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Is it more rational to manage interest rate risk than weather risk?. WRMA European Meeting 2006 Toulouse, october 4th Pr. Didier Marteau Graduate Business School of Paris, Aon France and Ralf Holz (PhD), Aon France. Is it more rational to manage interest rate risk than weather risk?.

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is it more rational to manage interest rate risk than weather risk

Is it more rational to manage interest rate risk than weather risk?

WRMA European Meeting 2006

Toulouse, october 4th

Pr. Didier Marteau Graduate Business School of Paris,

Aon France

and Ralf Holz (PhD), Aon France

is it more rational to manage interest rate risk than weather risk2
Is it more rational to manage interest rate risk than weather risk?
  • It’s in fact a serious question that every corporate should raise and be able to answer…
  • In reality, few firms have been modeling their weather exposure,… and most of them allocate more resources to managing financial risk than weather risk.
  • Managers, economists, politicians… pay a close attention to the monetary policy, but are we sure that a 25 basis point drop of the repo rate by the European Central Bank has a bigger effect on the economy than a 1°Celsius change of the average temperature in october ?
  • Some sectors are clearly more weather sensitive than interest rate or currency sensitive (energy, textile, food and beverage, leisure and tourism, distribution, transport, construction…)

So, how can we explain that corporates are still reluctant to manage weather risk ?

Is it not time to replace traders by climate experts and euro-dollar forecasting by weather forecasting…?

how can we explain that corporates are still reluctant to managing weather risk
How can we explain that corporates are still reluctant to managing weather risk ?

1. Imperfect knowledge

of weather risk compared

to financial risk

2. Modeling weather exposure

is relatively complex and hedging

solutions are still relatively new

4 basic raisons

3. Weather hedges

are assumed to be

« expensive »

4. Weather risk management

raises difficult questions

of corporate governance

slide4
1. Imperfect knowledge about weather risk compared to financial risk

1.1 Comparative analysis of the volatilities of weather variables and financial variables

1.2 Economic analysis of the weather sensitivity in some sectors

1 1 comparative analysis of the volatilities of weather variables and financial variables
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • In the financial world, volatility is expressed by the annualised standard deviation of asset returns.
  • If the distribution of asset returns is « normal », the confidence interval associated to ±1 standard deviation is 68%, and the interval associated to ±2 standard deviations is 95%.
  • Examples of historical volatility:
    • US stock index (01/1802 – 09/2006)
    • Euro-dollar exchange rates (04/01/1999 – 09/25/2006)
    • 10 year T-Bond yield (01/1962 – 09/2006)
    • Spot oil price (01/1987 – 09/2006)
    • Carbon emission prices - EUA allowances (07/2005 – 09/2006)
1 1 comparative analysis of the volatilities of weather variables and financial variables6
09/11/2001

Crash of 1929

Word War I

Crash of 1987

$

Word War II

War of secession

1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • US stock index 01/1802 – 09/2006 (logarithmic scale)

The slope is quite constant, with an average annual rate of return equal to +6.02% (continous time)

Oil crisis 1973

1 1 comparative analysis of the volatilities of weather variables and financial variables7
09/11/2001

Oil crisis 1973

Crash of 1929

Word War I

Crash of 1987

$

Word War II

War of secession

1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • 1$ invested in 1802 in a stock index gives 216 010$ in 2006.
  • 1$ invested in 1802 in a T-bond index gives 464$ in 2006 (3% continous time rate of return).

3% Bond Yield

1 1 comparative analysis of the volatilities of weather variables and financial variables8
Annualized volatility = 16%1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • US stock index 01/1802 – 09/2006 : Distribution of annual returns
1 1 comparative analysis of the volatilities of weather variables and financial variables9
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Euro-dollar exchange rates (01/1999 – 09/2006)
1 1 comparative analysis of the volatilities of weather variables and financial variables10
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Euro-dollar exchange rates – Distribution of daily variations (01/1999 – 09/2006)

