bid or ask prices. Volatility goes slightly down since the price stays at the same level. Each participant s trades, positions and calculated VaR before and after they perform the trade are shown in Table 5-2. Table 5-2: Participants trade, new positions and VaR numbers for each iteration simulation 1 Participant Iteration Trade New position VaR without trade VaR after trade NOK NOK NOK NOK Liquidity has gone slightly down after the trading round, and is now 45 MW Simulation 2: Domination of short speculators. Initial price increase Assumptions and choice of variables I now assume that speculators initially are net short. This could be true when hedgers as a group are long, which is usually the case in the Nordic power market. Hedgers are not considered (I assume that they hold their positions constant) Nine speculators are short 10MW each, and the last participant is long 10MW. In total their net position is -80MW short, and open interest is 90MW. Table 5-3: Participant data for simulation 2 Participant Confidence level Days Initial position (MW) VaR limit % 1-10 NOK % 1 10 NOK Net position -80 Open interest 90 As in simulation 1 the price initially increases from 245NOK/MWh to 250NOK/MWh Results All participants trade 1 MW in the first iteration. This leads to a trade with market maker of 8MW (one of the MWs that short participants need to buy is bought from the long participant), and the price is increased to 260 NOK/MWh. Volatility increases to some extent. In the new iteration the short participants reach their VaR limits again, and the same does the long speculator. Net there are traded 8 MWs, just as in the last iteration. Price increases to 270 NOK/MWh and standard deviation to 3,18 %. All participants trade in each of the following iterations until equilibrium is reached after nine iterations. At that moment price is at 345 NOK/MWh and standard deviation is 8,30 % - which is abnormally high. At this moment the first nine participants are short 2 MW each, and the long speculator possesses 2MW. So net position is 16 MW, and liquidity has diminished as open interest is down at 18 MW.

13 Table 5-4: Participants trade, new positions and VaR numbers for each iteration simulation 2 Participant Iteration Trade New position VaR without trade VaR after trade NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK Table 5-5: Trade and changes in market variables simulation 2 Iteration Net traded this iteration New price New stdev Open interest ,74 % ,18 % ,47 % ,11 % ,80 % ,22 % ,61 % ,30 % ,30 % 18 Table 5-6: Summary of market development simulation 2 Start End Position participants Position participants Open interest Price Forecasted daily standard deviation 2,65% 8,30% In this situation there are two aspects that should be commented. First of all, a daily standard deviation of 8,3 %, or annually 131%, is extremely high. In a market situation like this, with a daily price increase of 95 NOK, underlying assumptions for the standard deviation estimation would no longer be correct. In a market situation like this VaR is no longer a trustful risk measure, in the sense that VaR is only reliable under normal market conditions. Participants should start applying stress tests when they see a market behaviour like this. We would probably see some of the same result when stress tests were applied: positions are reduced

14 when price increases. However, these results illustrate well the dangers of a widespread use of this type of VaR Simulation 3: Domination of short speculators. Initial price decrease. Assumptions and choice of variables I now assume that price changes just as much as in previous cases, but the initial price change is downward.: from 245NOK/MWh to 240NOK/MWh. All other assumptions are the same as in simulation 2. Results The result is logical, but still a bit surprising. Price actually ends up at an extremely high level, just as when we initially had a price increase. This is of course due to the fact that participants in net are short, and they buy when VaR limits are hit even if VaR is increased because of higher volatility or higher price level. The downward change in price of 5NOK is not large enough to offset the increase in daily standard deviation. As price and standard deviation increases for each iteration open position goes dramatically down. In the end all participant holds 1 MW each, and open interest and net position at the end is the same as in simulation 2. Table 5-7: Participants trade, new positions and VaR numbers for each iteration simulation 3 Participant Iteration Trade New position VaR without trade VaR after trade NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK Table 5-8: Trade and changes in market variables simulation 3 Iteration Net traded this iteration New price New stdev Open interest ,23 % ,21 % ,67 % ,56 % ,25 % ,91 % ,91 % 9

15 It should be commented that in a situation like this, with an initial price increase that was quite large, there will possibly be many other trading strategies going in the opposite direction of what VaR limits force the portfolio holder to do Simulation 4: Historical VaR approach. Skewed return distribution. Domination of short speculators. Initial price increase Assumptions and choice of variables In this simulation I use exactly the same participant data as in the previous simulation. However, I now apply the historical VaR approach, based on historical returns for the summer contract in year Note that this data set might not be the most correct one to use when estimating risk attended with the FWSO-05 contract, but it is selected because it shows well what may happen when the return distribution is skewed.. Table 5-9: Participant data - simulation 4 Participant Initial position Limit Initial VaR NOK NOK NOK NOK NOK NOK Net -110 Open interest 140 Results Price is driven up, just as we saw when delta-var was applied. However, the increase stops at a price of 285 NOK and open interest is 103 MW. One probable explanation of why the price doesn t increase more is that, as mentioned earlier, the standard deviation does not affect the historical VaR number. Hence the price increase itself makes VaR go up, while with delta- VaR the increasing standard deviation contributed to driving VaR even further up. One conclusion from this observation is that historical VaR does not overreact to large market moves to the same extent as delta-var. Table 5-11: Participants trade, new positions and VaR numbers for each iteration simulation 4 Participant Iteration Trade New position VaR without trade VaR after trade NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK NOK

