Investing for retirement provision: the latest research

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A summary of the most recent research on retirement investing presented at the Inquire Europe seminar in Frankfurt in October 2016.

The recent Inquire Europe seminar in Frankfurt brought together almost a hundred investment professionals and academics to discuss the latest research on retirement investing. It was a special seminar. The Inquire organisation gave me and my colleague Raul Leote De Carvalho slots to present two of our most recent papers of relevance to the conference’s theme.

The first was recently published in the Journal of Investment Strategies. It proposes a new approach to protecting the downside of an investment portfolio. An upcoming post on this blog will be devoted to this.

The other presentation was about decomposing a defined benefit (DB) pension fund’s funding ratio risk into its main risk components. This research was recently accepted by the Journal of Portfolio Management for publication in 2017. Two posts were written on this topic (see part 1 and part 2).

Below are summaries of the key presentations at this seminar. First, I present a brief introduction to some academic principles of importance in the context of retirement investing.

Investing for the long run: the Samuelson-Merton model

In 1969 the later Nobel laureates Samuelson and Merton each wrote in the same issue of The Review of Economics and Statistics closely related articles (here and here) about “Lifetime Portfolio Selection”. Their starting point is a non-working individual with an initial financial capital that is allocated between a low-risk asset such as cash or a AAA rated bond and a risky asset such as equities. Periodically, some of the capital is released and used for consumption and paying the bills. Some more simplifying assumptions were made such as that one cannot forecast financial market returns in the shorter term.

In the Samuelson-Merton model the optimal relative asset allocation weights are constant through time given the investor’s risk aversion. They depend neither on the investor’s age nor on the available capital. This is an important fundamental result. At first sight it seems at odds with reality. Life-cycle or target-date funds and defined contribution (DC) plans work with conventional life-cycle allocations, often called glide-paths, that involve decreasing the relative weight to risky assets when the investor gets closer to the retirement date.

Does this then imply that the Samuelson-Merton model is of no use to practitioners? Well, not at all. In their model, a conventional glide-path can, for instance, still be justified if investors become more risk-averse as they get older. However, the academic literature mainly followed another path, namely one which integrates human capital into the capital concept. Obviously, this expansion makes the approach much richer in terms of its practical relevance. Someone’s human capital is namely nothing else than the present value of all (expected) future labour incomes. So, typically, human capital will be large at a young age, falling over time to zero at retirement. The conventional glide-paths can be justified by assuming that human capital behaves like a low-risk asset (see insert).


Justification of conventional glide-paths

When someone’s future labour incomes are (close to) certain, their present value, i.e. the human capital, behaves like the present value of a low-risk AAA rated fixed-income stream. Viewing human capital like this thus implies that young investors — via their human capital — already start with a high allocation to low-risk assets. Therefore, to comply with the Samuelson-Merton constant mix rule applied to the total capital, young investors have to allocate a large proportion of their financial capital to high-risk assets. As an  investor gets older, his human capital becomes smaller, while his financial capital should grow. Hence, to stay compliant with the constant mix rule, the proportion of the financial capital allocated to high-risk assets has to decline (the glide-path) over time. Upon retirement, the human capital segment is zero. Thereafter, the distinction between financial and total capital has disappeared so that the constant mix rule now applies to just the financial capital allocations.

I note that the glide-path of the allocation to high-risk assets would be reversed and become an ‘ascending path’ if for some reason someone’s human capital behaves more like high-risk assets. That would typically be the case for people working in the financial services industry, where incomes are often linked to the performance of risky assets such as equities.


The latest research

The Samuelson-Merton model and subsequent refinements make it clear that a one-solution-fits-all approach is in general not optimal for everybody. Crucial aspects deal in particular with someone’s risk aversion level, with someone’s human capital properties, with the extent to which the decision between consuming more or saving more is included and, finally, with being able to forecast market returns in the short term, i.e. market-timing. With these principles in mind, let us now turn to the recent research presented at the Inquire seminar.

