ALM methodology: how Portfolio Lab measures assets against liabilities

Q: Which discount rate should I choose?

The usual choice is the yield of high-quality bonds with a maturity similar to that of the liabilities. A higher rate makes the liabilities cheaper, but does not change the simulated payments.

Q: Why does the funded status including contributions show more than 100% even though paths fail?

Because contributions that only arrive later cannot pay for payments that fall due early. The assets needed at return = discount rate take this order into account.

Q: What does “ever” mean for funded status < 100%?

The share of paths whose funded status is below 100% today or at at least one year-end, not only at the end.

Q: Why do all portfolios run on the same paths?

So that differences between the portfolios come from their returns and not from the luck of the draw.

Q: Is the required return before or after costs?

Before costs: the running costs you set are deducted separately in the calculation.

Advanced6 min read · updated 24 October 2026 · 5 sources

This ALM methodology describes the ALM (asset-liability management) page: pensions, a foundation's payouts or a lump-sum settlement are entered as a payment schedule, valued at a fixed discount rate and set against the assets. A simulation then shows, for every portfolio in the grid, how often all payments are made and how the funded status develops. The basic idea is explained in the article Asset-liability management.

Payment schedule

There are four types: liability and contribution, each either recurring or one-off. Recurring amounts are entered as an amount per year and paid monthly at one twelfth each; one-off amounts fall due at the end of January of their year, or at the end of the first simulated month in the current year. Amounts are in today's prices and rise with the growth rate per calendar year from today, for example 2% for pensions with indexation. The schedule starts at the end of the current month, which counts as a full month, and ends in December of the last payment year. Rows lying entirely in the past are skipped. The page's example: pensions of $60,000 a year over 30 years with 2% growth, a lump-sum settlement of $150,000 in ten years and sponsor contributions of $25,000 a year for ten years, with $1 million in assets.

Present value and duration

All valuations use a fixed discount rate r (default 3%, selectable from −2% to 15%), discounted exactly on a monthly basis. In practice, this is the yield of high-quality bonds of matching maturity. The duration following Macaulay (1938) is the average payment time in years, weighted by present values; the modified duration D / (1 + r) measures roughly by what percentage the present value falls when the interest rate rises by one percentage point.

PV = Σ CF_m × (1 + r)^(−m/12) D = Σ (m/12) × CF_m × (1 + r)^(−m/12) / PV

CF_m: liabilities in month m
r: discount rate p.a.

Funded status and assets needed

The funded status is the assets divided by the present value of the liabilities still outstanding. The including contributions variant adds the present value of the outstanding contributions to the assets. It can make the position look too good if liabilities fall due before the contributions arrive, because the assets must not turn negative in the meantime. The page therefore also states the assets needed at return = discount rate: the largest cumulative present value of all net payments up to any given month.

assets needed = max(0; max_k Σ_(m ≤ k) (liability_m − contribution_m) × (1 + r)^(−m/12))

The page also calculates the required return: the smallest constant return p.a. before costs at which every payment is made, found by bisection between −10% and 30% in 50 steps on a path with a constant return; the running costs are deducted along the way. If even −10% is enough, it shows “below −10%”; if even 30% is not enough, “above 30%”.

Interest rate risk

The interest rate risk table recalculates the present value exactly at discount rates −1, −0.5, +0.5 and +1 percentage point away, not via the duration. If rates fall, the liabilities rise, considerably so for long pension schedules. A bond portfolio with a similar duration would partly offset this; this is immunization following Redington (1952) and Fisher and Weil (1971). In the simulation, however, the discount rate stays fixed: rate changes only affect this table, not the paths.

Simulation

Every portfolio in the grid that has weights is simulated, reset to its weights every month. The page draws the returns using the methods of the Monte Carlo methodology for all portfolios jointly (the same months for the bootstrap, the historical covariance for the parametric methods), so that differences do not stem from the luck of the draw. The defaults are block bootstrap and 2,000 paths (500 to 5,000) with a fixed seed; at least 36 common monthly returns are required.

Apply the monthly return and deduct running costs: factor (1 − costs)^(1/12), which after twelve months gives exactly the annual costs (selectable from 0 to 5%).
Credit the month's contributions.
Pay the liabilities. If the assets are not sufficient, only the available part is paid; the rest is a shortfall, and the assets stay at zero. There is no borrowing and no additional funding.

Comparing the metrics

All payments made: share of paths without any shortfall.
Funded status < 100% and < 80% (ever): share of paths whose funded status is below the threshold today or at at least one year-end. If it is already below today, the figure is therefore 100%.
Funded status in 5 and 10 years: median and 10th percentile at year-end; the fan chart shows the median and the 25th–75th and 10th–90th percentiles for as long as liabilities are outstanding.
Shortfall: present value of the unpaid amounts, averaged only over the paths with a shortfall; plus the first year with a shortfall (median).
Final assets: median and 10th percentile.
Initial assets for the target success rate (default 90%): the smallest amount of assets today with which that many paths make all payments. It is searched for on the same paths, starting from the present value of the liabilities, first doubling and then halving to within 0.2%; above a hundred times the nominal liabilities, it counts as unattainable.

Place in the research

The idea of judging a portfolio relative to the liabilities rather than in absolute terms comes from the surplus optimization of Sharpe and Tint (1990); Waring (2004) applies the efficient frontier to the surplus of assets over liabilities. Portfolio Lab does not optimize this surplus; instead, it shows how existing portfolios cope with the payment schedule. If you are looking for a mix, you can set up several variants in the grid and compare them on the same paths; the optimization itself is described in the optimization methodology.

Limitations

The discount rate is fixed; in the model there is no link between interest rates and portfolio returns, even though that link is exactly what bonds live on.
No taxes; the growth rate is fixed and not tied to fluctuating inflation.
Payments are certain: the model knows nothing of mortality, lapses or additional funding from the sponsor.
All payments are discounted at a single rate; a real yield curve would value short and long payments differently, and the duration would depend on it as well.

Frequently asked questions

Which discount rate should I choose?