Annualized volatility = 8,6%

1 1 comparative analysis of the volatilities of weather variables and financial variables11
$/Barrel1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Europe Brent Spot Price (01/1987 – 09/2006)
1 1 comparative analysis of the volatilities of weather variables and financial variables12
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Europe Brent Spot Price – Distribution of daily price variations (01/1987 – 09/2006)

Annualized volatility = 37%

1 1 comparative analysis of the volatilities of weather variables and financial variables13
€/t1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Carbon Emission Allowances – Powernext spot prices (07/2005 – 09/2006)
1 1 comparative analysis of the volatilities of weather variables and financial variables14
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Carbon Emissions Allowances – Distribution of daily price variations (07/2005 – 09/2006)

Annualized volatility = 75,8%

1 1 comparative analysis of the volatilities of weather variables and financial variables15
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • US 10 year government bond yields (01/1962 – 09/2006)

%

Data : Federal Reaserve

1 1 comparative analysis of the volatilities of weather variables and financial variables16
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • US 10 year government bond yields – Distribution of weekly variations (01/1962 – 09/2006)

Annualized volatility = 12,3%

1 1 comparative analysis of the volatilities of weather variables and financial variables17
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Monthly Mean Central England Temperature – August (1800 – 2006)

°C

Data : Hadley Centre

1 1 comparative analysis of the volatilities of weather variables and financial variables18
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Monthly Mean Central England Temperature – August (1800 – 2006) – Distribution of annual “returns”

Annual volatility = 9,9%

The « volatility » of temperature is at the same level as the exchange rate volatility.

1 1 comparative analysis of the volatilities of weather variables and financial variables19
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Monthly Mean Central England Temperature – November (1800 – 2006)

°C

Data : Hadley Centre

1 1 comparative analysis of the volatilities of weather variables and financial variables20
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Monthly Mean Central England Temperature – November (1800 – 2006) – Distribution of annual “returns

Annual volatility = 34%

Data : Hadley Centre

Exactly in the same way as interest rates volatilities, the « volatility » of temperatures increases when the average temperature decreases (the volatility of 3M interest rates on yen e.g. is much higher than that of 3M dollar interest rates).

1 1 comparative analysis of the volatilities of weather variables and financial variables21
40

35

30

25

20

15

10

5

0

10%

30%

50%

70%

-70%

-30%

-10%

-50%

1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Annual precipitation rate Paris (1800 – 2006)

Annual volatility = 27%

Data : Meteo-France

The « volatility » of annual precipitation rates is comparable to that of crude oil.

1 1 comparative analysis of the volatilities of weather variables and financial variables22
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Daily maximum hourly averaged wind speed (Vlissingen, Netherlands)

Data : KNMI

1 1 comparative analysis of the volatilities of weather variables and financial variables23
1.1 Comparative analysis of the volatilities of weather variables and financial variables
  • Daily maximum hourly averaged wind speed (Vlissingen, Netherlands)

Daily (!) volatility = 37,1%

Data : KNMI

1 1 comparative analysis of the volatilities of weather variables and financial variables24
1.1 Comparative analysis of the volatilities of weather variables and financial variables

Two main conclusions:

  • The volatility of the weather variables is at about the same level as the volatility of financial indices.
  • Consequently, there is no reason to hedge financial risk and bear weather risk… except if your firm is a « weather firm » or is less sensitive to weather risk. But in many sectors, this last assertion is clearly wrong…
1 2 economic analysis of the weather sensitivity in some sectors
1.2 Economic analysis of the weather sensitivity in some sectors

Beer consumption and temperature

  • Sensitivity = relative change in consumption per 1°C change in temperature
  • At 25°C : 1°C change signifies a ±7% change in consumption !!
  • R2 = explained volatility /total volatility = 0,80 :

If 80% of change of beer consumption is explained by a change in temperature, what does really explain the financial results in beer industry : quality of management, level of interest rates, marketing policy, coca-cola’s innovations … or weather ???

slide26
The beer-temperature correlation is quite instable geographically with two consequences: the need for defining precisely the local exposure,and paying attention to correlation riskif you cross-hedge.

