Zvi Bodie, zbodie@bu.edu, (617) 353 4160, Boston University School of Management, 595 Commonwealth Avenue, Boston, MA 02215.
Laurence J. Kotlikoff, kotlikof@bu.edu, (617) 353 4002, Boston University Department of Economics, 270 Bay State Road, Boston, MA 02215.

1. The Theory of Optimal Life-Cycle Saving and Investing, with Zvi Bodie and Paul Willen (CFA Future of Life-Cycle Saving and Investing Conference Volume – Session 1, Webcast available at http://www.cfawebcasts.org/cpe/what.cfm?test_id=656). Abstract: How much should a family save for retirement and for the kids' college education? How much insurance should they buy? How should they allocate their portfolio across different assets? What should a company choose as the default asset allocation for a mandatory retirement saving plan? We believe that the life-cycle model developed by economists over the last fifty years provides guidance for making such decisions. The theory teaches us to view financial assets as vehicles for transferring resources across different times and outcomes over the life cycle, and that perspective allows households and planners to think about their decisions in a logical and rigorous way. This paper lays out and illustrates the basic analytical framework from the theory in nonmathematical terms, with the aim of providing guidance to financial service providers, consumers, and policymakers. (Available as Federal Reserve Bank of Boston Public Policy Discussion Paper No. 07-3)

2. Making Investment Choices as Simple as Possible But Not Simpler, with Zvi Bodie (Financial Analysts Journal, 63, 3, May-June 2007). Abstract: Target-date funds (TDFs) for retirement, also known as life-cycle funds, are being offered as a simple solution to the investment task of participants in self-directed retirement plans. A TDF is a “fund of funds” diversified across stocks, bonds, and cash with the feature that the proportion invested in stocks is automatically reduced as time passes. Empirical evidence suggests that a simple TDF strategy would be an improvement over the choices currently made by many uninformed plan participants. This article explores a way to achieve even greater improvement for people who are very risk averse and have high exposure to market risk through their labor.

3. Making Investment Choices as Simple as Possible But Not Simpler: Author Response, with Zvi Bodie (Financial Analysts Journal, 63, 4, July-August 2007). Abstract: In his comment on our article, Jonathan Smith expresses concern about the fact that employers are outsourcing their employee retirement plans to mutual funds and asks what can be done to help financial advisors as they work with people who are planning for their own retirement. We share Mr. Smith’s concerns. We think that the investment companies that now hold much of the retirement savings of the next generation of retirees have not done an adequate job of providing safe investment options for these customers. We formulate a list of recommendations.

1. Life-Cycle Consumption Plans and Portfolio Policies in a Heath-Jarrow-Morton Economy, (ICFAI Journal of Financial Risk Management). Abstract: This paper applies the methods of Detemple, Garcia, and Rindisbacher (2003, 2005) and derives explicit optimal lifetime consumption-portfolio plans in an economy whose fixed-income sector is characterized by an N-factor Heath-Jarrow-Morton (1992) model that is Markovian in 3N state variables.

2. Contingent Claims Analysis and Life-Cycle Finance, with Zvi Bodie and Doriana Ruffino (American Economic Review, 2008 Papers and Proceedings). Abstract: This paper explores the application of contingent claims analysis (CCA) to two "hot" issues in life-cycle finance: (1) investing for retirement and (2) deciding when, if ever, to switch careers. Participants in individual retirement accounts do not have the time or the knowledge to make their own investment decisions. Today they are defaulted into life-cycle mutual funds that pass all the risk directly through to the participant. We use CCA to demonstrate how financial firms can design and produce guaranteed contingent benefit contracts that improve participant welfare at no additional cost to the system. These contracts combine features of traditional annuities (i.e., lifelong income benefits) and structured investment products (e.g., guaranteed minimum plus "upside" equity participation). In exploring the career-choice issue in the second part of the paper, we use CCA in a somewhat different way. The decision to switch careers is analogous to deciding when to exercise an American-style option to swap one asset for another. By applying the methods used to analyze the option-exercise decision to the career-switching problem, we gain some new insights beyond those derived from the traditional dynamic programming approaches.

