Target date: “There is ample room for added value between one size-fits-all solutions and do-it-yourself approaches to long-term investment decisions”

Retirement systems in most developed countries have experienced a substantial transformation in recent years, with a shift from defined benefit (DB) plans to defined contribution (DC) plans. Consequently, employees now increasingly rely on their own savings and investment decisions to fund their retirement. This is a serious concern, not only because of the induced risk transfer, but also because individual investors typically lack investment expertise and display a great deal of inertia. In response, the asset management industry has started to look into dedicated solutions to investors’ long-term investment needs, and one key innovation is the development of ‘life-cycle’ or ‘target date’ funds (TDF), which propose changing the stock exposure of the fund as a function of time remaining until target maturity date.

This is somewhat reminiscent of the rule of thumb put forward by Shiller’s working paper for the National Bureau of Economic Research, ‘The Lifecycle Personal Accounts Proposal for Social Security: A Review’, advocating a percentage allocation to equity given by 100 minus the investor’s age in years. This approach has enjoyed a great deal of success, with total TDF assets having multiplied more than 12-fold, to more than $180bn (€126bn), between 2002 and March 2008.

There is an intuitive justification to the advocated decrease in equity allocation: the presence of mean reversion in equity returns would justify that equities are less risky for the long term, and that the allocation to equities should decrease when approaching the horizon, reducing the impact of a fall in the stock market just before retirement. But it hardly seems plausible, on the other hand, that an allocation strategy depending purely on time horizon (time dependence), regardless of what happens in the economy (state independence), should be truly optimal. To address these questions, the EDHEC Risk and Asset Management Research Centre recently launched a research chair, supported by UFG, dedicated to the analysis of life-cycle investing. More specifically, the purpose of the initiative is to analyse the optimal dynamic asset allocation strategy that takes into account the stochastic features of the investor’s investment objective as well as the random features of the assets held in his portfolio. These questions can be analysed within the dynamic portfolio optimisation framework of Merton’s work, which opened a world of opportunities for more subtle dynamic asset allocation decisions, involving adjustments to the asset mix as time goes by.

Following Kim and Omberg’s 1996 paper, Dynamic Nonmyopic Portfolio Behavior, we propose to model a stochastic equity risk premium with a mean-reverting component. In the context of this model, we are able to show, on the one hand, that the optimal allocation involves not only a deterministic decrease of the al location to equity as the investor gets closer to the time-horizon, but also that the optimal strategy displays a state-dependent component, suggesting that the allocation to equity should be increased (respectively, decreased) when equity has become cheap (respectively, expensive), as measured through a proxy like dividend yield or price-earning ratios.

Our preliminary results suggest that omitting the state-dependent element in life-cycle investing, as done by available target date funds, leads to a severe efficiency cost (see Cairns, Blake and Dowd’s 2006 paper, Stochastic Lifestyling: Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans, for similar findings). To gain more intuition behind these results, we have developed a simple illustration, based on the following three heuristic long-term investment strategies over the period ranging from January 1973 to December 2008:

• A fixed-mix allocation strategy with 50% stocks and 50% bonds;
• A deterministic life-cycle strategy that starts at 90% stock, decreasing by 10% every three years;
• Stochastic life-cycle, where we add a stylised state-dependent element to the deterministic scheme (when the log dividend yield is above/below one standard-deviation, we add/subtract 40% to the equity allocation given by the deterministic scheme)

Overall, the stochastic strategy is similar to the deterministic strategy in that the returns of both become smoother when getting closer to the retirement horizon, but the state-dependent version strongly dominates the deterministic approach by avoiding buying and selling at the extremities.

More generally, relaxing the assumption of a self-financed portfolio to account for the presence of contribution and liability streams only reinforces the need to incorporate state dependencies. In this setting, the optimal asset allocation strategy involves a state-dependent allocation to three building-blocks:

• A performance-seeking portfolio, heavily invested in equities, but also in bonds and alternative classes such as real estate;
• An income-hedging portfolio, heavily invested in cassh but also invested in equities, which exhibit appealing wage inflation hedging properties, especially over long horizons;
• A pension-hedging portfolio, heavily invested in bonds for interest rate hedging motives, and also in real estate for inflation hedging motives

In infancy, the income hedging fund is the dominant low-risk component of the investment strategy, but as the retirement date approaches, there is a gradual, albeit non-deterministic, switch from income hedging into pension hedging. Again, this switching only superficially resembles deterministic life-cycle investing; instead of moving from high-risk assets to low-risk assets, as in the case of deterministic life-cycle investing, the optimal stochastic lifestyle strategy involves a switch between different types of hedging demands. Moreover, this switch takes place in a stochastic state-dependent, as opposed to deterministic, manner, as a function of the current level of various variables of interests.

Implementing such optimal strategies is a serious challenge, which requires a finer classification of plan participants based on factors other than the age of the participant. The challenge is to design a parsimonious partition of the investors/states-of-nature that will allow for different allocation strategies.

Broadly speaking, there are two sets of attributes that should be used to define the various categories of asset allocation decisions, namely the subjective attributes and the objectives attributes. The subjective attributes are unique to each investor and include, in addition to age - the sole determinant in current TDF products - risk aversion as well as funding status, defined as assets (financial assets, to which is added the present value of future contributions) in excess of required pension benefits.

The objective attributes apply for all investors, and relate to market conditions, with a proposed asset allocation decision that will be a function of the following three state variables: the current (estimated) level of risk premium (typically proxied by a function of dividend yield or price-earning ratios), the current level of interest rates and the current volatility level. A discrete partition of the states of the world can be used for these three variables, with suitably defined high, median and low values for risk premium, interest rate and volatility levels.

Overall, our research has significant potential implications for the design of stochastic, state-dependent, asset allocation policies, which stand in contrast to the deterministically time-dependent allocation strategies currently implemented in the context of target date funds. We strongly believe that there is ample room for added value between one-(allocation)-size-fits-all (investors with same age) solutions and do-it-yourself approaches to long-term investment decisions.