Mean-Variance Optimization, Pension Funding, and Return Assumptions
Summary
The document questions whether mean-variance optimization (MVO) works in practice and whether it explains the underfunding of defined benefit pension plans. The response argues that Markowitz portfolios can be numerically unstable, especially beyond two assets, while a two-asset case may help justify a familiar stock-bond allocation. It also attributes pension problems to governance, difficult funding mandates, and optimistic actuarial return assumptions.
The answer cites historical real returns for stocks and bonds, uncertainty over multi-decade horizons, and a shift toward lower expected equity returns. It describes pension plans adopting very high return assumptions in the late 1990s and alleges that some sponsors used those assumptions to divert funds. These claims are presented without supporting citations or a detailed empirical comparison of successful and underfunded funds. The response offers a critique of MVO’s practical stability and pension governance, but its historical and causal claims should be treated as claims made in the document, not a comprehensive evaluation.
Key ideas
- The response says MVO solutions can be numerically unstable, with greater stability in a two-asset case.
- It links pension underfunding to governance challenges and mandates that promise returns from risky investments.
- The answer argues that optimistic return assumptions can affect pension funding decisions.
- It emphasizes uncertainty in long-term asset returns and changing expectations for future returns.
- The document does not provide a comparative study of pension funds that succeeded with MVO.
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Full text
# Does mean variance optimization work in real life? If so, why are defined benefit pension funds so underfunded? # Does mean variance optimization work in real life? If so, why are defined benefit pension funds so underfunded? I understand the theoretical underpinnings of mean variance optimization and modern portfolio theory. But does the application of modern portfolio theory work in real life? If so, why are all the defined benefit pension funds so underfunded when they have all been applying this tool to construct their portfolios? Can anybody point to a pension fund or other institutional investor that has successfully applied this in constructing their portfolio to achieve their return goals? What are they doing differently from the majority of pension funds that are underfunded? ## Answer by Sebapi (score 6, accepted) https://quant.stackexchange.com/a/59377 You are asking two questions: - whether MVO works in real life and portfolio managers actually use it? - whether defined benefit schemes use this tool? Concerning 1. the answer is generally no, although it kind of works with 2 assets. The elegant Markowitz solution showing the theoretical Sharpe and minimal variance optimal portfolio are numerically unstable. This being said, the method is more stable with only two assets so that the 60/40 portfolio can be justified using an MVO and long term historical returns and correlation parameters. Concerning 2, defined benefit schemes are a disappearing species because of the intractable governance problem that they raise. Some DBS such as the French pension is financed by future workers contribution. There is no pretense of funding them with investment income. Some other DBS were set up with the contradictory mandate to produce guaranteed returns by investing funds from risky assets. ### Stock returned around 6% above inflation over the last 100 years According to data published after 2000 (in The Triumph of the Optimists), Equities returned 7% over inflation in the US and 5% over inflation in the world. Bonds returned 5% over inflation in the US and nearly 0 or negative returns in other countries (WWI and WWII led to inflation). But there is a lot of uncertainty about returns over 40 years. One should only withdraw 2% per year if one wants an endowment to last forever. ### Forecasters now assume 3% long-term return above inflation Given lower long-term economic growth and high stock valuation at the moment, one could expect as low as a 3% long-term annual return over inflation on stocks. Investing in bonds when they have below-inflation returns no longer makes sense at the moment. It should be understood that bonds had yield above 5% guaranteed in a gold backed currency for 300 years, and it is only since 1970 that currencies are no longer backed by gold. We don't have long term bond performance data under this regime. ### DBS switched to 9% return assumptions in the late 90s Some DBS decided to use rates above 9% in 1999: Actuaries for many cities in the US with DBS for their civil servants were also convinced to switch from a 7% to a 9% return assumption. The politicians effectively raided the pensions funds and spent them on their pet projects. While investment banks were sued and paid high damages for convincing retail investors to convert their DB pension into DC stock pensions on the assumption that stocks would "yield" above 10% no one got sued in the case of DB. The pension investment committee and actuaries were all investment professionals, but the long term stock return data was not published yet. In short, the schemes were set up with an impossible mandate making them subject to actuarial manipulation from their inception. Statistics that are now widely publicized were not available when these schemes were set up.
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