Download - Managing a Portfolio of Weather Derivatives
Managing a Portfolio Managing a Portfolio of Weather Derivativesof Weather Derivatives
June 14, 2000June 14, 2000
beyond The BoxThe Box
ThinkingThinking
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BackgroundBackground
Portfolio Risk / ReturnPortfolio Risk / Return
Portfolio OptimizationPortfolio Optimization
OutlineOutline
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Correlation of Underlying IndexesCorrelation of Underlying IndexesGlobal physical processes involve ocean Global physical processes involve ocean
and atmosphereand atmosphere
Indexes Not TradedIndexes Not TradedSpecial pricing considerationSpecial pricing consideration
Basis RiskBasis RiskPortfolio performance vs. hedged riskPortfolio performance vs. hedged risk
Why a portfolio of weather derivatives deserves Why a portfolio of weather derivatives deserves special attentionspecial attention
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Global climate variationGlobal climate variation
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Global climate variationGlobal climate variation
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Regional impactRegional impact
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Weather derivative: call, put, combinationsWeather derivative: call, put, combinations
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
BuyerBuyer
SellerSeller
Prem
ium
Prem
ium
Payo
utPa
yout
Weather Index
20 40 60 80 100
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CallCall
PutPut
StrikeStrike StrikeStrike
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Pricing weather derivativePricing weather derivative
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
No-Arbitrage Model Not ApplicableNo-Arbitrage Model Not ApplicableUnderlying index not tradedUnderlying index not traded
Pure Statistical Method Not AdequatePure Statistical Method Not AdequateHistorical data characterized by large-scale trend Historical data characterized by large-scale trend
and variation (natural and instrumental)and variation (natural and instrumental)
Combining Dynamic / Actuarial ApproachesCombining Dynamic / Actuarial ApproachesProbability distribution of weather indexes based Probability distribution of weather indexes based
on dynamic/statistical seasonal predictionon dynamic/statistical seasonal prediction
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Probabilistic perspectiveProbabilistic perspective
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
0 20 40 60 80 100
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Weather Index
Dynamic/Statistical ModelDynamic/Statistical Model
Weather Index (W)Weather Index (W)
Payout P = f ( W )Payout P = f ( W )
Weather Index
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Payout ( P )Payout ( P )
0 50 100 150 200
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Payoff
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ReturnReturn R = ( R = ( prpr + + iiii - - PP - - e e )) PDF of P ---> PDF of RPDF of P ---> PDF of R
RiskRisk Return volatility: Return volatility: RR / / RR
Value at risk: VValue at risk: VRR
Risk-based Return: E ( R ) / VRisk-based Return: E ( R ) / VRR
A single weather derivative: risk / returnA single weather derivative: risk / return
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Return
ReturnReturn
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Return
PDF of portfolio returnPDF of portfolio return
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Portfolio ReturnPortfolio Return
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Return
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Return
Return of Individual Return of Individual Derivative: Derivative: RR11
Return of Individual Return of Individual Derivative: Derivative: RRNN . . . . . . RRii . . . .
No general analytical solutionNo general analytical solution
R = R = ( R ( Rii x x ii ) )
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Joint PDF of { Joint PDF of { WWii } }
Three alternative approachesThree alternative approaches Assuming normal distribution of { Assuming normal distribution of { WWii } } Pattern analysis (EOF / Principal component )Pattern analysis (EOF / Principal component ) Pattern-preserving simulationPattern-preserving simulation
Calculating the PDF of portfolio returnCalculating the PDF of portfolio return
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Predicted PDF of individual Predicted PDF of individual WWii WWi i pattern of variationpattern of variation
Simulation based on derivative payout functionsSimulation based on derivative payout functions
Joint PDF of Joint PDF of { R{ Rii } }
PDF of PDF of RR
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Simulated Simulated weather indexesweather indexes
XX (M X N matrix)(M X N matrix)
M simulations, N indexesM simulations, N indexes
Simulation and pattern preservationSimulation and pattern preservation
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Predicted PDF of individual Predicted PDF of individual WWii WWi i pattern of variationpattern of variation
Y = Y = transformation transformation (X, A)(X, A)such that such that the correlation matrix for Y = Athe correlation matrix for Y = Athe PDFs of the columns of Y = those of Xthe PDFs of the columns of Y = those of X
Correlation matrixCorrelation matrix
AA (N X N matrix) (N X N matrix)
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Simulation and pattern preservationSimulation and pattern preservation
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Individual contract returnIndividual contract return
Z = g(Y, Z = g(Y, contract termscontract terms))(M X N matrix)(M X N matrix)
Portfolio returnPortfolio return
R = Z R = Z
(( N XN diagonal matrix containing positions of N XN diagonal matrix containing positions of individual contracts)individual contracts)
PDF of PDF of RR
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Return
Portfolio risk / returnPortfolio risk / return
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Expected Return: E ( R )Expected Return: E ( R )
RiskRisk Return volatility: Return volatility: RR / / RR
Value at risk: VValue at risk: VRR
Risk-based Return: E ( R ) / VRisk-based Return: E ( R ) / VRR
Other Measures of Risk / ReturnOther Measures of Risk / Return Depending on risk tolerance, Depending on risk tolerance,
financial objective, etc.financial objective, etc.
PDF of PDF of RR
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Atlanta
Chicago
CincinnatiNewYork
Dallas
Philadephia
Portland
Tucson
DesMoines
LasVegas
ExamplesExamples
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
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Hypothetical portfolioHypothetical portfolio
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
City StrikeOption Type
Risk Based Return (%)
Atlanta 509 call 5.49Chicago 233 put 7.44Cincinnati 363 call 5.86New York 362 put 8.78Dallas 681 call 6.86Philadelphia 351 put 9.26Portland 220 call 6.11Tucson 629 put 20.96Des Moines 389 call 4.04Las Vegas 691 put 5.18Portfolio 14.9
July 2000 Cooling Degree Day at $5,000/CDDJuly 2000 Cooling Degree Day at $5,000/CDD
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Hypothetical portfoliosHypothetical portfolios
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
City StrikeOption Type
Risk Based Return (%)
Chicago 233 put 7.44New York 362 put 8.78Philadelphia 351 put 9.26Portfolio 7.23
Chicago 233 put 7.44New York 448 call 5.11Philadelphia 351 put 9.26Portfolio 9.34
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Portfolio optimization: feasibilityPortfolio optimization: feasibility
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Scientific understanding Scientific understanding of the behavior and of the behavior and pattern of the pattern of the underlying weather underlying weather indexesindexes
Inefficient marketInefficient market
Various purposes of Various purposes of using weather using weather derivativesderivatives
Significant opportunity to build Significant opportunity to build
a high return / low risk portfolioa high return / low risk portfolio
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Portfolio optimization: strategyPortfolio optimization: strategy
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Existing PortfolioExisting Portfolio Market Bids / OffersMarket Bids / Offers
Buy / SellBuy / Sell
Portfolio Risk / Return OptimizerPortfolio Risk / Return Optimizer
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SummarySummary
Managing a Weather Derivative PortfolioManaging a Weather Derivative Portfolio
Unique characteristics of weather Unique characteristics of weather derivatives requires special attention in derivatives requires special attention in pricing and portfolio managementpricing and portfolio management
Scientific understanding of the global Scientific understanding of the global climate variability makes feasible building an climate variability makes feasible building an optimal portfolio of weather derivatives with optimal portfolio of weather derivatives with high return and low riskhigh return and low risk