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

Managing a Weather Derivative Portfolio Outline Background Portfolio Risk / Return Portfolio Optimization

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

Managing a Weather Derivative Portfolio Global climate variation

Managing a Weather Derivative Portfolio Global climate variation

Managing a Weather Derivative Portfolio Regional impact

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

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

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

Managing a Weather Derivative Portfolio A single weather derivative: risk / return 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

. . . Ri . . 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 . .

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

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

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

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

Managing a Weather Derivative Portfolio Examples

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

Managing a Weather Derivative Portfolio Hypothetical portfolios

Significant opportunity to build a high return / low risk portfolio 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

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

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