1.2 Economic analysis of the weather sensitivity in some sectors

Data : Météo-France

1 2 economic analysis of the weather sensitivity in some sectors27
R2 = 0.91

-2.5%/°C

+1%/°C

0%/°C

1.2 Economic analysis of the weather sensitivity in some sectors
  • Weekly electricity consumption in France as a function of temperature R2>90%
1 2 economic analysis of the weather sensitivity in some sectors28
GWh/j

CWV

1.2 Economic analysis of the weather sensitivity in some sectors
  • Consumption of natural gas (distribution zone around London) as a function of temperature (+ wind speed correction) R2>90%
1 2 economic analysis of the weather sensitivity in some sectors29
Wind speed

5km/h

25km/h

Productivity

Reference : Moselhi et al

Temperature (C)

1.2 Economic analysis of the weather sensitivity in some sectors
  • Productivity in the construction sector as a function of temperature and wind speed
1 2 economic analysis of the weather sensitivity in some sectors30
1.2 Economic analysis of the weather sensitivity in some sectors
  • With data from the French Textile Industry Office over the period 1977-2006, we studied the correlation betwen textile sales and temperature. For two seasons, spring and autumn, we obtain a R2 close to 0.8, with a positive correlation in spring and a negative one in autumn, especially september…
1 2 economic analysis of the weather sensitivity in some sectors31
Prêt à Porter Homme

Prêt à Porter Femme

Const

t

Beta

t

R2

Const

t

Beta

t

R2

Jan

2,32

-1,66

-0,62

-1,29

0,10

3,18

-2,35

-0,06

-0,13

0,00

Febr

-0,50

-0,29

0,79

-1,30

0,10

0,39

-0,25

1,21

-2,16

0,24

Mar

-2,06

-1,65

2,42

-2,68

0,32

-0,98

-0,71

2,82

-2,83

0,35

Apr

-1,06

-1,34

0,93

-1,85

0,19

-0,96

-1,06

1,67

-2,87

0,35

May

-1,20

-0,86

3,10

-3,97

0,51

-0,51

-0,37

3,05

-3,93

0,51

Jun

-0,35

-0,27

-0,70

-0,63

0,03

1,63

-1,57

1,56

-1,74

0,18

Jul

1,08

-0,85

-1,08

-1,40

0,12

3,21

-2,77

0,43

-0,61

0,03

Aug

-1,36

-1,51

-2,60

-4,02

0,54

0,74

-0,52

-2,22

-2,18

0,25

Sep

-1,58

-1,63

-4,75

-8,26

0,83

-0,16

-0,20

-5,29

-10,86

0,89

Oct

-1,46

-1,05

-4,72

-5,72

0,70

0,38

-0,30

-3,51

-4,79

0,62

Nov

-1,75

-1,33

-1,07

-2,04

0,23

0,60

-0,52

-0,48

-1,03

0,07

Dez

-1,53

-1,14

-0,32

-0,54

0,02

0,05

-0,04

0,01

-0,02

0,00

1.2 Economic analysis of the weather sensitivity in some sectors

Beta: relative change

in sales for 1°Celsius change

Women buy clothes whatever

the temperature

how can we explain that corporates are still reluctant to managing weather risk32
How can we explain that corporates are still reluctant to managing weather risk ?
  • Modeling weather exposure is relatively complex and hedging solutions are relatively new

Four basic differences betwen the financial risk and the weather risk:

1. Weather risk is generally a volume risk, not a price risk. If the euro-dollar moves up by 2%, your invoice in dollars moves up by 2%. If the 1 year interest rate moves up 25 basis points, your financial expenses move up by 0,25% * nominal. But if the october average temperature moves up by 1°C, your textile sales don’t move down by 1°C !!! So internal or external expert resources are required for analysing the weather sensitivity

2.Weather risk is a strategic risk, not a transactional risk. Transfering weather risk is a strategic decision related to the identity of the firm. Are Eurodisney or Parc Astérix « weather stocks » or « leisure stocks »? Does the equity holder invest in weather or entertainment ? If it’s in weather, the management has to bear the weather risk as a source of risk and return, and not to transfer it.

modeling weather exposure is relatively complex and hedging solutions are relatively new
Modeling weather exposure is relatively complex and hedging solutions are relatively new
  • From a theoritical point of view, temperature is a new financial asset.

