Why Mean-Variance Optimisation Isn’t Enough

Mean-variance optimisation remains one of the most influential ideas in portfolio construction.

It is elegant, intuitive, and practical. It offers investors a disciplined approach to evaluating the trade-off between expected return and risk, and establishes a common framework for comparing portfolios and identifying inefficient allocations.
However, for pension funds, endowments, or foundations, it is not sufficient.
The issue is not a mathematical flaw in mean-variance optimisation, but rather that it addresses a narrower problem than many long-horizon institutions encounter.
Traditional mean-variance optimisation is fundamentally a single-period framework. It poses a straightforward question:
What portfolio offers the best trade-off between expected return and risk over a specified horizon?
While valid, this does not address the full scope of challenges faced by long-term asset owners.
A pension fund invests over multiple periods. It must pay benefits over many years, respond to changes in funded status, manage contribution risk, maintain liquidity, rebalance after market shocks, and adapt as its liability profile evolves.
Endowments and foundations face similar challenges. They must support ongoing spending while preserving purchasing power for future generations. Early returns impact both future wealth and investment capacity. A significant drawdown today may not be offset by higher expected returns decades later.
These are inherently multi-period challenges, and a single-period optimiser cannot fully address these issues.

Why Mean and Variance Seem Sufficient

The usual theoretical justification for mean-variance optimisation comes from one of two assumptions.
The first is that returns are normally distributed.
If returns are fully described by their mean and variance, then an investor need not consider skewness, tail risk, or other distributional features.
The second is that investors have quadratic utility.
A simple quadratic utility function can be written as:
\[ U(W)=W−\frac{\gamma}{2}\cdot W^2 \]
Under this specification, expected utility depends only on the expected value and variance of terminal wealth. That creates a direct bridge to mean-variance analysis.
But quadratic utility comes with an uncomfortable implication. Its marginal utility is:
\[ U'(W)=1-\gamma\cdot W \]
Marginal utility therefore declines linearly with wealth. Beyond a certain point, it can become zero or even negative. In economic terms, the investor may appear to prefer less wealth once wealth becomes sufficiently high.
That is not a plausible description of most institutional investors.
More importantly, quadratic utility does not resolve the broader horizon challenge. It evaluates portfolios based solely on terminal wealth over a single period and does not account for the path of wealth, future contributions, liquidity needs, or the impact of current allocations on future opportunities.
The limitation is therefore not simply the shape of the utility function. It is the fact that the optimisation is static.

Long-Horizon Investors Care About the Path

For multi-period investors, the path of wealth is critical.
Two portfolios may share the same expected terminal wealth and variance, yet produce very different interim experiences.
One portfolio may experience a significant early drawdown, necessitating asset sales, increased contributions, reduced spending, or a shift in risk appetite. Another may provide a smoother trajectory, offering greater institutional flexibility.
A single-period framework may consider these portfolios equivalent. The institution, however, may not view them as such.
This is especially important when liabilities, spending, or cash flows are path-dependent. A pension plan with benefit payments cannot assume that all capital remains invested until the final horizon. An endowment with an annual spending rule cannot treat interim losses as irrelevant. A foundation may have grant commitments that continue even when markets fall.
In these contexts, risk extends beyond terminal volatility. Risk also encompasses the possibility of being forced to act at inopportune times.

The Opportunity Set Also Changes

Traditional mean-variance optimisation typically assumes that expected returns, volatilities, and correlations are estimated for a single horizon and used as fixed inputs.
In practice, however, the opportunity set evolves over time.
  • Expected returns change with valuations.
  • Interest rates change.
  • Liquidity changes.
  • Risk premia change.
  • Correlations often rise during stress.
  • Private-market commitments create future cash-flow obligations.
  • The liability profile itself evolves.
A multi-period investor therefore faces a series of interconnected decisions.
The portfolio chosen today determines tomorrow’s available wealth, which in turn influences future risk capacity. Market conditions will shape future opportunities, and rebalancing decisions depend on both factors.
This intertemporal connection is missing from a static mean-variance approach.

A Better Utility Framework

For long-horizon institutions, utility functions should more accurately distinguish among various dimensions of risk and time.
Constant relative risk aversion (CRRA) utility is one alternative:
\[ U(W)=\frac{W^{1-\gamma}}{1-\gamma} \]
This approach avoids the satiation issue inherent in quadratic utility and aligns risk aversion proportionally with wealth, rather than with an absolute wealth level.
However, even CRRA utility does not address all institutional challenges. If an investor values short-term consumption, long-term wealth, intertemporal substitution, and risk aversion differently, a more nuanced framework may be required.
Epstein–Zin preferences (recursive utility) are useful because they separate risk aversion (\( \gamma \) ) and willingness to substitute consumption across time (elasticity of intertemporal substitution-EIS, \(\Psi = \frac{1}{1-\alpha}\)).

