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Managing a Portfolio of Weather Derivatives

Thinking. The Box. beyond. Managing a Portfolio of Weather Derivatives. June 14, 2000. Managing a Weather Derivative Portfolio. Outline. Background Portfolio Risk / Return Portfolio Optimization. Managing a Weather Derivative Portfolio.

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Managing a Portfolio of Weather Derivatives

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  1. Thinking The Box beyond Managing a Portfolio of Weather Derivatives June 14, 2000

  2. Managing a Weather Derivative Portfolio Outline • Background • Portfolio Risk / Return • Portfolio Optimization

  3. Managing a Weather Derivative Portfolio Why a portfolio of weather derivatives deserves special attention • Correlation of Underlying Indexes Global physical processes involve ocean and atmosphere • Indexes Not Traded Special pricing consideration • Basis Risk Portfolio performance vs. hedged risk

  4. Managing a Weather Derivative Portfolio Global climate variation

  5. Managing a Weather Derivative Portfolio Global climate variation

  6. Managing a Weather Derivative Portfolio Regional impact

  7. Put Call Strike Strike Managing a Weather Derivative Portfolio Weather derivative: call, put, combinations Buyer Premium Payout Seller

  8. Managing a Weather Derivative Portfolio Pricing weather derivative • No-Arbitrage Model Not Applicable Underlying index not traded • Pure Statistical Method Not Adequate Historical data characterized by large-scale trend and variation (natural and instrumental) • Combining Dynamic / Actuarial Approaches Probability distribution of weather indexes based on dynamic/statistical seasonal prediction

  9. Payout ( P ) Payout P = f ( W ) Managing a Weather Derivative Portfolio Probabilistic perspective Dynamic/Statistical Model Weather Index (W)

  10. Return Managing a Weather Derivative Portfolio A single weather derivative: risk / return • Return • R = ( pr + ii - P - e ) • PDF of P ---> PDF of R • Risk • Return volatility: sR / mR • Value at risk: VR • Risk-based Return: E ( R ) / VR

  11. Managing a Weather Derivative Portfolio PDF of portfolio return Portfolio Return R = S ( Ri x ai ) No general analytical solution Return of Individual Derivative: R1 Return of Individual Derivative: RN . . . Ri . .

  12. Managing a Weather Derivative Portfolio Calculating the PDF of portfolio return Predicted PDF of individual Wi Wi pattern of variation Joint PDF of { Wi } Three alternative approaches • Assuming normal distribution of { Wi } • Pattern analysis (EOF / Principal component ) • Pattern-preserving simulation Simulation based on derivative payout functions Joint PDF of { Ri } PDF of R

  13. Managing a Weather Derivative Portfolio Simulation and pattern preservation Predicted PDF of individual Wi Wi pattern of variation Simulated weather indexes X(M X N matrix) M simulations, N indexes Correlation matrix A (N X N matrix) Y = transformation (X, A) such that the correlation matrix for Y = A the PDFs of the columns of Y = those of X

  14. Managing a Weather Derivative Portfolio Simulation and pattern preservation Individual contract return Z = g(Y, contract terms) (M X N matrix) Portfolio return R = Z l (l N XN diagonal matrix containing positions of individual contracts) PDF of R

  15. Managing a Weather Derivative Portfolio Portfolio risk / return • Expected Return: E ( R ) • Risk • Return volatility: sR / mR • Value at risk: VR • Risk-based Return: E ( R ) / VR • Other Measures of Risk / Return • Depending on risk tolerance, financial objective, etc. PDF of R

  16. Managing a Weather Derivative Portfolio Examples

  17. Managing a Weather Derivative Portfolio Hypothetical portfolio July 2000 Cooling Degree Day at $5,000/CDD

  18. Managing a Weather Derivative Portfolio Hypothetical portfolios

  19. Managing a Weather Derivative Portfolio Portfolio optimization: feasibility Scientific understanding of the behavior and pattern of the underlying weather indexes • Inefficient market • Various purposes of using weather derivatives Significant opportunity to build a high return / low risk portfolio

  20. Buy / Sell Managing a Weather Derivative Portfolio Portfolio optimization: strategy Existing Portfolio Market Bids / Offers Portfolio Risk / Return Optimizer

  21. Managing a Weather Derivative Portfolio Summary • Unique characteristics of weather derivatives requires special attention in pricing and portfolio management • Scientific understanding of the global climate variability makes feasible building an optimal portfolio of weather derivatives with high return and low risk

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