1. Alpine Investment and Development Summit 1 Harvey Stern Alpine Investment and Development Summit, Sydney, Australia, 19-21 Oct., 2005. CASE STUDY:WEATHER DERIVATIVES. WHY THEY ARE APPLICABLE TO YOU. Case Study: Evaluating the cost of protecting against global climate change: Options pricing theory and weather derivatives.

2. 2 THE NOAH RULE “Predicting rain doesn’t count; Building arks does”. Warren Buffett, Australian Financial Review,11 March 2002.

3. 3 FOUNDATION OF THE WEATHER MARKET “The foundation of today’s financial weather contracts is in the US power market … For the weather-sensitive end-user, not to hedge is to gamble on the weather.” Robert S. Dischell

4. 4 SHOULD COMPANIES WORRY? In the good years, companies make big profits. In the bad years, companies make losses. - Doesn’t it all balance out? - No. it doesn’t. Companies whose earnings fluctuate wildly receive unsympathetic hearings from banks and potential investors.

5. 5 IMPACT OF WEATHER "Shares in Harvey Norman fell almost 4 per cent yesterday as a cool summer and a warm start to winter cut into sales growth at the furniture and electrical retailer's outlets… Investors were expecting better and marked the shares down 3.8 per cent to a low of $3.55… Sales at Harvey Norman were hit on two fronts. Firstly, air conditioning sales were weak because of the cool summer, and a warmer than usual start to winter had dampened demand for heating appliances”. Source: The Australian of 18 April, 2002

6. 6 WEATHER RISK MANAGEMENT

7. 7 SECURITISATION The reinsurance industry experienced several catastrophic events during the late 1980s & early 1990s. The ensuing industry restructuring saw the creation of new risk- management tools. These tools included securitisation of insurance risks (including weather-related risks). Weather securitisation may be defined as the conversion of the abstract concept of weather risk into packages of securities. These may be sold as income-yielding structured products.

8. 8 WEATHER LINKED SECURITIES Weather-linked securities have prices which are linked to the historical weather in a region. They provide returns related to weather observed in the region subsequent to their purchase. They therefore may be used to help firms hedge against weather related risk. They also may be used to help speculators monetise their view of likely weather patterns.

9. 9 CATASTROPHE BONDS A catastrophe (cat) bond is an exchange of principal for periodic coupon payments wherein the payment of the coupon and/or the return of the principal of the bond is linked to the occurrence of a specified catastrophic event. The coupon is given to the investor upfront, who posts the notional amount of the bond in an account. If there is an event, investors may lose a portion of (or their entire) principal. If there is no event, investors preserve their principal and earn the coupon. Source: Canter & Cole at http://www.cnare.com.

10. 10 CATASTROPHE SWAPS A catastrophe (cat) swap is an alternative structure, but returns are still linked to the occurrence of an event. However, with swaps, there is no exchange of principal. The coupon is still given to the investor upfront, but the structure enables investors to invest the notional amount of the bond in a manner of his own choosing. Source: Canter & Cole at http://www.cnare.com

11. 11 WEATHER DERIVATIVES Weather derivatives are similar to conventional financial derivatives. The basic difference lies in the underlying variables that determine the pay-offs. In alpine regions, appropriate variables may include temperature, amount of snowfall, and number of clear days.

12. 12 DERIVATIVE OR INSURANCE? A Derivative: Has ongoing economic value; Is treated like any other commodity; Is accounted for daily (and may therefore affect a company’s credit rating); Is settled based entirely upon the value of the underlying (irrespective of loss). A Insurance Contract: Is not regarded as having ongoing economic value; Is not accounted for daily; Is settled based entirely upon establishment of loss.

13. 13 AN EXAMPLE OF A WEATHER DERIVATIVE

14. 14 A SEASONAL SNOWFALL WEATHER DERIVATIVE An example of a weather derivative for alpine interests is an “amount of seasonal snowfall” put option. Pay-off would occur should the accumulated seasonal snowfall be below some “critical” minimum total (referred to as the “strike”). If the accumulated seasonal snowfall fails to reach that “critical” minimum total, the seller pays the buyer a certain amount for each centimetre below that “strike”. Historical snowfall data would be used to calculate the “fair value” of such an contract.

