Case study on hedging wind farm operating revenues, from an external contributor, **Jens Juergens**.

## Comparison of fixed-price PPA with an OTC hedging strategy

What do you think of a power price hedging product, which not only limits your downside, but also let's you freely profit from each upside market movement? Additionally, you only must pay a premium once in a year and then get regular compensation payments for lower power prices. Sounds like the swiss-army knife of power markets and possibly like an alternative to standard fixed price PPAs, doesn't it?

In this post, we will compare two hedging strategies. First one involves only fixed price PPAs, second one only works with OTC products. After reading this post, we should have a more educated opinion, which one of the hedging approaches is more effective and efficient in an economical sense. We will take a usual wind production profile 50Hertz and DK2 prices from Nordpool for our case study.

## The PPA hedging strategy (Strategy I)

We check available PPA prices for 2020. We do not just buy a PPA for one year, because we want to have more flexibility. As a rule of thumb, let's say our quarterly PPA prices are 10%-15% below market prices of respective futures. The futures prices are built by adding the DK2 area price differential future on the NASDAQ system price future by matching the delivery period and expiry.

Comparison of discrete DK2 forward curve and quarterly PPA offers

The 10%-15% discount on the market price represents the compensation the PPA off-taker gets for the benefit of giving us a fixed price. He is charging his own margin, costs, our credit risk etc. into this fixed price, hence it must always be lower, than the respective futures market price at trade date. In addition, if at trade date in 2019 we take a PPA for the far-out fourth quarter in 2020, the PPA off-taker will surely charge us with a term premium. In other words, hedges, which will start far in the future are more expensive, than hedges close to the trading date.

It is common sense, that wind production in Winter is at its highest levels as well as observed prices. Concerning our PPA hedging strategy, we do not want to give away so much of the upside by fully hedging our production in Winter. We buy Q1 PPA with conditions in the plot above, but only with a hedge ratio of 50%. Contrary, in the summertime when production and demand are lower also power prices slide. Consequently, it is a good idea to extend the hedge ratio for Q2 2020 and Q3 2020 to 75% in order to safeguard the wind farm against severe losses.

When Autumn 2020 approaches, we reduce the hedge ratio again to 50%, hoping that revenues rise with upcoming Winter in 2021. With this painless gut strategy, we hopefully will be aggressive enough not to give away all the upside potential, the market is offering us. At the same time the strategy should be prudent enough to protect us against losses.

## The Asian put hedging strategy (Strategy II)

So far so good with the PPA strategy. We now call a trading desk to offer us an appropriate OTC product. Straightforward choice is a cash-settled Asian put option on the respective spot price with a periodic lookback. That means we pay a premium upfront and have a periodic settlement until expiry of the deal. At the end of each period we compare the daily average of the power price in this period with our pre-defined strike level. If we are in the money, we get a cash compensation from the Asian payoff for power prices, which a lower than the strike.

For this exercise, we choose the strike level of the average PPA prices of strategy I, so that both strategies approximately start on the same grounds. Our Monte-Carlo model (see next chapter) gives us a fair premium of 120,000 DKK/month for hedging 100% of our monthly production. Strike of the option is 279.34 DKK/MWh, effective date will be 1.1.2020 and expiry on 31.12.2020. As we monitor the cashflows of the wind farm on a monthly basis, we choose a monthly period for the Asian put option.

## How do we model wind farm operating revenues?

We will use a well-established Monte-Carlo simulation of the power price model and wind production model. We assume that both are not correlated, which is a simplifying one. Loosely speaking the more power is produced with demand staying at same levels, the higher the negative impact of this oversupply on the price would be. So, usually we observe a negative correlation between production and prices, but that is another story.

Daily risk-free simulation of DK2 power prices with 100.000 samples. Forward market-adjusted seasonality is in black. Confidence interval between 90% and 10% are shaped in orange. The grey line represents actual futures data as in the first plot.

The power price simulation is carried out with a risk-free measure, meaning that it not only represents features observed in historical prices like seasonality, mean reversion and volatility, but also matches prices seen in the available forward market. Technically speaking, the historical calibrated power price parameters are adjusted, so that they incorporate market price of risk seen in forward market prices. This market price of risk is established by the different hedging behaviour of power price consumers on the short end and power producers on the long end.

