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What’s wrong with mean-variance optimization (MVO)?

Insurance Consulting and Technology
Insurer Solutions

By Ash Belur | September 13, 2021

Investors should be aware of the constraints the modelling technique can place on SAA in the prevailing economic and regulatory climate

A prolonged low yield environment and increasing regulatory demands continue to raise question marks for real money investors’ SAAs.

Insurers, for example, are having to consider increasingly complex metrics following the introduction of Solvency II and taking into account the impending introduction of IFRS 17. Meanwhile, we have seen UK institutional multi-asset funds grapple with an absolute or ‘cash plus’ return objective, EMEA family offices seek large private market and equity allocations given their high risk tolerance and low liquidity needs, and UK pension funds attempt to reduce the ‘home country bias’ by allocating less to UK equities.

Regardless of each’s unique objectives and constraints, conditions have typically driven a need for more sophisticated modelling to encompass a multitude of factors and deliver robust allocations.

But the need for that enhanced sophistication raises questions about the models themselves.

While many strategic asset allocation (SAA) tools typically use a deterministic mean variance approach to create optimal client portfolios, there are various known limitations to this approach. Despite its theoretical appeal, an uncritical acceptance of Markowitz’s MVO technique, can result in portfolios that are unstable and not always pragmatic. MVO relies on a mathematical framework that uses expected returns, standard deviations and correlations between the asset classes as inputs to assemble a portfolio of assets that maximises return for a given level of risk or, conversely, minimises risk for a given level of return.

The theory holds subject to assumptions which include that investors are expected utility maximisers, are risk averse, and either (1) asset returns are normally distributed or (2) utility functions are quadratic. In some cases, it also works approximately even when assumptions (1) or (2) are violated.1

But there are three reasons why MVO may fall short of expectations in the current economic and regulatory climate.

  1. Firstly, MVOs can produce unstable results. The method can be extremely sensitive to small adjustments of the inputs. Small changes in inputs can result in large changes in optimal asset allocations which is undesirable for institutional investors trying to communicate a long-term investment strategy. This instability also results in highly concentrated portfolios that do not offer adequate diversification benefits. This often leads to investors creating superficial constraints on particular asset classes. Or conversely, to overlook portfolios that could provide similar risk and return outcomes within the insurer’s appetite.

  2. Second, by construction, MVO generates portfolios with the highest expected return for the level of volatility. However, from a pragmatic point of view, investors typically need to transition from their current portfolios towards new SAAs. The transaction costs associated with such a transition are important. In fact, there may be portfolios just below the efficient frontier that are close to optimal in the MVO framework, are easier to communicate internally and offer lower transaction costs.

  3. Third, increasingly investors are seeking a broader measure of ‘risk’. For example, a more standard MVO model might have private equity with a high level of return per unit volatility. This may allow it to be introduced into optimal portfolios along the efficient frontier. However, this allocation to private equity will clearly increase the liquidity risk of the portfolio which may not be fully measured by the more blunt volatility measure. In addition to illiquidity, ESG (environment, social, governance) orientation will not be incorporated in a volatility measure. It also limits a broader optimization strategy that uses broader measures of risk such as Value at Risk, Conditional Value at Risk, the Solvency II Standard Formula market risk metrics, or a more customised measure.

Organisations will benefit from having their eyes open to these potential limitations.

So, given the limiting factors of MVO, what options are there for insurers trying to determine their optimum SAA? Our belief for some time has been that investors need greater choice and flexibility to develop resilient SAAs that better cater to their specific objectives, align with customer needs, that are practical to implement, and reflect the external environment.

The way to achieve this is by using more sophisticated modelling techniques that take explicit account of insurer-specific issues (such as IFRS 17 and Solvency II), to simultaneously explore the outcomes of multiple portfolio scenarios that can then be filtered across the risk-return spectrum. This may seem obvious but, until recently, achieving this has been difficult, time-consuming and costly – and all too often, more of an art than a science. However, for those who see the potential benefits of looking beyond MVO as a way to set the optimum SAA, our new cloud portfolio solution, Willis Towers Watson Optimum SAA, offers a cost-effective, robust and leading-edge alternative.

Footnote

1 Markowitz, H.M. (1952). “Portfolio Selection,” Journal of Finance, 7(1):77-91. https://www.math.ust.hk/~maykwok/courses/ma362/07F/markowitz_JF.pdf

Author

Director, Insurance Investment Team

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