Life-cycle funds: Much Ado about Nothing?

Abstract

The core idea of life-cycle funds or target-date funds is to decrease the fund's equity exposure and conversely increase its bond exposure towards the fund's target date. Such funds have been gaining significant market share and were recently set as default choice of asset allocation in numerous defined contribution schemes or related old-age provision products in several countries. Hence, an assessment of life-cycle funds' risk-return profiles -that is, the probability distribution of returns -is essential for sustainable financial planning of a large group of investors. This paper studies the risk-return profile of life-cycle funds in particular compared to simple balanced or lifestyle funds that apply a constant equity portion throughout the fund's term instead. In a Black-Scholes model, we derive balanced funds that reproduce the risk-return profile of an arbitrary life-cycle fund for single and regular contributions. We then analyze the accuracy of our results under more complex asset models with stochastic interest rates, stochastic equity volatility and jumps. We further show that frequently used 'rule of thumb approximations' that only take into account the life-cycle fund's average equity portion are not suitable to approximate a life-cycle fund's risk-return profile. Our results on the one hand facilitate sustainable financial planning and on the other hand challenge the very existence of life-cycle funds since appropriately calibrated balanced funds can offer a similar (often dominating) risk-return profile.

Insurance customer behavior: Lessons from behavioral economics

“…There is evidence that Prospect Theory is getting worse in predicting actual investment decisions the longer the considered time horizon. For example, life cycle funds, life cycle models in fund‐linked insurance products, year‐to‐year guarantee features or cliquet‐style guarantee features enjoy great popularity, although they usually should neither be taken out by an investor under Expected Utility Theory nor under Prospect Theory, cf., for example, Graf () or Ebert et al (). So in these examples, not only Expected Utility Theory but also Prospect Theory fails to predict actual human behavior.…”

As you like it: Explaining the popularity of life‐cycle funds with multi cumulative prospect theory

“…Results in Graf (), who has analyzed life‐cycle funds for single and regular contributions and under different asset models, imply that for any given life‐cycle fund, a rational investor (maximizing expected utility) can find a corresponding superior balanced fund. Nevertheless, life‐cycle funds have been and continue to be extremely successful.…”

“…The results of Graf () imply that in most cases, the sharp contrast between optimal utility maximizing behavior (in terms of terminal wealth)—that is, not invest in life‐cycle funds—and observed actual behavior—that is, invest in life‐cycle funds—can also not be explained by Cumulative Prospect Theory (CPT), the most popular behavioral counterpart to Expected Utility Theory (EUT) that was introduced by Tversky and Kahneman ().…”

“…Considering academic literature on life‐cycle funds, three main streams of research can be identified: The first one is concerned with comparing possible returns of arbitrary deterministic life‐cycle funds and—in contrast to Graf ()—arbitrary (unrelated) balanced funds or guaranteed products. The second strain of literature relates to finding “optimal” life‐cycle funds.…”

“…However, a sound opinion or common understanding, whether a balanced fund or a life‐cycle fund with some deterministic glide path preferred by a certain type of investor does not exist. Based on the results from Graf () and applying MCPT as well as a combined model of CPT and MCPT, we will show that even if a life‐cycle fund's terminal value distribution is “practically” stochastically dominated by a suitably designed balanced fund it will still be preferred by a large group of investors. Hence, our findings offer an explanation for inferior decisions in saving for retirement.…”