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

1
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

2
Is it more rational to manage interest rate risk
than weather risk?

• Its 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 1Celsius 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?

3
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
4

• 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

5
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)

6
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
7
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
8
1.1 Comparative analysis of the volatilities of
weather variables and financial variables

• US stock index 01/1802 09/2006 Distribution
  of annual returns

9
1.1 Comparative analysis of the volatilities of
weather variables and financial variables

• Euro-dollar exchange rates (01/1999 09/2006)

10
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
11
1.1 Comparative analysis of the volatilities of
weather variables and financial variables

• Europe Brent Spot Price (01/1987 09/2006)

12
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
13
1.1 Comparative analysis of the volatilities of
weather variables and financial variables

• Carbon Emission Allowances Powernext spot
  prices (07/2005 09/2006)

14
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
15
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
16
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
17
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
18
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.
19
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
20
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).
21
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.
22
1.1 Comparative analysis of the volatilities of
weather variables and financial variables

• Daily maximum hourly averaged wind speed
  (Vlissingen, Netherlands)

Data KNMI
23
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
24
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

25
1.2 Economic analysis of the weather sensitivity
in some sectors

• Beer consumption and temperature
• Sensitivity relative change in consumption
  per 1C change in temperature
• At 25C 1C 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-colas
  innovations or weather ???

26
The beer-temperature correlation is quite
instable geographically with two consequences
the need for defining precisely the local
exposure, and paying attention to correlation
risk if you cross-hedge.
1.2 Economic analysis of the weather sensitivity
in some sectors
Data Météo-France
27
1.2 Economic analysis of the weather sensitivity
in some sectors

• Weekly electricity consumption in France as a
  function of temperature R2gt90

28
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) R2gt90

29
1.2 Economic analysis of the weather sensitivity
in some sectors

• Productivity in the construction sector as a
  function of temperature and wind speed

30
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

31
1.2 Economic analysis of the weather sensitivity
in some sectors
Beta relative change in sales for 1Celsius
change

Women buy clothes whatever the temperature
32
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 1C, your textile sales dont move down by 1C
  !!! 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
  its in weather, the management has to bear the
  weather risk as a source of risk and return, and
  not to transfer it.

33
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.

34
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
35
Modeling weather exposure is relatively complex
and hedging solutions are relatively new


36
Contrat Chicago
Contract HDD January
Moyenne (10 ans). 1228
Moyenne (10 ans) 908
Moyenne (10 ans) 910
37
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.

38
How can we explain that corporates 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?

39
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 its 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 .

40
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 15C
• 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
  8C or 12C
• What is your forward price ?

41
Pricing a forward contract on euro-dollar
(1.36 F)100
1.36
1.30
(1.24 F)100
1.24
spot
Pay-off of buying forward

• You duplicate buying forward by buying spot X
  euros, borrowing X1.30 dollars at 5, and
  lending X euros at 3.
• The value of your portfolio at expiration is
  following
• X1.30(15/4) X(13/4)1.36 (1.36
  F)100
• X1.30(15/4) X(13/4)1.24 (1.24
  F)100
• 2 equations, 2 unknown variables, one unique
  solution for forward pricing
• (1 54)
• X - 100 / (1 3/4) and F
  1.30 -------------------
• 
  (1 34)

42
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 15C, and storing it
  (1 euro/month).
• Your forward august temperature is 15C (1
  310/12) 10
• euros ?????????????????????????
• Other models are needed, which take into
  account the weather expectations, and include
  logically a risk 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.

43
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
Hedge is costless no risk premium
Risk premium paid by the hedger
44
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, it cannot hedge riskless by borrowing
  euros (he can!), buying temperature spot (today
  is 12C !), and carrying it till AugustThe bank
  or insurer will hedge its contract through
  diversification within a larger porfolio and
  require logically a risk premium.

45
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 that the 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 premiumor to use
  Black-Scholes and adjust the price because
  riskless hedging is not possible.

46
How can we explain that corporates are still
reluctant to managing weather risk ?

• IV. Weather hedge raises an important corporate
  governance question

47
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 dont want to bear any
  weather risk? In any case, the management has to
  communicate about its weather hedging policy.

48
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 managersjob. The only theoretical reason for
  hedging weather, from the managements
  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 dont 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 managements
  performance evaluated on the basis of absolute
  criteria or relative criteria? Do you hedge your
  competitivity?

49
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 connectedShould
  we manage globally these new environmental risks
  in a Value at Risk approach or separately ?

50
 The end  Time is over and weather not cold
enough for a chocolate break. We go for an other
presentation.
Source Météo Franceobviously
51
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 21C,
  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
  1C change in temperature led to an 6 decrease
  in earnings. This linear approximation is assumed
  to be correct between 18C and 24C. 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?

52
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 20.5C
• For simplicity, we assume that 1C is equals 20
  euros

53
Do I sell or buy contracts?

• Clearly, you.sell contracts

Temperature DOWN
54
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

You sell contracts
Assumption your budget-temperature is the
traded future temperature
55
How many?

• Scenario 1 the average temperature next august
  is finally 18.5Cand 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 (18.5C 21C) - 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 (21C) higher than
  the forward traded temperature (20.5C). So dTe /
  dF was not 1.
• YOU CANNOT HEDGE YOUR OWN EXPECTATION, BUT ONLY
  LOCK-IN THE FUTURES OR FORWARD PRICE . Thats
  true on any market (foreign exchange, interest
  rates).

56
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 20.5C, you
  cannot lock-in a 21C temperature indexed
  budget.
• ? Thats 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.

57
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.

58
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 dFA x
  31)
• As dTe and dFA are correlated random variables,
  we try to minimize the variance of dE and obtain
  
• 6 10 000 000
  sdT
• H ------------------------ x ? x ----
• 20 31 sdF

Meteo France delivers this information
(correlation coefficient)
59
What are the residual risks? Optimal hedge ratio
takes into account correlation risk

• Example
• Correlation South of France Paris
• ? 0.75
• Temperatures volatility in Paris and South of
  France
• sdF 10
• sdT 12
• Optimal hedge ratio
• 968 x 0.75 x 12 / 10 871 contracts
• We call correlation risk the risk that the
  correlation ? 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 times ?2
• ? 1 reduction 100
• ? 0.75 reduction 56
• ? 0.5 reduction 25
• ? 0 reduction 0

60
What are the residual risks? Optimal hedge ratio
takes into account correlation risk
Data Meteo-France, Powernext