Asset-liability management: aligning your wealth with future spending

Advanced7 min read · 6 sources

In asset-liability management (ALM), the focus is not on return but on whether your assets will cover future payments. Pension funds and insurers work this way, and the same principle helps private investors who want to supplement their retirement income, fund an education or pay off a mortgage. Risk here does not mean fluctuation; it means running out of money at the end.

Present value of the liabilities

With only $100,000, the funded status would be 76.5%. The assets would then have to earn more than the discount rate: the required return at which the present value comes to exactly $100,000 is 4.97% a year. That is considerably riskier.

The present value answers the question: how much money would I have to invest safely today to make all future payments? The discount rate should therefore be the yield on safe investments of matching maturity. If you discount at the expected equity return, you make the gap look smaller and hide the risk in the rate.

Funded status and surplus

• Funded status above 100%: the goal can be reached with safe investments. The surplus can take on risk.
• Below 100%: it cannot be done without risk, or the payments have to be reduced.
• Interest rate changes alter the present value. When rates rise, it falls; bonds with a matching duration move in step and protect the funded status.

In the example, the surplus is $250,000 − $130,754 = $119,246. Sharpe and Tint (1990) proposed optimizing portfolios not on their own return and volatility, but on the return and volatility of this surplus. An investment is then risky if it behaves differently from the liabilities. For a pension fund, a long-dated bond can be the safest investment even though its price fluctuates strongly.

Interest rate risk: the duration of the liabilities

The duration of the liabilities is the average timing of the payments, weighted by their present value. It shows how strongly the present value reacts to interest rate changes, just as with a bond. The concept goes back to Macaulay (1938).

If, on the other hand, the $250,000 were invested in bonds whose payments exactly match the withdrawals, their value would rise in step by 15.0% as rates fell, and the funded status would stay at 191.2%. This principle is called immunization: Redington (1952) described it for life insurers, and Fisher and Weil (1971) showed how to protect a bond portfolio against interest rate changes with a matching duration.

Simulation instead of a point estimate

How often the funded status falls below 100% in bad markets is shown by a Monte Carlo simulation with the payments as outflows: shortfalls per year, the starting assets needed for a desired success rate, and a comparison of different portfolios. The simulation replaces the single discount rate with many possible return paths and shows how much security a larger starting amount or a more cautious investment buys.

Advanced: liability-driven investing

Institutional investors often split their assets into two pots: a hedging portfolio that replicates the liabilities (bonds with matching duration, and inflation-linked bonds for inflation-linked payments), and a return-seeking portfolio of equities and other risky assets that is meant to grow the surplus. The size of the hedging portfolio depends on the funded status and on the capacity to bear risk.

Waring (2004) extends the idea: liabilities have two durations, one with respect to real interest rates and one with respect to inflation. Pensions that rise with inflation behave differently from fixed payments; equities have a different sensitivity to inflation than nominal bonds. The hedge should therefore match both durations: first the surplus is optimized, then the durations are adjusted.

For private investors, there is one more item: human capital, i.e. the present value of future earned income. Cocco et al. (2005) show that a secure income acts like a bond within total wealth. If you are young and have a stable salary, you can therefore hold more equities; with age, human capital shrinks and the optimal equity allocation falls (see equity allocation by age).

ALM in five steps

1. List the payments: which expenses are due and when, recurring (supplementing retirement income, long-term care) or one-off (college, home renovation, remaining mortgage debt)? Amounts in today's prices with a realistic rate of increase.
2. Calculate present value and funded status: using the yield on safe investments of matching maturity. If the funded status is well above 100%, the plan can be achieved even with little risk.
3. Secure what has to be safe: invest the part of your assets that covers the present value of the essential payments in bonds or fixed-term deposits with matching maturities.
4. Invest the surplus: anything beyond that can take on risk, for example in a broadly diversified equity portfolio. A loss then does not hit your basic provision.
5. Review regularly: update the funded status, interest rates and payment schedule once a year. If the funded status rises, you can secure more; if it falls, payments or risk have to be adjusted.

Limitations

• Predictable payments: ALM works best when the amount and timing of expenses are well known. Uncertain expenses need buffers.
• Discount rate: a fixed rate is a simplification. In reality it changes constantly, and the funded status changes with it.
• Inflation: if payments are planned in today's prices, the investment has to preserve real value. Nominal bonds alone do not protect against rising prices.
• Longevity: if you live longer than planned, you have payments that are missing from the plan. A lifetime annuity can cover this part.

How Portfolio Lab calculates

The ALM page records liabilities and contributions as a payment schedule: amounts per year in today's prices with annual indexation, recurring payments monthly at one twelfth each, one-off payments in January of the respective year. Using a fixed discount rate, it calculates the present value (discounting with (1 + r) to the power of months / 12), the Macaulay and modified duration, the funded status (optionally including the present value of future contributions) and a table for interest rate changes of ±0.5 and ±1 percentage point. On top of that come the assets needed if payments fall due before the contributions, and the required return. The simulation uses the same methods as Monte Carlo: if money runs short, only the available part is paid and the rest is reported as a shortfall. Up to three portfolios can be compared, including the starting assets for a target success rate. The discount rate stays fixed in the simulation. More in the ALM methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.