15. 15 PRICING A WEATHER DERIVATIVE There are three approaches that may be applied to the pricing of derivatives. These are: Historical simulation (applying "burn analysis"); Direct modelling of the underlying variable’s distribution (assuming, for example, that the variable's distribution is normal); and, Indirect modelling of the underlying variable’s distribution (via a Monte Carlo technique).

16. 16 CASE STUDY: Evaluating the cost of protecting against global climate change: Options pricing theory and weather derivatives. In a 1992 paper presented to the 5th International Meeting on Statistical Climatology, the author introduced a methodology for calculating the cost of protecting against global warming. The paper described what was the first application of what later was to become known as 'weather derivatives'. It presented a methodology that used options pricing theory from the financial markets evaluate hedging and speculative instruments that may be applied to the impact of climate fluctuations on: (1) industrial output; and, (2) a manufacturer of ski equipment.

17. 17 BACKGROUND Since the early 1990s, the global mean temperature appears to have risen further. The methodology is 'revisited' with a view to recalculating the cost taking into account the additional, more recent, data.

18. 18 THE RISING GLOBAL TEMPERATURE

19. 19 PURPOSE Using a data set of land, air, and sea surface temperature anomalies (1861-2003), from the United Kingdom Meteorological Office: the purpose of the current work is to determine to what extent the cost of protection may have been rising [the data set is accessible at http://www.met-office.gov.uk/research/hadleycentre.html]. http://www.met-office.gov.uk/research/hadleycentre.html

20. 20 METHODOLOGY (1) Firstly, one regards the global mean temperature (GMT) in the same manner as one would a financial commodities futures contract and values it, and associated options, accordingly. On this basis the theoretical value of a GMT futures contract will equal the dollar equivalent of the current GMT (for example, the theoretical value of a GMT futures contract, when the GMT is 287.79K, would be $287.79). Secondly, one assumes that GMT futures contracts are available to be bought and sold.

21. 21 METHODOLOGY (2) One also assumes that associated put and call option contracts are available to be written or taken, and so alter the risk-return characteristics associated with the GMT contract. The strategy, therefore, is to establish the economic consequences of movements in the GMT. These economic consequences are then applied across the complete range of scales; that is, from the global economy down to the smallest company.

22. 22 CALCULATION Utilising the Black and Scholes (1973) call option formula, as modified for future style options (Gastineau, 1988) C = HS – B, where C = call option value H = N(d 1 ), where N( ) is the cumulative standard normal distribution function. S = price, X = strike, R = interest rate  = standard deviation of returns (volatility) T = time to expiry d 1 = ((ln(S/X)+(R+  2 /2)T)/(   T), d 2 = d 1 -   T, H = N(d 1 ) B = Xexp(-RT) N(d 2 )

23. 23 GASTINEAU’S MODIFICATION Gastineau (1998) proposes a "future style option" contract to replace many conventional options on futures contracts where: "unlike with conventional options, the buyer of the futures style option does not prepay the premium. Buyers and sellers post margin as in a futures contract, and the option premium is marked to the market daily. Valuation differs from conventional options primarily in the analysis of cash flows associated with the buyer's premium non-payment". For this reason one employs the assumption of an interest rate of 0% in the calculation.

24. 24 PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT (1) Hypothetical Example 1 scenario: Assume that the rate of increase in industrial output is unaffected by global warming as the GMT rises, until the temperature reaches 289.34K. A temperature increase from this point is assumed to adversely affect industrial output, causing it to decline in a linear manner as GMT rises further to 290.34K. At this point the annual rate of increase in industrial output is zero. Continued rise in GMT from this point is assumed to lead to an adverse effect increasing at the same rate. So, by the time the GMT 291.34K, the rate of decline in global industrial output is equivalent to the current rate of increase.