\[ U_t = \left( (1-\beta) C_t^\alpha + \beta \mathbb{E}_t \left[ U_{t+1}^{1-\gamma}\right]^\frac{\alpha}{1-\gamma}\right)^\frac{1}{\alpha}\]
This distinction is important for long-horizon investors. An institution may be highly averse to permanent losses but willing to accept short-term volatility. A single quadratic objective does not capture this nuance effectively.
For pension funds, the objective may need to go further still. The relevant state variable may not be asset wealth alone, but funded status, contribution stability, benefit security, or a measure of solvency risk.
For an endowment or foundation, the objective may need to balance current spending with preservation of real wealth.
In other words, the appropriate utility function should align with the institution’s mandate.

From Portfolio Optimisation to Policy Optimisation

This represents the underlying challenge.
Mean-variance optimisation selects a portfolio. A long-horizon institution, however, needs to select a policy.
That policy may include:
  • a strategic risk target,
  • a reference portfolio,
  • rebalancing rules,
  • liquidity reserves,
  • spending or contribution policies,
  • private-market pacing,
  • hedge ratios,
  • and responses to changing funded status or market conditions.
These decisions interact over time and cannot be reduced to a single portfolio allocation determined at a single point in time.
A multi-period framework, therefore, poses a different question:
What sequence of portfolio decisions is most likely to fulfil the institution’s mandate across a variety of future states?
This is much closer to the actual challenge institutions face.

Mean-Variance Still Has a Role

None of this means mean-variance optimisation should be discarded.
It remains useful as:
  • a diagnostic tool,
  • a way to identify obvious inefficiencies,
  • a local approximation,
  • a method for comparing candidate portfolios,
and a component within a broader decision framework.
The mistake is not using mean-variance optimisation. The mistake is treating it as the complete solution.
For long-horizon investors, portfolio optimisation cannot be separated from future decisions, cash flows, liabilities, liquidity, and governance. The investment problem remains dynamic, even if the model does not reflect this.
A pension fund is not maximising one-period terminal wealth. An endowment is not investing for a single date. A foundation is not indifferent to the path between today and the final horizon.
They are managing a series of obligations and decisions over time. This requires more than simply identifying an efficient frontier. It requires a multi-period decision framework tailored to the institution’s mandate.

Comments

Post a Comment

Popular posts from this blog

Stockholm, Market Timing, and Broadening the Total Portfolio Conversation

Earlier this week, I visited Stockholm to participate in the Nordic Pension Tour. Thank you to Mirjam Guldemond, Sophie Baker, and Pensions & Investments for organizing an excellent program. It was one of those trips that reminds you why these conversations matter. Stockholm itself helped: the weather was beautiful, the city was full of that calm Scandinavian clarity, and even a short visit to the Nobel Prize Museum made it feel like a place where ideas still carry real weight. Before the World Pension Summit, I visited AP3, Alecta, and FTN. Each institution provided a unique perspective on how long-term asset owners think about their investment. At Alecta, I noted the central role of benchmarks. For liability-aware institutions, benchmarks are deeply embedded in the investment process. While this can be helpful, it raises an important question: when does a benchmark clarify the mandate, and when does it begin to replace it? At FTN, together with AP7, we discussed defined contribut...
Read more

The Mandate Comes First

Image
One of the more enduring rewards of this year’s ALTSLA, once again, was the people. The quality of the conferences is usually assessed by the quality of their panels, the relevance of the themes, or the prominence of the speakers. All of that matters. But what stays with me most is usually the less formal part — the conversations between sessions, the chats over coffee, the passing comments that turn into more substantive discussions. For all the attention this industry gives to ideas, it is people who ultimately shape them. That was on my mind as I rode the train from Los Angeles to San Diego after the conference, enjoying the improbably warm weather compared with the East Coast. Over time, ALTSLA has become something of an annual ritual, and the two days of rest that follow it have become part of that rhythm as well — an opportunity to step away from the noise, reflect, and reset. Looking out at the ocean, I found myself returning to a question that strikes me as basic, but not basic...
Read more

Leadership Starts with Motivation

The older I get, the more I think leadership is less about authority and more about motivation. A leader’s job is not just to set direction, make decisions, or evaluate performance. Those things matter, of course. But if the people around you no longer feel motivated to contribute, improve, and stay, then a lot of the rest begins to break down. Motivation has never meant just compensation. Pay matters. Performance-based rewards matter. Fairness matters. But motivation also comes from something more basic: being treated with respect, being seen as an individual, and having a working relationship with your manager that feels human rather than mechanical. Every workplace is, in the end, a human system. People may stay for a while because of prestige, compensation, or obligation. But very few people do their best work for long in an environment where they feel invisible, unfairly treated, or repeatedly drained by the people around them. That is why I think good leadership requires more tha...
Read more