Modeling Long-Horizon Pension VaR Across Assets and Liabilities
Summary
The note frames pension risk as uncertainty in capital, defined by the difference between assets and liabilities. A long-horizon VaR estimate must account for the fact that these sides evolve differently: assets are often fund investments that managers rebalance, while liabilities are obligations whose duration declines as payments are made. Future obligations may also arise but are not yet known.
The proposed approach simulates assets using a stochastic model that reflects typical fund rebalancing and investment strategy. It projects liability cash flows while incorporating interest-rate and longevity uncertainty, potentially through Monte Carlo simulation. This is presented as more representative than treating both sides as static holdings. The source offers a conceptual recommendation rather than a calibrated model, validation, or numerical results; assumptions about future contributions, new obligations, manager behavior, and liability risks would materially affect the estimate.
Key ideas
- Pension capital risk depends on the joint evolution of assets and liabilities.
- Fund assets should be simulated with rebalancing and investment behavior represented.
- Liability projections should reflect cash flows and relevant interest-rate and longevity uncertainty.
- Static buy-and-hold assumptions may not represent how a pension balance sheet evolves over a long horizon.
- The suggested framework is conceptual and requires assumptions about future obligations and investment practices.
Tags
Full text
# How is VaR calculated for a pension company? # How is VaR calculated for a pension company? A pension company has an asset side and a liability side, and some capital. The key equation is $$A = L + C$$ Let's say the company wants to compute a 10-year VaR of its capital C. Normally, this would be easy. We just simulate the assets forward in time, and simulate the liability forward in time, and compare. But, for a pension company, the assets are typically fund investments. The liability is typically a set of obligations, which can be represented as a bond. This means that as time goes by, the funds, which are managed by somebody else, will regularly rebalance, react to changing market conditions, buy new bonds and get rid of old ones, and so on, all to ensure that the risk profile is kept of a similar level. But as time goes by for the liability, it's risk profile changes drastically, as obligations are met and the duration profile goes down. Obviously new obligations will arise in the future, but we do not know what these "new obligations" are just yet, so we cannot model them. How does a pension company then compute its VaR? Does it assume that both the assets and liabilities are static buy-and-hold investments, over 10 years? Or does it simulate the assets as the fund investments that they are, while keeping its liability static? The former seems more comparable but not realistic since we do not hold the asset-side funds' underlying positions directly. The latter seems less comparable but is what would actually happen if the pension company just waited 10 years. ## Answer by eFinancialModels (score 0) https://quant.stackexchange.com/a/85865 To compute a 10-year VaR for a pension company, it is essential to capture the dynamic nature of both assets and liabilities. A practical approach is to simulate the asset side using a stochastic model that mirrors the rebalancing and investment strategies typical of fund investments. For the liabilities, you might use a cash flow projection model that incorporates known obligations and adjusts for expected changes in interest rates and longevity risk. This could involve Monte Carlo simulations to reflect the uncertainty in future obligations and interest rates. By doing so, you account for the evolving nature of both sides of the balance sheet, rather than assuming a static buy-and-hold strategy, which is less realistic. This approach should provide a more accurate reflection of the pension company's potential risk exposure over the 10-year horizon.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.