Pension Asset-Liability Management and Liability-Driven Investment Optimization

Project Overview

This project develops an immunization strategy for a "closed and frozen" defined benefit (DB) pension plan. The objective is to construct an optimal fixed-income portfolio from 310 tradable securities to cover 80 quarters (20 years) of inflation-indexed benefit payments while minimizing the total economic cost to the plan sponsor.

The Challenge: Actuarial Complexity

Managing a pension fund requires balancing precise cash flow matching with rigorous risk and regulatory constraints:

• Liability Matching: Covering 80 quarters of expected benefit payments indexed to CPI inflation.
• Diverse Security Universe: Selecting from Nominal Treasuries, TIPS, Corporate Inflation-Protected Securities (CIPS), and Secondary Market Annuities (SMAs). Each bond class has certain features in cash flows and payment.
• Inflation Risk: Deflating nominal cash flows to match real liability values (used projected 3.0% per year for simplicity).
• Credit Risk Management: Assigning each bond a certain credit score and make sure the total dollar-weighted portfolio credit score under some threshold (used 0.4). Also, the ratings for bond has been adjusted, and the Default & Downgrade risk needs to be considered, risk reserve (cash) is needed when the portfolio grows

Methodology & Optimization Logic

1. Objective Function

The model utilizes Linear Programming to minimize the total cost ($Z$), defined as: $$Min \ Z = \sum (x_i \cdot P_i) + c_0 + c_{80}$$ Where:

• $x_i \cdot P_i$: Total cost of bond purchases.
• $c_0$: Initial cash deposit.
• $c_{80}$: Surplus funds remaining after 20 years (to minimize tax inefficiency).

2. Constraint Framework

• Benefit Coverage: Ensuring $(Cash \ Available)_t \geq (Benefit \ Payment)_t$ for all $t \in [1, 80]$.
• Allocation Caps: Diversification limits prevent over-exposure: TIPS (80%), Nominal Bonds (80%), CIPS (30%), and SMAs (10%)].
• Structural Cash Flow Limit: Nominal cash flows (non-indexed) are capped at 20% of total portfolio cash flows to control long-term inflation exposure.

3. Actuarial Techniques

• Sensitivity Analysis (Shadow Pricing): Evaluated the economic impact of relaxing credit quality and allocation constraints to identify cost-saving opportunities.
• Cash Reinvestment: Modeled excess funds (cash) earning a risk-free nominal interest rate between quarterly payment cycles (use 2.0% for simpliciy). Note that, the rate should be adjusted with the inflation rate

Tech Stack

• Language: R
• Solver: Rglpk (GNU Linear Programming Kit)
• Reporting: R Markdown & LaTeX

How to Run

1. Ensure BenefitPayments.txt, BondData.txt, NomCashflow.txt, and RealCashflow.txt are in the /data directory.
2. Run src/bond_optimizer.R to execute the solver and generate the optimal purchase list.