Can someone walk through surplus optimization for a pension fund step by step?

Surplus optimization is MVO applied to *surplus returns* instead of *asset returns*. The surplus is the difference between plan assets and plan liabilities. **Setup:** Let's say a pension fund has: - Assets: $800M - Liabilities (PV of obligations): $700M - Surplus: $100M - Funded ratio: 800/700 = 114% **Surplus Return:** R_surplus = R_assets − (L/A) × R_liabilities Where L/A is the liability-to-asset ratio (700/800 = 0.875) **How It Differs from Asset-Only MVO:** In regular MVO, you maximize: E(R_portfolio) − (λ/2) × σ²_portfolio In surplus optimization, you maximize: E(R_surplus) − (λ_s/2) × σ²_surplus **The critical difference:** Surplus volatility depends not only on asset risk, but on the *correlation between assets and liabilities.* Assets that are highly correlated with liabilities *reduce* surplus volatility, even if they're risky in isolation. **Practical Example:** Consider two asset classes: - **Long-duration government bonds:** 4% expected return, 8% volatility, but 0.9 correlation with pension liabilities - **Emerging market equities:** 9% expected return, 22% volatility, 0.1 correlation with liabilities In an asset-only MVO, EM equities look attractive (high return). But in surplus optimization, long bonds are far more valuable because they *hedge the liabilities.* When interest rates fall and liabilities increase, long bonds also increase, stabilizing the surplus. **Three-Step Process:** 1. Estimate expected returns, volatilities, and correlations for all asset classes *and* the liability portfolio 2. Convert asset-space inputs to surplus-space inputs using the surplus return formula 3. Run MVO on surplus returns with the pension fund's surplus risk tolerance **The Liability Glide Path:** As the funded ratio improves, the fund should systematically shift from return-seeking assets (equities) to liability-hedging assets (long bonds matching liability duration). This is the "glide path." A fully funded plan should be nearly 100% in liability-hedging assets. | Funded Ratio | Liability-Hedging | Return-Seeking | |---|---|---| | 80% (underfunded) | 40% | 60% | | 100% (fully funded) | 70% | 30% | | 120% (overfunded) | 90% | 10% | **Exam Tip:** If a vignette describes a pension fund, expect to identify whether surplus optimization, hedging/return-seeking, or a glide path is the most appropriate technique. Explore pension-focused asset allocation in our CFA Level III course.