Raimond Maurer

Betting on Death and Capital Markets in Retirement: A Shortfall Risk Analysis of Life Annuities versus Phased Withdrawal Plans

How might retirees consider deploying the retirement assets accumulated in a defined contribution pension plan? One possibility would be to purchase an immediate annuity. Another approach, called the “phased withdrawal” strategy in the literature, would have the retiree invest his funds and then withdraw some portion of the account annually. Using this second tactic, the withdrawal rate might be determined according to a fixed benefit level payable until the retiree dies or the funds run out, or it could be set using a variable formula, where the retiree withdraws funds according to a rule linked to life expectancy. Using a range of data consistent with the German experience, we evaluate several alternative designs for phased withdrawal strategies, allowing for endogenous asset allocation patterns, and also allowing the worker to make decisions both about when to retire and when to switch to an annuity. We show that one particular phased withdrawal rule is appealing since it offers relatively low expected shortfall risk, good expected payouts for the retiree during his life, and some bequest potential for the heirs. We also find that unisex mortality tables if used for annuity pricing can make women’s expected shortfalls higher, expected benefits higher, and bequests lower under a phased withdrawal program. Finally, we show that delayed annuitization can be appealing since it provides higher expected benefits with lower expected shortfalls, at the cost of somewhat lower anticipated bequests.

Self-Annuitization, Consumption Shortfall in Retirement and Asset Allocation : the Annuity Benchmark

The present paper considers a retiree of a certain age who is endowed with a certain amount of wealth and is facing alternative investment opportunities. One possibility is to buy a single premium immediate (participating) annuity-contract. This insurance product pays a life-long pension payment of a certain amount, depending e.g. on the age of the retiree, the operating cost of the insurance company and the return the company is able to realize from its investments. The alternative possibility is to invest the single premium into a portfolio of mutual funds and to periodically withdraw a fixed amount that is assumed to be equivalent to the consumption stream generated by the annuity. The particular advantage of this self annuitization strategy compared to the life annuity is its greater liquidity and the possibility of leaving out money for heirs. However, the risk of self annuitization is to outlive assets before the uncertain date of death. The risk can thus be specified by considering the probability of running out of money before the uncertain date of death. The determination of this personal probability of consumption shortfall with respect to German insurance and capital market conditions is the objective of this paper.

Variable payout annuities and dynamic portfolio choice in retirement

Many retirees hope to continue earning capital market rewards on their saving while avoiding outliving their funds during retirement. We model a dynamic utility maximizing investor who seeks to benefit from holding both equity and longevity insurance. She is free to adjust her portfolio allocation of her financial wealth as well as of the annuity over time, and she can purchase variable payout annuities any time and incrementally. In this setting, we show that the retiree will not fully annuitize even without bequests; rather, she will combine variable annuities with withdrawals from her liquid financial wealth so as to match her desired consumption profile. Optimal stock exposures decrease over time, both within the variable annuity and the withdrawal plan. Welfare gains from this strategy can amount to 40% of financial wealth, depending on risk parameters and other resources; additionally, many retirees will do almost as well as the fully optimized outcome if they hold variable annuities invested 60/40 in stocks/bonds.

Optimal Gradual Annuitization: Quantifying the Costs of Switching to Annuities

We compute the optimal dynamic annuitization and asset allocation policy for a retiree with Epstein/Zin preferences, uncertain investment horizon, potential bequest motives, and pre-existing pension income. In our setting the retiree can decide each year how much he consumes and how much he invests in stocks, bonds, and life annuities, while the prior literature mostly considered restricted so-called deterministic or stochastic switching strategies. We show that postponing the annuity purchase is no longer optimal in the gradual annuitization case since investors are able to attain the optimal mix between liquid assets (stocks and bonds) and illiquid life-annuities each year. In order to assess potential utility losses, we benchmark various restricted annuitization strategies against the unrestricted gradual annuitization strategy.

