Mortality Contingent Claims: Impact of Capital Market, Income, and Interest Rate Risk

In this paper, we consider optimal insurance, portfolio allocation, and consumption rules for a stochastic wage earner with CRRA preferences whose lifetime is random. In a continuous time framework, the investor has to decide among short and long positions in mortality contingent claims a.k.a. life insurance, stocks, bonds, and money market investment when facing a risky stock market and interest rate risk. We find an analytical solution for the complete market case in which human capital is exactly priced. We also extend the analysis to the case where income is unspanned. An illustrative analysis shows when the wage earner’s demand for life insurance switches to the demand for annuities.

Optimal gradual annuitization : quantifying the costs of switching to annuities

We compute the optimal dynamic asset allocation policy for a retiree with Epstein-Zin utility. The retiree can decide how much he consumes and how much he invests in stocks, bonds, and annuities. Pricing the annuities we account for asymmetric mortality beliefs and administration expenses. We show that the retiree does not purchase annuities only once but rather several times during retirement (gradual annuitization). We analyze the case in which the retiree is restricted to buy annuities only once and has to perform a (complete or partial) switching strategy. This restriction reduces both the utility and the demand for annuities

Deferred Annuities and Strategic Asset Allocation

We derive the optimal portfolio choice and consumption pattern over the lifecycle for households facing labor income, capital market, and mortality risk. In addition to stocks and bonds, households also have access to deferred annuities. Deferred annuities offer a hedge against mortality risk and provide similar benefits as Social Security. We show that a considerable fraction of wealth should be annuitized to skim the return enhancing mortality credit. The remaining liquid wealth (stocks and bonds) is used to hedge labor income risk during work life and to earn the equity premium. We find a marginal difference between a strategy involving deferred annuities and one where the investor can purchase immediate life annuities.

Life-Cycle Asset Allocation with Annuity Markets: Is Longevity Insurance a Good Deal?

We derive the optimal portfolio choice over the life-cycle for households facing labor income, capital market, and mortality risk. In addition to stocks and bonds, households also have access to incomplete annuity markets offering a hedge against mortality risk. We show that a considerable fraction of wealth should be annuitized to skim the return enhancing mortality credit. The remaining liquid wealth (stocks and bonds) is used to hedge labor income risk during work life, to earn the equity premium, and to ensure estate for the heirs. Furthermore, we assess the importance of common explanations for limited participation in annuity markets.

Optimal Life Cycle Portfolio Choice with Variable Annuities Offering Liquidity and Investment Downside Protection

This paper assesses optimal life cycle consumption and portfolio allocations when households have access to Guaranteed Minimum Withdrawal Benefit (GMWB) variable annuities over their adult lifetimes. Our contribution is to evaluate demand for these products which provide access to equity investments with money-back guarantees, longevity risk hedging, and partially-refundable premiums, in a realistic world with uncertain labor and capital market income as well as mortality risk. Others have predicted that consumers will only purchase such annuities late in life, but we show that they will optimally purchase GMWBs prior to retirement, consistent with their recent rapid uptick in sales. Additionally, many individuals optimally adjust their portfolios and consumption streams along the way by taking cash withdrawals from the products. These products can substantially enhance consumption, by up to 10% for those who experience highly unfavorable experiences in the stock market

Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion

Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion, stochastic capital markets, and uncertain lifetimes. The resulting portfolio allocation, when fixed as of retirement, is then compared to phased withdrawal strategies such a "self-annuitization" plan or the 401(k) 'default' pattern encouraged under US tax law. Surprisingly, the fixed percentage approach proves appealing for retirees across a wide range of risk preferences, supporting financial planning advisors who often recommend this rule. We then permit the retiree to switch to an annuity later, which gives her the chance to invest in the capital market and "bet on death." As risk aversion rises, annuities first crowd out bonds in retiree portfolios; at higher risk aversion still, annuities replace equities in the portfolio. Making annuitization compulsory can also lead to substantial utility losses for less risk-averse investors.

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.

Extending Life Cycle Models of Optimal Portfolio Choice: Integrating Flexible Work, Endogenous Retirement, and Investment Decisions with Lifetime Payouts

This paper derives optimal life cycle portfolio asset allocations as well as annuity purchases trajectories for a consumer who can select her hours of work and also her retirement age. Using a realistically-calibrated model with stochastic mortality and uncertain labor income, we extend the investment universe to include not only stocks and bonds, but also survival-contingent payout annuities. We show that making labor supply endogenous raises older peoples’ equity share; substantially increases work effort by the young; and markedly enhances lifetime welfare. Also, introducing annuities leads to earlier retirement and higher participation by the elderly in financial markets. Finally, when we allow for an age-dependent leisure preference parameter, this fits well with observed evidence in that it generates lower work hours and smaller equity holdings at older ages as well as sensible retirement age patterns.

Optimizing the Retirement Portfolio: Asset Allocation, Annuitization, and Risk Aversion

Retirees must draw down their accumulated assets in an orderly fashion so as not to exhaust their funds too soon. We derive the optimal retirement portfolio from a menu that includes payout annuities as well as an investment allocation and a withdrawal strategy, assuming risk aversion, stochastic capital markets, and uncertain lifetimes. The resulting portfolio allocation, when fixed as of retirement, is then compared to phased withdrawal strategies such a %u201Cself-annuitization%u201D plan or the 401(k) %u201Cdefault%u201D pattern encouraged under US tax law. Surprisingly, the fixed percentage approach proves appealing for retirees across a wide range of risk preferences, supporting financial planning advisors who often recommend this rule. We then permit the retiree to switch to an annuity later, which gives her the chance to invest in the capital market and %u201Cbet on death.%u201D As risk aversion rises, annuities first crowd out bonds in retiree portfolios; at higher risk aversion still, annuities replace equities in the portfolio. Making annuitization compulsory can also lead to substantial utility losses for less risk-averse investors.