On one hand, the weather market is « incomplete », raising problems for pricing weather derivatives. For instance, you cannot duplicate buying forward by borrowing, buying spot and carrying. Consequently, you cannot price the forward temperature as:

Spot temperature + cost of financing – carry of temperature

The forward temperature will be traded close to the expected spot temperature adjusted by a risk premium, and not with the cash and carry relationship. So, prices may be considered by end-users as less transparent.

On the other hand, the asset price is not affected by the continuous-time arrival of new informations,as every other financial asset. It implies for temperature a low volatility till 10 days before the beginning of the reference month, followed by a high volatility, the short term temperature forecasting horizon being an obstacle for involving traders and reducing the risk premium.

modeling weather exposure is relatively complex and hedging solutions are relatively new34
Modeling weather exposure is relatively complex and hedging solutions are relatively new

Falling emission prices

UN approval for N20 CDM projects in Korea and Brazil

contrat chicago
Contrat Chicago

Contract HDD January

Moyenne (10 ans). = 1228

Moyenne (10 ans) = 908

Moyenne (10 ans) = 910

modeling weather exposure is relatively complex and hedging solutions are relatively new37
Modeling weather exposure is relatively complex and hedging solutions are relatively new

4. European end-users still suffer from a lack of information about weather markets (how many corporates know the number of European towns traded on the CME?), and have not yet defined the internal organisation and responsabilities for hedging weather risk. The weather issue can be taken in charge, either by the Treasurer (technical skills about derivatives), the Chief Financial Officer (strategic decision level), the Risk Manager (in charge of managing the global risk exposure) or even the marketing department (hedging commercial risk). Weather risk management is a cross-preoccupation.

how can we explain that corporates are still reluctant to managing weather risk38
How can we explain thatcorporates are still reluctant to managing weather risk ?

3. Weather hedges are assumed to be « expensive »

  • Weather hedging is frequently considered as « expensive » by end-users, and its cost considered as an obstacle to the development of the weather markets. Reality or perception?
why weather hedges are assumed to be expensive
Why weather hedges are assumed to be « expensive »

The issue here is that corporates are used to hedge their financial risk on « complete markets », with prices built on arbitrage strategies and easy to understand, whereas the weather market is « incomplete » and appears less transparent.

  • An asset is traded on a « complete » market if its future pay-off can be « duplicated » by a combination of other existing assets: it’s the case of most of forward contracts, options contracts (Black-Scholes)… In this case, the asset price is simply the price of the duplicating portfolio. This pricing methodology is also called « no-arbitrage pricing ».
  • In a « complete » market, the asset price does not depend on risk aversion and consequently does not require any « risk premium ». In a complete market, hedging looks as « free ».
why weather hedges are assumed to be expensive40
Why weather hedges are assumed to be « expensive »

You are a US importer and want to You are an energy producer and want to

hedge your short 100 euros 3M hedge your December exposure by buying

exposure by buying forward. the DEC temperature forward.

Market data:

Spot euro-dollar: 1.30 October temperature: 15°C

US 3M interest rate: 5% Euro 3M interest rate: 3%

Euro 3M interest rate: 3% Storage cost: to be determined (!)

Expectations:

Assume a binomial model, with Assume a binomial model, with 2 forecast

2 forecast values for the , values for the temperature spot in

spot in 3M, either 1.36 or 1.24 december, either 8°C or 12°C

What is your forward price ?

pricing a forward contract on euro dollar
Pricing a forward contract on euro-dollar

You duplicate buying forward by buying spot X euros, borrowing X*1.30 dollars at 5%, and lending X euros at 3%.

