Risk aversion matters: life-cycle design

Life-cycle funds – also known as target date funds – de-risk the investor’s pension savings account as they progress toward retirement. Underlying this de-risking is the assumption of wage income that plays the role of a low-risk asset. This allows more risk to be taken in the pension account when this asset is of greater value early in the life-cycle. As the investor progresses through their working years, the value of the wage-related asset declines while the value of the pension account grows. Growth asset exposure in the pension account thus needs to be wound back to keep risk and return in balance.

A key issue in life-cycle fund design is how to set the ‘glide path’ for switching from growth to defensive assets over time. Recently, me and my colleagues considered the potential role for pension fund balance and investor risk aversion in determining the optimal glide path (How sub-optimal are age-based life-cycle investment products?). We found that accounting for both aspects can improve life-cycle fund design, but that risk aversion is the far more important of the two.

The set-up was basic, but sufficient to draw out the key concepts. We modelled an investor with known wage income of which a fixed percentage is contributed to their pension account over 40-years until retirement. The pension account could be invested in a risk-free asset or equities, with the latter generating a higher but random return. The distribution of balance at retirement was evaluated using a power utility function, which considers outcomes directly without assuming any particular target.

We analysed 13 investment strategies. The benchmark strategy was optimal under the set-up, and dynamically altered the asset mix in response to fluctuations in balance. Four strategies were proposed that pre-set the glide path with reference to projected balance levels. Five life-cycle strategies were selected to represent those seen in the market, including some actual funds from four countries. Three constant weight strategies were also examined.

With regard to balance, our main interest was investigating the importance of dynamically adjusting the asset mix in response to fluctuations in balance. We found that these dynamic adjustments did indeed add value, but the gains were relatively modest. Further, these gains could be mostly captured through any one of our proposed strategies. The results suggest that considering balance may be only of modest relevance for life-cycle fund design, but with a caveat.

Of far more importance was whether the risk aversion assumption on which the strategy is based happens to align with the risk aversion of the investor. If (say) a strategy designed for low risk aversion was taken up by an investor with high risk aversion, the utility loss could be similar to forfeiting one to two years of wage income. It turns out that the general level of exposure to equities over the accumulation phase is more important than the shape of the glide path. That is, an investor with high risk aversion will prefer to hold less equity exposure overall. A glide path designed around low risk aversion would be too elevated for such an investor, even if the broad trajectory was about right.

Our research raises a note of caution over offering a single, one-size-fits-all life-cycle fund. Such a fund may be suitable for some investors but not others, depending on whether their willingness to take on risk happens to match the strategy design. Nevertheless, a single life-cycle product is offered by most fund providers in three of the four countries from which we drew the representative life-cycle funds: US, UK and Australia. The exception was Denmark, where it is more typical to offer a range of life-cycle funds.

Providers have embraced the need to cater for differences in risk aversion for constant weight strategies under banners like conservative/balanced/growth/high growth. Doing the same for life-cycle funds is rarer. It is almost as if there is a presumption that glide path de-risking suffices to address risk. Our research questions any such presumption.

One caveat is in order. While our finding that risk aversion matters should be robust to changes in the set-up, the same need not be true for the findings regarding balance. Here our results will be driven in part by the use of power utility. If the investor had a target in mind – such as requiring a certain balance to support a desired level of retirement income – we suspect that dynamically responding to changes in balance may make a greater difference.

The research, which was written by Geoff Warren and Gaurav Khemka from ANU together with Mogens Steffensen of the University of Copenhagen.