Optimal and Simple,Nearly Optimal Rules for Minimizing the Probability Of Financial Ruin in Retirement

Abstract

The increasing risk of poverty in retirement has been well documented; it is projected that current and future retirees’ living expenses will significantly exceed their savings and income. In this paper, we consider a retiree who does not have sufficient wealth and income to fund her future expenses, and we seek the asset allocation that minimizes the probability of financial ruin during her lifetime. Building on the work of Young (2004) and Milevsky, Moore, and Young (2006), under general mortality assumptions, we derive a variational inequality that governs the ruin probability and optimal asset allocation. We explore the qualitative properties of the ruin robability and optimal strategy, present a numerical method for their estimation, and examine their sensitivity to changes in model parameters for specific examples. We then present an easy-to-implement allocation rule and demonstrate via simulation that it yields nearly optimal ruin probability, even under discrete portfolio rebalancing.     

Saving and investing for early retirement: A theoretical analysis

We study optimal consumption and portfolio choice in a framework where investors adjust their labor supply through an irreversible choice of their retirement time. We show that investing for early retirement tends to increase savings and reduce an agent's effective relative risk aversion, thus increasing her stock market exposure. Contrary to common intuition, an investor might find it optimal to increase the proportion of financial wealth held in stocks as she ages and accumulates assets, even when her income and the investment opportunity set are constant. The model predicts a decrease in risk aversion following strong market gains like those observed in the nineties.     

Risk-neutral investors do not acquire information

Give a risk-neutral investor the choice to acquire a costly signal prior to asset market equilibrium. She refuses to pay for the signal under general conditions. The reason is that a risk-neutral investor is indifferent between a risky asset or a safe bond in optimum and expects the same return to her portfolio ex ante, whether or not she acquires information. Risk neutrality thus implies the absence of costly information from asset price in competitive asset markets.     

Worries and plans as individuals approach retirement

The primary objective of an employment-based retirement plan is to provide a secure and adequate income for workers throughout retirement. In the defined contribution (DC) framework, asset accumulation is a means to the end, but not the end. Drawing retirement income from savings and paying for health care expenses in retirement are the two issues that concern individuals the most as they approach retirement. This article examines the attitudes of near-retirees regarding these risks and their plans for managing them. The author discusses how DC plan design can have a major impact on how individuals convert their retirement savings to retirement income; differences in survey responses between those who have consulted a financial advisor or other financial professional and those who have not; and the role of trust in implementing advice.     

Forced retirement risk and portfolio choice

Current literature on the effect of labor income on portfolio choice overlooks that workers face a risk of being forced to retire before their planned retirement age. Using data from the Health and Retirement Study, this paper finds that the forced retirement risk is both significant and highly correlated with stock market fluctuations. Using a life-cycle portfolio choice model, this paper shows that forced retirement risk makes labor income near retirement stock-like. Therefore, contrary to conventional wisdom, those who are still working but near retirement should have a lower share of risky assets in their financial portfolios than retirees do.     

Portfolio Choice and Asset Prices: The Importance of Entrepreneurial Risk

Using cross-sectional data from the SCF and Tax Model, we show that entrepreneurial income risk has a significant influence on portfolio choice and asset prices. We find that households with high and variable business income hold less wealth in stocks than other similarly wealthy households, although they constitute a significant fraction of the stockholding population. Similarly for nonentrepreneurs, holding stock in the firm where one works reduces the portfolio share of other common stocks. Finally, we show that adding proprietary income to a linear asset pricing model improves its performance over a similar model that includes only wage income.     

The Role of Learning in Dynamic Portfolio Decisions

This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of an investor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending on whether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely on the Ibbotson and Sinquefield (1995) data.     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

Equilibrium Incentives to Acquire Precise Information in Delegated Portfolio Management

This paper investigates how a linear contract offered to a portfolio manager affects her incentives to acquire precise information. I show that increasing the manager's portfolio share increases her demand for precise information. This result contrasts with the existing irrelevance results where the manager's portfolio share does not affect her precision choice. The irrelevance result relies on the manager facing a constant asset price, regardless of her demand. In a noisy rational expectations framework, increasing the manager's share decreases her demand and results in a less informative asset price. Thus, the manager gathers more precise information when offered a larger fraction of portfolio returns.     

Portfolio choice and equilibrium in capital markets with safety-first investors

This paper develops optimal portfolio choice and market equilibrium when investors behave according to a generalized lexicographic safety-first rule. We show that the mutual fund separation property holds for the optimal portfolio choice of a risk-averse safety-first investor. We also derive an explicit valuation formula for the equilibrium value of assets. The valuation formula reduces to the well-known two-parameter capital asset pricing model (CAPM) when investors approximate the tail of the portfolio distribution using Tchebychev's inequality or when the assets have normal or stable Paretian distributions. This shows the robustness of the CAPM to safety-first investors under traditional distributional assumptions. In addition, we indicate how additional information about the portfolio distribution can be incorporated to the safety-first valuation formula to obtain alternative empirically testable models.     