The value of your portfolio at expiration is following

X*1.30*(1+5%/4) + X*(1+3%/4)*1.36 = (1.36 – F)*100

X*1.30*(1+5%/4) + X*(1+3%/4)*1.24 = (1.24 – F)*100

2 equations, 2 unknown variables, one unique solution for forward pricing:

(1 + 5%4)

X = - 100 / (1 + 3%/4) and F = 1.30 -------------------

(1 + 3%4)

(1.36 – F)*100

1.36

1.30

(1.24 – F)*100

1.24

spot

Pay-off of buying forward

pricing a forward contract on euro dollar42
Pricing a forward contract on euro-dollar

The euro forward rate does not depend on individual expectations about the behavior of the spot rate (you may replace 1.36 et 1.24 by any values, you will find the same result), and is a « no-arbitrage » price. It does not require any risk premium.

Imagine the same pricing methodology for weather…

Your duplication portfolio consists in borrowing euros, buying

october temperature spot at 15°C, and storing it (1 euro/month).

Your forward august temperature is 15°C (1 + 3%*10/12) – 10

euros ?????????????????????????

Other models are needed, which take into account theweather expectations, and include logically arisk premium.…For these two reasons, the end-users, who are used to trade on « complete » markets with a no-arbitrage pricing, have more difficulties with weather.

complete and incomplete markets
Complete and incomplete markets

Complete markets:

Forward price =

Spot price + cost of

carry

Incomplete markets:

Forward price =

Expected spot price

+/- risk premium

Reverse cash and carry

faces limits (convenience

yield): oil prices…

The asset cannot

be carried: power…

The asset is not traded

on the spot market and

cannot be carried:

weather indices

Risk premium paid

by the hedger

Hedge is costless:

no risk premium

complete and incomplet markets the case of options
Complete and incomplet markets: the case of options
  • On complete markets (most of currency, interest rates and equity markets), the forward price is simply the spot price +/- cost of carry.The hedger does not pay any risk premium.
  • On incomplete markets, as the weather derivatives market, the forward price cannot be extracted from the cash and carry relationship (!).So, the bank or insurer cannot hedge itself riskless, and includes logically a risk premium in its price.
  • Ex: if the bank quotes euro-dollar 3M, it can itself hedge by borrowing dollars, buying euros spot and lending euros. Its forward price will be 1.305. No risk premium is included in the forward price.
  • But if the bank trades August temperature for a client, itcannot hedge risklessby borrowing euros (he can!), buying temperature spot (today is 12°C !), and carrying it till August…The bank or insurer will hedge its contract through diversification within a larger porfolio andrequire logically a risk premium.
complete and incomplet markets the case of options45
Complete and incomplet markets: the case of options
  • The « magic » idea of Black-Scholes (Journal of Political Economy october 1973: « Corporate liabilities and option pricing »), is that buying a call can be duplicated by borrowing and buying delta stocks. Consequently,the price of an option is the price of the duplicating portfolio. No risk premium is required.A fundamental assumption to this model is thatthe market is complete.
  • If you ask for a call on temperature to your bank or insurance company, it cannot hedge riskless by borrowing and buying spot delta temperature…. Consequently,it will be obliged to use an other model and include a risk premium…or to use Black-Scholes and adjust the price because riskless hedging is not possible.
how can we explain that corporates are still reluctant to managing weather risk46
Measuring the

weather exposure

If weather risk is a specific

risk, hedging (costless)

through diversification

Firm’s identity

Stockholders

If weather risk

is a systematic

risk, hedging

through insurance,

banks or markets

Transferring

the weather risk

Keeping the weather

risk, as a source of

return and identity

Managers

Risk /

Expected return

Market/product

diversification

Banks

Insurers

Financial

markets

Securitization

How can we explain thatcorporates are still reluctant to managing weather risk ?

