Financial Time Series Analysis • • • • • • • • • • • •
Patrick McSharry firstname.lastname@example.org www.mcsharry.net Trinity Term 2010 Dartington House Seminar Room 1 Mathematical Institute University of Oxford
1. Data analysis, probability, correlations, visualisation techniques 2. Time series analysis, random walk, autoregression, moving average 3. Technical analysis, trend following, mean reversion 4. Nonlinear time series analysis 5. Nonlinear modelling, regime switching, neural networks 6. Parameter estimation, model selection, forecast evaluation 7. Volatility forecasting, GARCH, leverage effect 8. Risk analysis, value at risk, quantile regression 9. Energy consumption, demand forecasting 10. Ensemble prediction, wind power generation 11. Weather derivatives, index-based insurance 12. Quantitative trading strategies, algorithmic trading
Copyright © 2010 Patrick McSharry
• Historical weather observations • Future projections • Weather indices • Weather derivatives • Index-based insurance
British rainfall extremes
British Rainfall (Symons, G. J.,1885) lists all observed 24 hour rainfall depths which exceeded 2.5 inches (63.5mm). See Rodda et al. (2008)
Extreme rainfall trend
Source: Little et al. (2008)
Change in mean annual precipitation by the end of this century
Change in mean annual temperature by the end of this century
Weather risk • Fluctuations in the weather affect the revenues of many sectors (agriculture, energy, retail, transportation and construction) • Weather risk tends to influence demand rather than price and adjustments of the latter are rarely adequate to compensate for lost revenues • Insurance offers cover for low-probability extreme events but it does not provide compensation for the reduced demand that may result from slight variations in the weather such as the temperature being warmer or colder than expected.
Electricity load and temperature
Electricity and temperature • Electricity demand displays a non-linear U-shaped dependence on temperature • Demand increases both for decreasing and increasing temperatures
• Pardo et al. (2002) analysed the dependence of electricity load on a population weighted temperature index in Spain
Summer and winter regimes • The nonlinearity in the response function prompted a separation of the effect into summer and winter regimes • Typically 18oC (or 65 oF) is used as a threshold variable to switch between summer and winter regimes • Within each regime, the response is approximately linear which facilitates traditional linear time series analysis
• This results from the use of electric heating appliances in winter and air conditioners in summer • There is a minimum around 18oC where the demand is inelastic to temperature changes
Heating and cooling degree-days • Heating degree-day (HDD) and cooling degreeday (CDD) are indices designed to reflect the demand for energy needed to heat or cool:
• HDD measures the intensity and duration of cold in the winter • CDD measures the intensity and duration of heat in the summer
Weather and revenues
• Weather derivatives are financial instruments that can form a risk management strategy to mitigate risk associated with adverse or unexpected weather conditions
• By creating a weather index that can be linked to the revenues of a particular organisation, it is then possible to trade the weather in order to mitigate the risk of adverse weather conditions
• Unlike other derivatives the underlying asset (temperature, rainfall, wind, frost or snow) has no direct value
• Advantages of decreased earnings volatility are efficient use of equity, improving the company value to stakeholders and availability of lower debt costs and higher advance rates
• Weather derivatives, in contrast to insurance, provide protection against low-risk high-probability events by treating the weather as a tradable commodity, similar to a stock price or interest rate
• The Chicago Mercantile Exchange (CME) introduced exchange-traded weather derivatives in 1999 and now provides standardised contracts for 18 US, nine European, six Canadian and two Japanese cities
Derivative pricing • Approaches employed for pricing weather derivatives vary greatly, reflecting different assumptions made about the variability of future weather conditions over the duration of the contract • The disparity results from the availability of a range of atmospheric and statistical models • Further complications arise from the inclusion of the effect of El Niño in the model.
Energy utility case study • If an energy utility believes that November may be hotter than usual, possibly leading to reduced revenues, it could take out a HDD swap • Suppose the reference was 18oC and the actual average temperature on each day was 16oC, the utility would receive 60 (30 x 2) times the agreed sum of money for each degree-day • Alternatively if the average temperature on each day was 19oC, the utility would have to pay 30 (30 x 1) the agreed sum of money for each degree-day
Restaurant case study • In May 2002, Element Re announced a new weather derivative transaction with The Rock Garden, a London restaurant. • The contract was designed to protect the restaurant against financial loss from colderthan-normal weather from March 1-June 30. • The contract will pay out if the maximum daily temperature is less than a pre-agreed level for that month for more than a specified number of days (8.5oC in March; 11oC in April; 14.5oC in May; 18oC in June).