25. 25 PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT (2)

26. 26 PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT (3)

27. 27 PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT (4) Protecting against hypothetical Example 1 scenario: Calculate the cost of an American call option contract on the value of a futures GMT contract with the following characteristics (protection is required for 100 years – expiry date): Spot = Current GMT (this is regarded as the GMT for the most recent year, 2003, which has a value of 288.49K) Strike = 289.34K Standard Deviation of Returns (Volatility) = 0.000436 (based on the United Kingdom Meteorological Office data series) Interest rate = 0% (assuming that the only money which changes hands is that associated with variation margins).

28. 28 PROTECTING AGAINST DIMINISHING INDUSTRIAL OUTPUT (5) Calculation for protecting against hypothetical Example 1 scenario: Utilising the Black and Scholes (1973) call option formula, as modified for future style options (Gastineau, 1988), the calculation yields: $0.1878 for 2003. So, for protection under the aforementioned assumptions: The full cost of protection is $18.78 for every $100 of the future rate of industrial growth, or 18.78% of that rate of industrial growth.

29. 29 PROTECTING AGAINST THE VALUE OF A COMPANY DECLINING (1) Hypothetical Example 2 scenario: Assume that the value of a company (a manufacturer of ski equipment) is unaffected by global warming as the GMT rises, until the temperature reaches 289.34K. A temperature increase from this point is assumed to adversely affect company value, causing it to decline in a linear manner as GMT rises further to 290.34K. At this point the value is reduced to zero. Continued rise in GMT from this point has no further effect upon the company's value, as it cannot decline in value below zero..

30. 30 PROTECTING AGAINST THE VALUE OF A COMPANY DECLINING (2)

31. 31 PROTECTING AGAINST VALUE OF A COMPANY DECLINING (3)

32. 32 PROTECTING AGAINST VALUE OF A COMPANY DECLINING (4) Protecting against hypothetical Example 2 scenario: This is equivalent to calculating the difference between the cost of the following two American call option contracts on the value of a futures GMT contract with the following characteristics (protection is required for 100 years – expiry date) : First contract (bought)- This is the same contract as the one valued in for the hypothetical Example 1 scenario, hence, its value is $0.1878.

33. 33 PROTECTING AGAINST VALUE OF A COMPANY DECLINING (5) Second contract (sold)- Spot = Current GMT (this is regarded as the GMT for the most recent year, 2003, which has a value of 288.49K) Strike = 290.34K Standard Deviation of Returns (Volatility) = 0.000436 (based on the United Kingdom Meteorological Office data series) Interest rate = 0%

34. 34 PROTECTING AGAINST VALUE OF A COMPANY DECLINING (6) Calculation for protecting against hypothetical Example 2 scenario: Utilising the Black and Scholes (1973) call option formula, as modified by Gastineau (1988) for futures contracts, the calculation yields $0.0399 for the second contract. So, the cost of protection is the cost of the first contract (which is bought) minus the cost of the second contract (which is sold), namely, $0.1479, or 14.79% of the future value of the company. Note again that no money changes hands initially, and it is possible that only at the end of the options' life will settlement occur. So, for protection under the aforementioned assumptions, the full cost of protection is $14.79 for every $100 of the future value of the company.

35. 35 THE GROWING COST OF PROTECTION (1) The outcomes of calculations for the two examples from 1861 to 2003: They show, in the case of protecting against the risk of reduced industrial output: That the cost has risen from about 4 cents in the dollar circa 1860, To about 9 cents in the dollar 100 years later (circa 1960), and thence To accelerated to reach about 19 cents in the dollar in 2003.

36. 36 THE GROWING COST OF PROTECTION (2) They show, in the case of protecting against the risk of the value of a company declining: That the cost has risen from about 3 cents in the dollar circa 1860, To about 7 cents in the dollar 100 years later (circa 1960), and thence To accelerate to reach about 15 cents in the dollar in 2003.

37. 37 THE GROWING COST OF PROTECTION (3)

38. 38 CONCLUSION A methodology for calculating the cost of protecting against the risk of financial loss associated with global warming has been presented. It has been shown - Both in the case of protecting against the risk of reduced global industrial output, And also in the case of protecting against the risk of the value of a company declining, That the cost of that protection has risen over the years, and that the rate of that rise has accelerated recently.

39. 39 CASE STUDY: WEATHER DERIVATIVES. WHY THEY ARE APPLICABLE TO YOU. Thank You