Lifecycle Portfolio Choice with Systematic Longevity Risk and Variable Investment — Linked Deferred Annuities

This paper assesses the impact of variable investment-linked deferred annuities (VILDAs) on lifecycle consumption, saving, and portfolio allocation patterns given stochastic and systematic mortality. Insurers have taken two approaches to manage systematic mortality risks, namely self-insurance and risk transfer to purchasers of the annuity products. We demonstrate that self-insurance leads to high loadings, so that households offered a choice would favor the risk transfer scheme. Reservation loadings on the actuarially fair VILDA price for non-participation are 0.5-8%; if insurers cannot hedge within this range, they will transfer systematic longevity risks to the annuitants. Our findings have implications for new payout products that may be attractive to older households seeking to protect against retirement shortfalls.

Return and risk of German open‐end real estate funds

Open‐end real estate funds (so‐called ‘Offene Immobilienfonds’) play a major role in the German market for securitized real estate investments. Such funds are pools of money from many investors, which are invested in real estate by special investment management companies. This study seeks to identify the risk and return profile of this investment vehicle (before and after income taxes), to compare it with those of other major asset classes, and to provide implications for their appropriate role in a mixed‐asset portfolio. Additionally, an overview of the institutional architecture and role of German open‐end real estate funds is given. Empirical evidence suggests that the financial characteristics of open‐end real estate funds are in many respects similar to those reported for direct real estate investments. Accordingly, German open‐end real estate funds qualify for medium and long‐term investment horizons, rather than for shorter holding periods.

Total Return Strategies for Multi-Asset Portfolios

Traditional balanced funds with a more or less constant stock allocation cannot solve the conflict of the varying investment horizons most institutional investors face. To generate capital gains, the investor must accept large allocations in risky asset classes like equities, which is often difficult to reconcile with short-term requirements such as avoiding annual losses. One way around this problem is a risk-based total return strategy that explicitly controls for shortfall risk and at the same time uses the available risk budget effectively to enhance performance potential in the long run. Because such a strategy allows for greater shifts in asset class weights over time, it can start with larger allocations to stocks or other risky asset classes than static strategies. An extensive simulation study comparing this risk-based strategy to several dynamic asset allocation approaches in a backtest quantifies its short-run hedging effectiveness and long-run hedging costs.