Weather Risk Management • A survey carried out for the Weather Risk Management Association by PricewaterhouseCoopers in 2006 concluded that: • The total value of trades in the 2005/6 survey reached $45.2 billion, compared to $9.7 billion in the 2004/5 survey • The CME experienced significant increases in both the number of trades (increasing by a factor of 4) and the value of those trades (increasing by a factor of 8) • HDD remains most common type of trade
Agriculture • Farmers are exposed to financial risk arising from the variability in crop yield that occurs due to different weather conditions. • Crop yield and price are weather-dependent. In the case of corn, both temperature and precipitation provide significant explanatory variables. • Drought in particular presents a substantial risk. Many farmers depend upon pre-financing against their future revenue streams for seed, fertilizer, and other agro chemical products.
Global warming index • In April 2007, UBS launched a Global Warming index (UBS-GWI) allowing businesses most affected by the uncertainty of climate change to hedge their profits against it in a simple and transparent fashion • The index is based on weather derivative contracts for winter and summer traded on the Chicago Mercantile Exchange (CME) • The index is currently based on 15 US cities, including New York, Chicago, Atlanta and Las Vegas • If you think Mr Gore is an alarmist sensationalist, you would sell the Index.
Appetite for weather derivatives
Index-based insurance (IBI)
• “I think it’s a perfect market. You can’t spook it, you can’t manipulate it. You can’t make people think it’s going to be 110 degrees in London next week,” he says. “And of course, weather is absolutely uncorrelated [to other asset classes].” - Peter Brewer, Cumulus Weather Fund
• IBI is an innovative means of managing weather risk by assessing risk in terms of expected loss of income by affected people whose livelihoods depend on agriculture/ farming that is highly susceptible to weather.
• No contract is too small. We’ve sold a weather derivative contract for a dollar” - David Friedberg, Weatherbill • Weatherbill’s clients include car wash companies, hair salons and golf courses. “The other day one farmer rang me up and said his sows wouldn’t make a move to mate if the temperature went above 95 degrees Fahrenheit. He wanted to hedge against that.”
• Traditional insurance products are based on an individual's circumstances and losses. • In developing countries or remote rural areas, traditional insurance services may not be available because of high administration costs. • IBI is a more appropriate as it is based on a fixed trigger mechanism not directly related to any individual farm. This could be calculated on average crop yields, area average livestock mortality rates, cumulative rainfall or even data from satellite imagery.
Source: FT, 20 June, 2007
Advantages of IBI
• Index-based insurance can be effectively delivered through a wide range of products.
• Where traditional insurance products aren't available (too costly or impractical)
• Government or international aid agencies can purchase famine insurance based on a weather index tied to the likelihood of droughts.
• Where moral hazard is high
• Individual producers can purchase insurance privately from insurance providers, local banks, NGOs or some partnership of these. • Insurance clauses can be folded into loan agreements whereby indexes triggered by adverse events relax the terms of the loan or pay it off.
How IBI works • Crop- and area-specific estimates are aggregated and mapped to income via price estimates, and then converted into a livelihood loss index. • If weather data gathered throughout the contract period indicates that rainfall was significantly below historic averages the insurer pays out. • No moral hazard, no complication of counting dead cows.
• A means of reducing risk exposure for vulnerable agricultural producers, giving them confidence to invest in inputs and strategies that will potentially give them higher returns in other years.
Livestock insurance in Mongolia • In Mongolia, livestock husbandry accounts for 87% of agricultural GDP and supports at least half the population. • The country is prone to extreme climatic events that can cause high rates of livestock mortality. • The insurance sector is immature and under capitalised. • Livestock insurance is a key element of risk mitigation but the conventional approach, based on individual herder losses, has been ineffective in Mongolian conditions. It has proved unpopular with both insurers and herders with a high cost of verification and moral hazard. • The government has now introduced an indexed mortality product which embraces risks exposure of the herders • Risks are covered by the private insurance sector in Mongolia • A disaster recovery program is to be provided by Government (maybe in years ahead by international reinsurers).
Drought protection in Ethiopia • In 2006 the Ethiopian Government, in partnership with the World food Program insured its farmers against rainfall failure. • In return for a premium of US$930,000, the insurance company would have paid out anything up to $7.1 million in the case of severe drought. • This money would have been given to the Ethiopian Government on the condition that it would be used for emergency relief and recovery. • This means that the World food Program can rely on the insurance money to pay for their relief work if there is a climatic emergency, rather than having to depend on donations, which can entail long delays.
IBI challenges • Lack of accurate climate models in developing countries • Limited availability of reliable and objective data. • Lack of weather stations in remote areas. • Models that make index-based insurance contracts attractive to both buyers and sellers.