"Variable Annuities and the Option to Seek Risk: Why Should You Diversify?" 

ANTJE MAHAYNI, Mercator School of Management
Email: antje.mahayni@uni-due.de
JUDITH C. SCHNEIDER, University Duisburg Essen
Email: judith.schneider@uni-due.de

We analyze the impacts of an additional rider which is incorporated in recent retirement planning products. The payoff of these products is linked to the performance of a multi asset investment strategy and includes a minimum interest rate guarantee on the contributions. In addition, the buyer receives the option to decide on the investments dynamically. Prominent examples are so called Variable Annuities, in particular guaranteed minimum accumulation benefits (GMABs). Due to the embedded guarantee, these products are interesting for risk averse investors who, in general, benefit from diversification. However, to stay on the safe side the price setting of the provider must take into account the most risky strategy. We show that this implies an incentive to invest more riskily than without the additional rider. In particular, we quantify the trade-off between the utility of diversification and the utility of a more valuable guarantee relying on realistic examples. In addition, it turns out that a product design including the additional flexibility on the investment decisions causes significant utility losses.

"Revisiting Retirement Withdrawal Plans and Their Historical Rates of Return" 

CHRISTOPHER O'FLINN, ELM Income Group Inc
Email: cwoflinn@verizon.net
FELIX SCHIRRIPA, Financial Designs, LLC
Email: felix@incomerx.com

This paper examines the historical record of the so-called 4% rule, the popular guideline for sustainable real annual withdrawals in a self funded retirement.

Our findings indicate that a withdrawal plan following this rule (“4R”) carries an historical risk of failure for a long retirement that is much higher than generally acknowledged. For example, we find that 15% of the historical 35-year retirements failed when funded with equal parts of stocks and bonds. The “real” withdrawal plans that generated no historical failures were all less than 4%, sometimes far less, when retirements exceeded 25 years. The historical failure rates that we find for a 5R plan are higher than a 4R plan by a factor of at least three for all retirement periods.

The historical failures are not random. Rather they occur in clusters of years in which the majority of new retirement withdrawal plans fail. A key driver of these failures was a rapid, significant and lasting increase in the rate of inflation - this event increased withdrawals and contributed to a declining real rate of return that was ultimately unable to support the withdrawal plan.

Although TIPS bonds and inflation-adjusted annuities are both too new for historical analysis, we note they may offer an opportunity to curtail income plan failures in the future. This is because they (1) offer a known real rate of return and (2) adjust for inflation close to the time at which inflation impacts withdrawals.

Our review of the prior literature and a detailed description of the methodology used in the study appear at the end of the paper, after the Summary and Conclusions section.

"Accounting for Non-Annuitization" 

FRB of Chicago Working Paper No. 2010-03

SVETLANA PASHCHENKO, Federal Reserve Banks - Federal Reserve Bank of Chicago
Email: svetlana.pashchenko@chi.frb.org

Why don't people buy annuities? Several explanations have been provided by the previous literature: large fraction of preannuitized wealth in retirees' portfolios; adverse selection; bequest motives; and medical expense uncertainty. This paper uses a quantitative model to assess the importance of these impediments to annuitization and also studies three newer explanations: government safety net in terms of means-tested transfers; illiquidity of housing wealth; and restrictions on minimum amount of investment in annuities. This paper shows that quantitatively the last three explanations play a big role in reducing annuity demand. The minimum consumption floor turns out to be important to explain the lack of annuitization, especially for people in lower income quintiles, who are well insured by this provision. The minimum annuity purchase requirement involves big upfront investment and is binding for many, especially if housing wealth cannot be easily annuitized. Among the traditional explanations, preannuitized wealth has the largest quantitative contribution to the annuity puzzle.

"Good Strategies for Wealth Distribution in Retirement" 

GAOBO PANG, Towers Watson
Email: gaobo.pang@towerswatson.com
MARK J. WARSHAWSKY, Towers Watson
Email: mark.warshawsky@watsonwyatt.com

This analysis puts forward good wealth distribution strategies for individuals and couples in retirement, considering trade-offs of wealth preservation and income security. We search among strategies that combine systematic mutual fund withdrawals with purchases of fixed payout life annuities. The search looks at a rich range of tactics including ages for annuity purchase, withdrawal rates, degrees of annuitization, and initial asset allocations. These strategies produce retirement account balances and incomes and we evaluate them using stochastic simulations of asset and annuity returns with overlays of rare financial and economic catastrophes as well as bankruptcies of insurers.