Bayesian Asset Allocation and U.S. Domestic Bias

U.S. investors hold much less international stock than is optimal according to mean–variance portfolio theory applied to historical data. We investigated whether this home bias can be explained by Bayesian approaches to international asset allocation. In comparison with mean–variance analysis, Bayesian approaches use different techniques for obtaining the set of expected returns by shrinking the sample means toward a reference point that is inferred from economic theory. Applying the Bayesian approaches to the field of international diversification, we found that a substantial home bias can be explained when a U.S. investor has a strong belief in the global mean–variance efficiency of the U.S. market portfolio, and in this article, we show how to quantify the strength of this belief. We also found that one of the Bayesian approaches leads to the same implications for asset allocation as the mean–variance/tracking-error criterion. In both cases, the optimal portfolio is a combination of the U.S. market portfolio and the mean–variance-efficient portfolio with the highest Sharpe ratio. The benefits of international diversification have been the subject of a controversial and ongoing debate in recent decades. According to standard mean–variance portfolio theory, an internationally diversified equity portfolio has risk–return characteristics that are preferable to those of a domestic-only benchmark portfolio. The behavior of investors, however, is often inconsistent with this normative theory. For example, U.S. investors hold much less non-U.S. stock than portfolio theory predicts should be optimal: According to mean–variance analysis, U.S. investors should allocate 30–40 percent of portfolio wealth to non-U.S. equities, but the actual allocation is 8–10 percent. This discrepancy is known as the “home bias puzzle.” To explain the home bias puzzle, some researchers have applied approaches other than mean–variance analysis, such as behavioral finance or nonexpected utility theory. Surprisingly little effort has been made to investigate approaches that are consistent with mean–variance analysis and that might establish a link between normative and descriptive research on international diversification. The key is to focus on the estimation of the input parameters for mean–variance optimization. The most crucial input for asset allocation is the set of expected returns. Expected returns can be estimated from historical returns, derived from a forecasting model, or inferred from an asset-pricing model. In each case, a substantial amount of uncertainty is attached to the estimates. The problem with mean–variance analysis is that it uses only a single set of estimates: Asset allocation is based only on sample means, in the case of identically and independently distributed data, or on personal judgments about the future performance of asset classes. Furthermore, estimated expected returns are treated as if they were true values. A better approach would be to assess the information content of the various information sources and combine them into a single estimate, which is the basic idea of Bayesian statistics. Bayesian inference combines extra-sample, or prior, information with sample returns. The sample means are shrunk toward a reference point that is inferred from economic theory. We investigated whether three Bayesian approaches can explain the home bias of U.S. investors. In the first approach, the mean–variance-efficient portfolio with the highest Sharpe ratio, which is called the tangency portfolio, is shrunk toward the minimum-variance portfolio. In the second approach, the tangency portfolio is shrunk toward the market portfolio. The prior expected returns are inferred from the capital asset pricing model, and the shrinkage effect depends on the degree of sample information in the data and the investors confidence in the pricing model. In the third model, historical returns are discarded as worthless for estimating expected returns and the investor is allowed to express subjective views about future expected returns. These views and the investors level of conviction determine the extent of deviation from the market portfolio. In addition to evaluating the three Bayesian approaches, we investigated the mean–variance/tracking-error (MVTE) criterion, under which an investor is concerned not only with expected portfolio return and its variance but also with regret aversion—the risk of underperforming a benchmark portfolio (U.S. equities in our case). Interestingly, the Bayesian approach of shrinking toward the market portfolio led to conclusions similar to those based on portfolios formed under the MVTE criterion. In our empirical study, we found that a substantial home bias can be explained when a U.S. investor has both a strong belief in the global mean–variance efficiency of the U.S. market portfolio and a high aversion to falling behind the U.S. market portfolio. (In this article, we also show how to quantify the strength of this belief.) We also found that the current level of the home bias can be justified whenever regret aversion is significantly greater than risk aversion. Furthermore, the results held qualitatively for non-U.S.-based investors. Finally, to assess the potential of various approaches for adding value in tactical asset allocation, we conducted an out-of-sample study to compare the risk-adjusted performance of the Bayesian approaches with the risk-adjusted performance of mean–variance analysis. We found mixed results. The Bayesian approaches proved to be superior to mean–variance tangency portfolios that rely on sample means, and the Bayesian portfolios exhibited higher risk-adjusted returns and lower turnover. The Bayesian approaches were not found to be systematically superior to heuristic strategies, however, such as the market portfolio or the minimum-variance portfolio. Thus, the empirical results confirm the well-known fact that accurately estimating expected returns from historical returns alone is hard.

Money in Motion: Dynamic Portfolio Choice in Retirement

Retirees confront the difficult problem of how to manage their money in retirement so as to not outlive their funds while continuing to invest in capital markets. We posit a dynamic utility maximizer who makes both asset location and allocation decisions when managing her retirement financial wealth and annuities, and we prove that she can benefit from both the equity premium and longevity insurance in her retirement portfolio. Even without bequests, she will not fully annuitize; rather, her optimal stock allocation amounts initially to more than half of her financial wealth and declines with age. Welfare gains from this strategy can amount to 40 percent of financial wealth (depending on risk parameters and other resources). In practice, it turns out that many retirees will do almost as well by purchasing a variable annuity invested 60/40 in stocks/bonds.

Total Return Fixed-Income Portfolio Management

The fixed–income portfolio strategy investigated here is designed to generate positive returns and be completely risk–based; it does not require any forecasts about future yield curve movements. The idea is to control the shortfall risk of a fixed–income portfolio dynamically, allowing portfolio managers to spend their available risk budgets flexibly (taking duration, yield curve, and credit positions). The total risk of the portfolio is adjusted on a daily basis to produce positive total returns (or a total return above a prespecified minimum–return threshold).