IV. Weather hedge raises an important corporate governance question

slide47
Hedging or not hedging ?Four questions to raise before answering…
  • Is the weather a strategic element of my business?What is the pertinent market for a theme park? Leisure market, culture market,…weather market? What is the relative contribution of each risk factor, and especially weather, to my earnings?
  • What do stockholders know about my weather exposure?Do investors consider that they hold a « weather stock » and do they expect a return for that? Or do they consider that they bought a « leisure » stock and don’t want to bear any weather risk? In any case, the management has to communicate about its weather hedging policy.
slide48
Hedging or not hedging ?Four questions to raise before answering…
  • If the weather is not considered to be a strategic element of business, and has to be transferred, who is responsible for hedging weather risk? Managers or stokholders? The financial theory teaches that stockholders can hedge themselves through diversification, and that hedging a diversifiable risk is free and not a managers’job. The only theoretical reason for hedging weather, from the management’s perspective, is then avoiding default. But is weather risk a specific risk, or a systematic risk, and thus not diversifiable…?
  • What do my competitors do?According to game theory, if you hedge by your own, and if your competitors don’t hedge, you bear an additional risk to have a lower financial result (because of hedging losses) if the weather has a positive impact on your business. Is the management’s performance evaluated on the basis of absolute criteria or relative criteria? Do you hedge your competitivity?
conclusion
Conclusion
  • Weather risk is not restricted to extreme events and is associated to the normal volatility of weather indices.
  • Most economic sectors, and not only energy, are weather sensitive, and have more reasons to manage weather risk than interest rate risk…
  • As the weather market is « incomplete », a risk premium has to be paid by the hedger, what explains that weather hedging looks sometimes « expensive ».
  • Weather hedging has to be implemented either by the stockholders or by the managers, essentially through diversification, bank and insurance products, or financial markets.
  • Temperature, energy prices, carbon emissions allowances prices, are tightly connected…Should we manage globally these new environmental risks in a Value at Risk approach or separately ?
slide50
The end…  « Time is over … and weather not cold enough for a chocolate break. We go for an other presentation….»

Source: Météo France…obviously

illustration a simplified case study
Illustration: a simplified case study
  • You are a beer producer and want to hedge your weather risk in South of France over august.
  • Your sales budget in this region has been built on a historical average temperature of 21°C, maybe corrected for a warming trend, and the treasurer is in charge of protecting the 10 millions euros of expected earnings.
  • A correlation analysis showed that, in august, a 1°C change in temperature led to an 6% decrease in earnings. This linear approximation is assumed to be correct between 18°C and 24°C. The historical volatility in august is 10%.

You decide to hedge your exposure on the CME through the CAT futures contract.

Four questions:

    • What is the CAT futures contract?
    • Do I sell or buy contracts?
    • How many?
    • What are the residual risks?
what is the cat futures contract
What is the CAT futures contract?

COMMODITY SPECIFICATIONS:Cumulative Average Temperature (CAT)

  • Each particular CME European CAT Index is the accumulation of like daily average temperatures over a calendar month. The accumulation period of each CME European CAT Index futures contract begins with the first calendar day of the contract month and ends with the last calendar day of the contract month.
  • The daily average temperature is defined as the arithmetic average of the maximum temperature (Tmax) and minimum temperature (Tmin), measured at the following times for each location, as reported by Earth Satellite Corporation.
  • Paris-Orly, France (WMO 07149): Between 0600 UTC the current day and 0559 UTC the following day for Tmax, and between 1800 UTC the previous day and 1759 UTC the current day for Tmin
  • On october 4, 2006, the Paris CAT index August 2007 is supposed to be traded at 635, i.e an average temperature of 635/31 = 20.5°C
  • For simplicity, we assume that 1°C is equals 20 euros
do i sell or buy contracts
Exposure

Hedge

Temperature UP

Do I sell or buy contracts?
  • Clearly, you….sell contracts

Temperature DOWN

how many
How many?