New solution procedure allowing market-timing

In their presentation David Jessop of UBS and Professor James Safton of Imperial College London discussed a new framework for finding optimal glide-paths solutions that allows scaling up the dimensionality of the problem. A single household case study was presented. Three asset classes — cash, bonds and equities — were used. Labour income was modelled as a function of aggregated real income and random shocks. The new procedure allows the incorporation of dynamic allocation decisions on the basis of views on market-timing. Additionally, the model was further expanded by assuming some predictability for bond and equity markets via predictor variables (term spread, dividend yield and GDP).

The main takeaways are threefold. Firstly, on average around 20% of the annual income should be reserved for retirement investing. Secondly, the long-run strategic allocations, which ignore return predictability, bestow a greater weight to bonds than is typically observed at conventional glide-paths. The intuition behind this is that bonds provide, over the business cycle, a better hedge than equites against drops in aggregated real income and interest rates. Lastly, during the post-2008 financial crisis recovery the modelled return predictability would have implemented an equity overweight at the expense of bonds.

Amalgamating more individual information

Magnus Dahlquist, professor at the Stockholm School of Economics, presented recent research that integrates realistic cases of individual heterogeneity with a more or less standardly enriched Samuelson-Merton model in the context of a DC pension plan. The research is based on unique Swedish data for more than 300 000 individuals covering holdings in a DC pension plan, investment holdings outside the pension system and social information such as date of birth, education level, labour income and financial wealth. Investors were divided further into subgroups depending on whether they opted for the default allocation offering in the DC plan.

The study shows that capturing detailed individual information improves expected pensions. For the defaults, age is indeed important when determining the optimal size of the equity exposure. Two other characteristics are also important: the size of the individual’s DC account and equity ownership outside the pension system.

Investing in the decumulation phase

Using the Samuelson-Merton model as a starting point, Theo Nijman, professor of Tilburg University in the Netherlands, examined various decumulation set-ups. The key results are as follows. Firstly, some equity risk-taking is optimal in most models used in academia. Secondly, the optimal decumulation rate is lower than the asset allocation expected return. Lastly, Nijman’s opinion is that the Samuelson-Merton approach implies excessively large, sudden negative pension shocks that could easily lead to a lower pension for many years. Most people are strongly averse to this outcome. He therefore suggests to take such habit formation into account in the decumulation set-up, for instance, by smoothing shocks over five years or so.

Protection overlays for bad times

Nijman’s presentation touched upon dealing with unpleasant events. The same issue was addressed in two other presentations. Professor David Laibson of Harvard University and Dr Mark-Jan Boes of VU University Amsterdam both argued that DC solution designs can be improved by implementing a protection overlay. Some part of the regular DC inflows should then go to the sub-account. However, they each advocated different approaches.

Laibson developed his idea for the US context where individuals are often allowed to withdraw money from their retirement plan at the accumulation stage. This offers a cheap funding option in comparison to highly expensive commercial borrowing contracts. In this way a lot of retirement savings leak away since such leakage is often aggravated by a tax-favourable treatment. Laibson’s recommendation is to put 85% of an individual’s retirement capital in a lock-box account. The remaining 15% should then go into a lightly penalised rainy-day account to provide liquidity for emergency expenses.

In his talk Boes made a strong case for adding on top of the ordinary assets of a DC pension fund a collective and cautiously invested protection pool of capital. Around 10% of the DC contributions should enter that extra protection fund. This funding is to be employed whenever a generation vintage threatens to receive a pension that would structurally be below some pre-determined floor, for example, below 70% of an individual’s average past salary. The underlying idea is that intergenerational return- and risk-sharing leads in the long run to improved pension results at the aggregated level.

Final remarks

In an earlier blog post the recent academic position on how to organise retirement investing from the perspective of a DB pension fund was discussed. The subject of this post was the way in which it should be dealt with from an individual contribution scheme or a collective DC pension fund. Recent research discussed in this post illustrates once again that academia can contribute a lot in this area by providing interesting practical ideas for improving the set-up of DC-type solutions.


Erik Kroon

Research Manager Financial Engineering

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