3.6  Sensitivity analysis

To investigate the sensitivity of risk to changes in key parameters in the model, we report results using more extreme choices for volatility, correlation, and discount-rate parameters. We find that the results are materially sensitive to changes in these parameters.

Changing the volatilities of all the individual asset and liability classes in the model linearly changes aggregate volatility. Thus, a 10% increase in volatility of all entities would increase aggregate risk by 10%. An extreme scenario would be to assume a doubling of all volatilities, which would double the measured volatility of aggregate net worth.

Correlations are a focus of risk analysis because they are critical and yet difficult to estimate accurately and can change over time. We report the sensitivity of results to more extreme correlations in Table 9. The more extreme assumptions lead to a doubling of the estimate of the Crown’s exposure to risk. The single most important correlation coefficient in the model is that between primary revenue and primary spending. In the base case, this parameter is set to 0.5. It is less than 1 because we have an assumption of unchanged policy commitments (unexpected revenue increases are not assumed to be perfectly correlated with increased spending or decreased taxes). The economic intuition for the positive value is that even with current policy commitments, much spending is positively correlated to revenue because both are influenced by economic growth (for example, New Zealand Superannuation payments are indexed to the average wage and public-sector wages tend to increase with average wages). Sensitivity to this parameter is tested using correlation values of between 0 and 1. We also look at changing all other correlation coefficients in the model. The base case correlation coefficients are reported in Appendix 2 and average 0.4 in magnitude. To test sensitivity, we set all asset–asset and liability–liability correlations to 0.8 and correlations between assets and liabilities to –0.8.

The discount rate used to calculate the present value of the primary balance is set to 10% (nominal) in the base case. The choice of discount rate is largely arbitrary, but is approximately consistent with the Treasury's estimate of the social opportunity cost of capital as being 8% real (New Zealand Treasury, 2008). An increase in the discount rate decreases the size of the tax asset and the spending liability and therefore decreases the dollar value of the risk. However, this risk as a percentage of tax revenue is higher because the risk exposure of GAAP net worth is unchanged, while the tax asset is smaller. A 6% discount rate would mean that annual volatility in comprehensive net worth would be $71 billion (2.6% tax change) and applying a 14% discount rate would mean an exposure of $23 billion (4.0% tax change). This compares with the base case value of $30 billion (3.2% tax change).