Two steps :

  • First, we define the weather sensitivity of earnings by the relative change in earnings divided by the absolute change in temperature

dE/E

S = ------------ (1)

dT

From (1) we derive: dE = S x E x dTe = 6% x 10 000 000 x dTe (2)

Equation (2) is your « exposure equation »

  • Then, you sell H (optimal ratio) futures contracts at a price F, transforming your « exposure equation » (2) in:

dE = ( 6% x 10 000 000 x dTe )+ (H x 20 euros x dF ) (3)

or dE = (6% x 10 000 000 x dTe )+ (H x 20 euros x dFA x 31)

The optimal hedge ratio H can be deduced as following:

6% * 10 000 000 dTe

You want dE = 0 and find H = - ----------------------------- x --------- = 968

20 * 31 dFA

contracts with the assumption dTe = dFA

You sell

contracts

Assumption: your « budget-temperature »

is the traded future temperature

how many55
How many?
  • Scenario 1 : the average temperature next august is finally 18.5°C…and beer sales are lower than expected

The CAT contract expires at 573 (18.5 x 31)

    • Exposure loss (compared to budget):

6% x 10 000 000 x (18.5°C – 21°C) = - 1 500 000 euros

    • Futures gain: 968 x 20 x (635 – 573) = + 1 200 000 euros
    • Your « physical » loss is largely offsett by your « futures » gain.

Why not totally? Because your sales budget was based on your own expectation (21°C) higher than the forward traded temperature (20.5°C). So dTe / dF was not 1.

YOU CANNOT HEDGE YOUR OWN EXPECTATION, BUT ONLY LOCK-IN THE FUTURES OR FORWARD PRICE . That’s true on any market (foreign exchange, interest rates…).

how many56
How many?
  • If you are a US importer and want to hedge your 3 month short exposure, you can only « lock-in » a 1.31 euro-dollar (3 month forward rate) and not the 1.30 spot rate. The euro-dollar premium is « against » you and in favor of the US exporter.
  • If the yield curve is sharply increasing, you cannot « lock-in » the spot interest rate, but a largerly higher forward rate.
  • If the temperature is traded at 20.5°C, you cannot « lock-in » a 21°C temperature indexed budget.

→ That’s the reason why I recommend to use the forward rate as the

« budget exchange rate » or « budget interest rate » , and the « forward temperature » as the « budget temperature », because no treasurer is able to hedge a different rate without taking risks.

what are the residual risks
What are the residual risks?
  • Some corporates hesitate to hedge weather because of « correlation risk » between the temperature which affects their business and the traded temperature.

Three answers:

  • The optimal hedge ratio takes obviously into account the imperfect correlation between « physical » and « future » temperature.
  • Correlation risk is not specific to weather, and corporates face it regularly when they hedge interest rate risk …
  • Correlation risk is a residual risk, lower than weather risk itself.
  • Banks and insurance companies can offer tailored hedges….
what are the residual risks optimal hedge ratio takes into account correlation risk
What are the residual risks? Optimal hedge ratio takes into account correlation risk
  • Consider again the beer producer… His risk is in South of France and the CAT contract is related to the Paris temperature :

dE = (6% x 10 000 000 x dTe )+ (H x 20 x dFAx 31)

As dTe and dFA are correlated random variables, we try to minimize the variance of dE and obtain:

6% * 10 000 000 σdT

H = ------------------------ xρx ----

20 * 31 σdF

Meteo France

delivers this

information (correlation

coefficient)

what are the residual risks optimal hedge ratio takes into account correlation risk59
What are the residual risks? Optimal hedge ratio takes into account correlation risk

Example :

  • Correlation South of France – Paris:

ρ = + 0.75

  • Temperature’s volatility in Paris and South of France:
      • σdF = 10%
      • σdT = 12%
  • Optimal hedge ratio:

968 x 0.75 x 12% / 10% = 871 contracts

We call correlation risk the risk that the correlation ρ moves over the hedging period. But the model takes into account the imperfect correlation between Paris

and South of France by adjusting the hedge ratio.

EVEN A BAD CORRELATION REDUCES THE WEATHER RISK !

Theoretically, the reduction of variance of the initial exposure is equal to the initial variance timesρ2 :

      • ρ = 1 reduction = 100%
      • ρ = 0.75 reduction = 56%
      • ρ = 0.5 reduction = 25%
      • ρ = 0 reduction = 0%
what are the residual risks optimal hedge ratio takes into account correlation risk60
What are the residual risks? Optimal hedge ratio takes into account correlation risk

Data : Meteo-France, Powernext

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