3.2 Modeling the Crown’s exposure to risk
To model the components that contribute to the Crown's aggregate risk, we decompose the comprehensive balance sheet into entity-based classes. The most significant GAAP assets are those of state-owned enterprises, Crown financial institutions[10] and physical assets such as roads, schools, hospitals, and state houses. Among the most significant GAAP liabilities are the unhedged debt managed by the Debt Management Office, the insurance liabilities of the Accident Compensation Corporation (ACC), and pension liabilities of the Government Superannuation Fund (GSF). The net assets of smaller entities are aggregated into an ‘other' category. Along with these reported assets and liabilities are the present values of primary revenue and spending, which are derived from the long-term fiscal projections using a nominal discount rate of 10%. Assets and liabilities could be broken down into smaller constituent parts if desired. We have not done this, in part to limit the number of parameters that we have to estimate.
To model the Crown's exposure to risk, we essentially integrate a standard analysis of the risk of a portfolio of assets and liabilities with an analysis of the risks created by uncertain future spending and tax revenue.[11] We estimate some results analytically (that is, with the use of closed-form formulas) and others with Monte Carlo simulation.[12] Appendix 1 describes the mathematical structure of the model.
To derive the results we need an estimate, for each class of asset and liability, of the expected return, the variance of the return, and the correlation of the return with the returns of other assets and liabilities. The most difficult parameters to estimate are the correlations. We look at historical data, typically using historical time series of indices that we believe are reasonable proxies for the assets and liabilities in the model. For some parameters we have had to use our judgement. Appendix 2 describes the estimation of the parameters in the model.
Notes
- [10]The financial asset portfolios of the NZSF, Accident Compensation Corporation, the Earthquake Commission and the Government Superannuation Fund.
- [11]The literature on empirical risk quantification of sovereign net worth is limited, but see Adrogué (2005), Barnhill and Kopits (2003), Barnhill (2006), and Burnside (2004).
- [12]Monte Carlo simulation enables us to numerically construct projected frequency distributions. Deriving frequency distributions analytically would be infeasible owing to the complicated nature of the functional forms in the model. All the results presented in this paper that are derived using the Monte Carlo technique are the result of running the model with 10,000 simulations.