16 Table 5-10: Trade and changes in market variables simulation 4 Iteration Net traded this iteration New price Open interest Observations and implications from simulation results We have seen many interesting effects from using VaR as risk measure. I have revealed relationships between market reaction after a market move and choice of VaR method and underlying assumptions. Some of the most important conclusions are the following: o Constellation of short and long speculates is essential for the development after a relatively large change in the market situation o Underlying assumption of skewed return distributions may give quite different VaR numbers for short and long participants, and consequently make them act differently after an initial price change. o Employment of various VaR approaches can give very different risk signals. I will now present what impact the choice of and various assumptions has on prices and liquidity Conclusions that can be drawn and discussion about other relationships are discussed in the next sections Choice of confidence levels, time horizons, position sizes, limits As confidence level and time horizon of VaR differ between participants, their estimated VaR numbers of course differ too. They do also have different VaR limits depending on their risk/return strategy. This means that each single participant probably responds somewhat different to any market move Domination of short or long speculators After an initial price increase the domination of short speculators using delta-var leads to a significant increase in price and volatility, and open interest goes down. When long speculators dominate price goes down, but open interest still decreases. These results depend on the fact that participants have a relatively high VaR usage. An aspect that should not be forgotten is the fact that speculators would probably apply stress tests and not VaR in a situation like this. Still, there would probably be a large market move as positions are closed due to stress test limits. Sensitivity analysis of the result with respect to initial position sizes show that a large price move depends on a significant dominance of either short or long participants Zero net position for speculators We can actually see a net trade different from zero even when net position is zero, but this depends on VaR limits of participants and their position sizes. For example if there are many short participants with small positions and one long participant with a large position, an initial price increase would mean that all participants hit their limits, and in net need to buy from the market maker. If there are enough short participants this can drive market maker s price further up. In the opposite situation (many long and few short speculators) price would go down Reaction to initial price decrease We have shown that VaR can go up even after a price decrease. This occurs when relative change in standard deviation is larger than relative change in price. When initially price

17 decreases and there is a significant domination of short speculators we see that the price actually increases just the way we observed from an initial price increase (Table 5-12). With a market dominated by long speculators the price goes down, but not as much as after an initial price increase. This indicates that price change is more dependent on the net position of speculators than of the direction of the initial price change. Table 5-12 Changes in price and open interest with respect to initial price change and domination of short/long speculators Delta-VaR-method Initial price increase Initial price decrease Domination of short speculators Domination of long participants Price dramatically up Price dramatically down Price dramatically up Price down to a certain extent When historical VaR is applied an initial price decrease will never lead to a price increase since historical VaR always goes down when price decreases Historical VaR The application of 95% Historical VaR based on various return data sets show that when 95% highest return is larger than the 95% lowest return, short participants have a higher VaR and consequently a lower maximum position. Results from simulations with historical VaR depend on the return data set. When using set of more variable historical returns maximum position is higher, and this could lead to lower open interest. We see that applying historical VaR can lead to trade in situations where delta VaR lead to zero trade, for example when short and long participants have equal positions and limits. This means that in these situations use of delta-var can lead to a more stable market situation than applying historical VaR. However, historical VaR does not overreact to large price moves to the same extent as delta- VaR Skewed distributions When historical return distribution is skewed, calculated VaR will be different for short and long participants. This would also be the case if we assumed that return distribution of the delta-var or Monte Carlo VaR was skewed. Higher VaR means that maximum position with respect to the VaR limit is lower, and this could lead to dominance of short or long speculators. A dominance of either group could lead to a one-sided market. Skewed distribution could also mean that VaR changes more for one speculator group than the other. If VaR increases more for short than for long participants for a certain price increase this could lead to a one-sided market and an intensified price increase Return distributions with fatter tails When a speculator calculates VaR under assumption of return distribution with fatter tails, VaR turns out to be higher and max position is lower than when delta-normal VaR is applied. However, even if the risk is higher, the market reactions will be the same if participants have a consistently higher calculated risk Effects on market liquidity Open interest tends to go down as limits are reached. However, this should not be surprising since the only trading strategy that is employed involve a reduction of positions. Open interest can therefore not be used as a good quantification of the effects from use of VaR. However, we have recovered for what situations liquidity is likely to go down; the more conservative the risk measures are, the lower the liquidity will get. If participants integrate liquidity risk or choose other VaR approaches that give higher VaR, reported risk measure will be higher. The