"When can Insurers Offer Products that Dominate Delayed Old-Age Pension Benefit Claiming?" 

Netspar Discussion Paper No. 04/2010-011

LISANNE SANDERS, Tilburg University - CentER for Economic Research, Netspar
Email: L.Sanders@tilburguniversity.nl
ANJA DE WAEGENAERE, Tilburg University - Center for Economic Research (CentER)
Email: A.M.B.deWaegenaere@uvt.nl
THEO NIJMAN, Tilburg University - Center and Faculty of Economics and Business Administration
Email: Nyman@uvt.nl

It is common practice for public pension schemes to offer individuals the option to delay benefit claiming until after the normal retirement age and adjust the annual benefit level as a result. This adjustment is often not actuarially neutral with respect to the age at which benefits are claimed. The degree of actuarial nonequivalence varies by interest rates as well as individual characteristics such as gender and age. In this paper we show that actuarial nonequivalence can imply that deferring benefit claiming is suboptimal, irrespective of the preferences of the individual. Specifically, we derive preference-free conditions under which delaying benefit claiming is dominated by claiming benefits early, and using them to buy super-replicating annuity products from an insurance company. We find that the degree of actuarial nonequivalence in public pension schemes is such that such dominating strategies can exist even when the purchase of annuities would be significantly more costly than what is currently observed. If individuals choose to strategically exploit these dominating strategies, this will affect benefit claiming behavior, which in turn affects long run program costs.

"Optimal Time of Annuitization in the Decumulation Phase of a Defined Contribution Pension Scheme" 

CAREFIN Research Paper No. 01/10

MARINA DI GIACINTO, University of Cassino - Faculty of Economics
Email: digiacinto@unicas.it
BJARNE HOJGAARD, Aalborg University
Email: BJH@MATH.AUC.DK
ELENA VIGNA, University of Turin - Faculty of Economics
Email: elena.vigna@econ.unito.it

We consider the problem of finding the optimal annuitization time in the decumulation phase of a defined contribution pension scheme, exploiting the model of Gerrard, Højgaard and Vigna (2010). We make extensive numerical investigations on the optimal annuitization time, size of final annuity upon annuitization, extent of improvement when annuitization is not immediate and comparison between optimal annuitization and immediate annuitization. We find that the optimal annuitization time depends on the retiree's risk aversion, on her perception of remaining lifetime and on the risk premium of the risky asset. Intuitively, optimal annuitization should occur a few years after retirement with high risk aversion, low risk premium and/or short remaining lifetime, and many years after retirement in an opposite scenario. We also measure the cost of sub-optimality of a pension system where immediate annuitization is compulsory, in terms of loss of expected present value of consumption from retirement to death. We find that this cost varies between 6% and 40% in relative terms, depending on the risk aversion.

This paper is currently reserved to Carefin sponsors and will be made public on SSRN after a short embargo. Please visit the CAREFIN website to learn more on how to get the paper.

"Individual Annuity Demand Under Aggregate Mortality Risk" 

Journal of Risk and Insurance, Vol. 77, Issue 2, pp. 423-449, June 2010

ROMAN N. SCHULZE, affiliation not provided to SSRN
THOMAS POST, Maastricht University - School of Business and Economics - Department of Finance, Netspar
Email: T.Post@maastrichtuniversity.nl

Aggregate mortality risk - the risk that the mortality trend in a population changes in a nondeterministic way - and its implications for corporate decisions has recently been the subject of lively scientific discussion. We show that aggregate mortality risk is also a key determinant for individual annuitization decisions. Aggregate mortality risk appears to be a risk very difficult to transfer for individuals. Whether its existence leads to a higher or lower annuity demand depends on objective factors (e.g., insurers’ vulnerability to aggregate mortality changes). Subjective factors (i.e., individuals’ preferences) determine only the intensity of the annuity demand reaction to aggregate mortality risk. Our results are of significant importance not only for financial planning approaches of individual annuity buyers but also for strategic decisions in insurance companies and for solvency regulators. Furthermore, consideration of aggregate mortality risk may alleviate, but also intensify, the annuity puzzle.