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

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. Managing a Weather Derivative Portfolio
Weather derivative: call, put, combinations
Call
Put
Strike
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. Dynamic/Statistical Model
Managing a Weather Derivative Portfolio
Probabilistic perspective
Dynamic/Statistical Model
Payout ( P )
Weather Index (W)
Payout P = f ( W )

10. 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

11. . . . 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 . .

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. 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

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

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