Investment and Asset-Liability Management
This domain tests how insurers match long-dated, interest-sensitive liabilities against market assets under Chinese solvency and investment rules. Questions typically combine duration and convexity mechanics with the regulatory limits on asset classes and the economics of participating and universal-life accounts.
Measurement toolkit
- Macaulay duration D = Σ t·PV(CF_t)/PV; modified duration D* = D/(1 + y) measures the percentage price change per unit yield change; convexity captures curvature for larger moves.
- Redington immunization requires PV(assets) = PV(liabilities), D_A = D_L and convexity of assets above that of liabilities.
- Cash-flow matching (dedication) removes reinvestment risk entirely but is capital-intensive and hard to achieve in thin Chinese credit markets.
Chinese regulatory and market context
- 保险资金运用 is governed by 资产负债匹配监管 with ceilings on equities, real estate and overseas assets, and by 偿二代二期 capital charges that differ sharply by asset class - a long-dated government bond can be cheaper in capital terms than an equity with the same expected return.
- Life liabilities routinely have durations of 15–25 years while domestic bond supply is concentrated at shorter maturities, creating structural duration mismatch and 再投资风险.
- In a low-rate environment the dominant risk is 利差损: guaranteed crediting rates on 分红险 and 万能险 exceed achievable asset yields.
- 万能险 accounts carry a 最低保证利率, a declared 结算利率 and a smoothing mechanism; the guarantee is an embedded option whose cost must be recognised.
Worked example
Assets are 100亿 with duration 6; liabilities are 90亿 with duration 12. Surplus is 10亿. Surplus duration = (100 × 6 − 90 × 12)/10 = (600 − 1,080)/10 = −48. A one percentage point fall in yields raises liabilities by roughly 90 × 12 × 0.01 = 10.8亿 and assets by 6.0亿, so surplus falls by about 4.8亿. To immunise, set asset duration to 90 × 12/100 = 10.8, which requires extending the portfolio. Note the negative surplus duration means the surplus is hurt by falling rates - the opposite of the intuition many candidates carry in.
Traps that cost marks
- Using modified duration in one part of the gap formula and Macaulay in another.
- Ignoring convexity when the yield shock exceeds about 100bp.
- Treating the 最低保证利率 as costless.
- Forgetting that solvency capital charges make pre-tax yield comparisons misleading.