Optimal portfolio choice in real terms: Measuring the benefits of TIPS

In this paper we solve an optimal portfolio choice problem to measure the benefits of Treasury Inflation Indexed Securities (TIPS) to investors concerned with maximizing real wealth. We show how the introduction of a real riskless asset completes the investor asset space, by contrasting optimal portfolio allocations with and without such assets. We use historical data to quantify gains from availability of TIPS in the presence of other asset classes such as equities, commodities, and real estate. We draw a distinction between buy-and-hold long-term investors for whom TIPS fully displace nominal risk-free assets and short-term investors for whom TIPS improve the investment opportunity set of real returns. Finally, we show how gains from TIPS are tempered by the availability of alternative assets that covary with inflation, such as gold and real estate.     

Life-Cycle Portfolio Choice with Additive Habit Formation Preferences and Uninsurable Labor Income Risk

This article explores the implications of additive and endogenoushabit formation preferences in the context of a life-cycle modelof an investor who has stochastic uninsurable labor income.To solve the model, I analytically derive the habit-wealth feasibilityconstraints and show that they depend on the worst possiblepath of future labor income and on the habit strength, but noton the probability of the worst income. When there is only aslim chance of a severe income shock, the model implies muchmore conservative portfolios. The model also predicts that forsome low to moderately wealthy households, the portfolio shareallocated to stocks increases with wealth. Because of this feature,the model can generate more conservative portfolios for youngerthan for middle-aged households. The effects of habits on portfoliochoice are robust to income smoothing through borrowing or flexiblelabor supply. One controversial finding is that for high valuesof the habit strength parameter, usually required for the resolutionof asset pricing puzzles in general equilibrium, the life-cyclemodel predicts counterfactually high wealth accumulation. (JEL:G11, G12)     

Optimal Portfolio Choice for Long-Horizon Investors with Nontradable Labor Income

This paper examines how risky labor income and retirement affect optimal portfolio choice. With idiosyncratic labor income risk, the optimal allocation to stocks is unambiguously larger for employed investors than for retired investors, consistent with the typical recommendations of investment advisors. Increasing idiosyncratic labor income risk raises investors' willingness to save and reduces their stock portfolio allocation towards the level of retired investors. Positive correlation between labor income and stock returns has a further negative effect and can actually reduce stockholdings below the level of retired investors.     

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

The Role of Learning in Dynamic Portfolio Decisions

This paper analyzes the effect of uncertainty about the meanreturn on the risky asset on the portfolio decisions of an investorwho has a long investment horizon. Building on the earlier workof Detemple (1986), Dothan and Feldman (1986), and Gennotte(1986), it is shown that the possibility of future learningabout the mean return on the risky asset induces the investorto take a larger or smaller position in the risky asset thanshe would if there were no learning, the direction of the effectdepending on whether the investor is more or less risk tolerantthan the logarithmic investor whose portfolio decisions areunaffected by the possibility of future learning. Numericalcalculations show that uncertainty about the mean return onthe market portfolio has a significant effect on the portfoliodecision of an investor with a 20 year horizon if her assessmentof the market risk premium is based solely on the Ibbotson andSinquefield (1995) data.     

Redemption risk and cash hoarding by asset managers

Open-end mutual funds face investor redemptions, but the sale of the underlying assets depends on asset managers’ portfolio decisions. If asset managers use cash holdings as a buffer to meet redemptions, they can mitigate fire sales of the assets. If they hoard cash in response to redemptions, they will amplify fire sales. We present a global game model of investor runs and identify conditions under which asset managers hoard cash. In an empirical investigation of bond mutual funds, we find that cash hoarding is the rule rather than the exception, and that less liquid bond funds display stronger cash hoarding.     

Portfolio optimization with a defaultable security

In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function. We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities.     

On the Asset Allocation of a Default Pension Fund

We characterize the optimal default fund in a defined contribution (DC) pension plan. Using detailed data on individuals' holdings inside and outside the pension system, we find substantial heterogeneity within and between passive and active investors in terms of labor income, financial wealth, and stock market participation. We build a life‐cycle consumption‐savings model, with a DC pension account and an opt‐out/default choice, that produces realistic investor heterogeneity. Relative to a common age‐based allocation, implementing the optimal default asset allocation implies a welfare gain of 1.5% during retirement. Much of the gain is attainable with a simple rule of thumb.     

Algorithmic portfolio choice: lessons from panel survey data

Automated asset management offerings algorithmically assign risky portfolios to individual investors based on investor characteristics such as age, net income, or self-assessment of risk aversion. Using new German household panel data, we investigate the key household characteristics that drive private asset allocation decisions. This information allows us to assess which set of variables should be included in algorithmic portfolio advice. Using heavily cross-validated classification trees, we find that a combination of household balance sheet variables—describing the ability to take risks (e.g., net wealth)—and household personal characteristics—describing the willingness to take risks (e.g., risk aversion)—best explain the cross-sectional variation in household portfolio choice. Our empirical evidence is in line with models of portfolio choice under decreasing relative risk aversion and fixed investment costs. The results suggest the utility of a more holistic modeling of household characteristics. Including background risks in the form of household leverage not only makes investment sense, but is also the new regulatory reality under MIFID II rules. Robo-advisors are strongly advised to act accordingly.     

Income Drawdown Schemes for a Defined-Contribution Pension Plan

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution personal pension plan. The optimal asset allocation is defined so that it minimizes the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk-free investment and the price of an annuity. The fair-value income drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitization is recommended if the expected fair-value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitization age is calculated for a Gompertz mortality distribution function and a power law loss function.