Consumers are hedging against spikes in power prices, which would add further cost on their liability side. For the sake of limiting the impact of spiking prices on the cost side, this party is willing to add a risk premium on the spot price. Hence, short end futures are usually above spot price levels. Vice versa producers are hedging against long-term sliding markets, which could badly impact their revenues.

Hence, they are willing to take a discount on the spot price in order to get their revenues hedged. That is why the long end of our forward curve is below current spot level, which of course also applies to our fixed price PPAs.

First purpose of our model will be to calculate the fair premium for our Asian put with the power price Monte-Carlo framework. Hence, we use the risk-free world so that neither seller, nor buyer should have a competitive advantage at trade date and we consequently arrive at a fair premium for the derivative. As the payoff is also path-dependent, we need such a complex framework in order to correctly evaluate the Asian payoff.

Secondly, we want to discover how strategy I and strategy II perform under really a lot of different future scenarios, which are bound by volatility and seasonality we observe in spot and forward markets.

## Hedging evaluation: Which strategy is more economical?

Stating the question is easy, the answer highly depends on the PPA hedge ratios of strategy I and the strike for the Asian put. Clearly far out of the money will be cheaper for wind farm, but the protection will only be activated on substantial downward slides in the market. On the other hand, the put must not to be too expensive, otherwise the premium to be paid will have substantial negative impact on our monthly cashflows. Latter surely not only depends on strike, but also on the implied volatilities given at trading date. So, timing of the trade is crucial as well.

If we take the PPAs as described in strategy I and price level of Asian Put as outlined in strategy II, we arrive at the following forward revenue profile in 2020:

Probability densities of revenues minus hedging costs per month for hedging strategy I and hedging strategy II.

### How do we interpret the simulation?

Do not get confused, the plot above is not an album cover from Joy Division. The picture was created by simulating production as well as power price with 100.000 sample paths and calculating revenues on them. For strategy I monthly revenues are generated by respecting given quarterly PPA prices as well as the hedge ratio. Production, which is not hedged, is sold in the market. One clearly observes that the monthly revenues of strategy I are quite comparable for each separate quarter.

Strategy II was evaluated on the same samples by respecting the Asian option payoff at the end of each month. Apart from the payoff, full production is sold on the market. If the power markets slide, the put is in the money and should compensate for lower market sales, stabilising the monthly cashflows in strategy II.

With the data depicted above, we could compare different statistical measures e.g. monthly profit at risk, but let's keep it vivid and examine only mode and variance of monthly revenue probability densities per month. Modes are represented by the red and blue lines in the plot above, variance can be perceived by the wideness/narrowness of the monthly density plots. The mode can be interpreted as the most probable monthly revenue, the variance should tell us about the variability of wind farm revenues per month.

### Which strategy is better?

Purely optical, Strategy I has more narrow densities than strategy II. This makes perfect sense, as strategy I locks in a price per quarter and should therefore concentrate the revenues around the fixed Price of the PPA. In other words, the PPA limits upside as well as downside of the revenue and really stabilises the cashflow. The intensity of this limitation is steered by the hedge ratio, which we adjust every quarter.

On the contrast, densities of strategy II are more skewed to the right and occur a bit wider. Loosely speaking, the Asian put gives us more upside potential, than a PPA. Both limit the downside, but the Asian put bears a bit more risk. Remember that in strategy II all is sold to power market and the put only pays off on the average price. With strategy I a fixed portion of production is sold at a fixed price, which certainly limits the downside risk in a stronger way than strategy II.

Simply said, from spring to summer the PPA strategy not only outperforms the put strategy, but also limits the downside risk. From a risk-reward perspective strategy I, is attractive for these seasons. In winter 2020 the put strategy is more alluring, than a PPA. In Winter 2020 also variance is higher than strategy I, but revenues are more skewed to the upside.

When looking at autumn 2020 the hedge ratio for the quarterly PPA is too high, limiting also our upside potential. In addition, we must pay a term premium on the PPA, giving us not the best price for this period. Hence also in Autumn 2020 strategy II is setting the stage and promises better revenues. Not to forget, that it bears more risk, which is identified in a higher variance.

If we mindlessly take the average revenue over each month, we get a bit higher revenue with strategy I, than with strategy II. On the other hand, good timing of the deal and optimisation of the strike level would certainly give both strategies a real tournament. Given the analysis here there is nothing wrong with trying both strategies under real market conditions. As it is often the case: The final proof of the pudding is in the eating.

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