1. Human Capital Risk Management: The Optimal Exercise of Career Options (Job Market Paper), with Doriana Ruffino. Abstract: Financial economists increasingly view a person's human capital as being analogous to a portfolio of risky stocks and bonds. We demonstrate that, more generally, human capital exhibits the complex structure of a derivatives portfolio. In particular, the ability to permanently change occupations over one's career is isomorphic to an American spread option of the Margrabe type. Studying this career option from the perspective of contingent claims analysis, we consider the optimal choice of one's initial occupation and the decision to change occupations later in life when the individual faces a choice between two occupations -- one relatively safe and the other relatively risky. We show that starting out in the riskier occupation is optimal only if earnings volatility is high and switching costs low. We also find that the option to change occupations is quite valuable, raising human capital wealth by as much as 8 percent.
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2. Repeated Career Options: A Contingent Claims Approach. Abstract: This article studies the behavior of an individual who can repeatedly alternate between two occupations. Such a career option is analogous to an exotic derivative security: an American reset option. Despite infinite opportunities to change occupations, an individual faced with mobility costs is shown to always allow time to go by between occupation changes. In addition, for economically motivated calibrations, the average number of occupation changes declines steadily over time. These results mirror the behavior of real-world individuals, who change occupations more often in the early stages of their professional lives. Finally, it is proved analytically that the individual is unambiguously more reluctant to change occupations when she does not have the assurance that she may return to her initial occupation at a later date. The model demonstrates that the flexibility of repeated career options adds much value over their once-in-a-lifetime counterparts.

3. Automatic for the People? Hedge Funds, Traditional and Clones. Abstract: While some herald the development of hedge fund replicators as marking the industry's own ETF revolution, others are expressing concern over the clones' properties since traditional hedge funds are human-capital intensive financial operations and the high concentration of specialized talent is the reason for the industry's remarkably high remuneration structure. Taking much of the human capital out of hedge fund strategies is a pre-requisite for bringing the costs of replicators down, but it is one that many feel comes at a high price in terms of adaptivity, dynamic flexibility, and risk selection. In this article, I study a continuous-time model of arbitrage selection, which sheds light on this trade-off and provides added perspective on the issue. Several important results are obtained. First, a hedge fund's optimal trade selection criterion depends on a risk-reward trade-off that balances the expected gains from the trade and the uncertainty surrounding the trade's speed of convergence. Furthermore, the ability to select potential arbitrage trades generates a value for the fund's net discounted cash flows that resembles prototypical option-pricing formulas. In addition, the value added of human capital to a hedge fund's operations is dramatically enhanced when the fund deals in potential arbitrage trades for which there is a significant amount of uncertainty regarding the speed of convergence or the chances of divergence. Additional observations are made. (All About Alpha column about this paper, Institutional Investor column about this paper)

4. Lumps and Clusters in Duopolistic Investment Games: An Early Exercise Premium Approach, with Doriana Ruffino. Abstract: This paper investigates strategic investment policies in a duopolistic continuous-time real options game. Our contribution is twofold, economic and methodological. The former is the recognition that, under fixed costs of investment and time-to-build, a firm's exercise of its capital-replacement option leads to a significant temporary reallocation of the firm's revenues to its competitor. The latter is the introduction of the early exercise premium representation as a valuable device for the characterization of optimal exercise policies in real options games. Assuming exogenous firm roles, we find that (i) as the leader installs its newly purchased capital, the follower's optimal investment policy displays a markedly convex and monotonically decreasing pattern over time, which finds its justification in the temporary transfer of the leader's consumer demand to its competitor, and (ii) once the leader has completed its investment process, the follower's trigger boundary -- i.e., the level of market demand that renders capital replacement optimal -- is time-independent. Moreover, we demonstrate that the follower's willingness to delay investment is enhanced by a longer time-to-build and a more volatile market demand, while it is weakened by a higher quality improvement upon replacement and by a higher expected growth in market demand. Finally, we study the probability that the follower mimics the leader's decision within the leader's time-to-build window. We conclude that, while a higher quality advancement upon investment and a higher growth rate in market demand make it more likely for the follower to exercise its investment option promptly, a higher market uncertainty and a longer time-to-build alter the probability of an investment cluster non-monotonically.
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5. Optimal Age-Based Portfolios with Stochastic Investment Opportunity Sets, with Doriana Ruffino. Abstract: In an environment with stocks and short-term debt, random changes in the risk-reward frontier produce hedging demands for equities, implying that portfolio policies supporting optimal life-cycle consumption are rarely mean-variance efficient. Pursuing optimal life-cycle portfolio policies is technologically feasible but it represents a significant burden for individuals and financial firms acting as fiduciaries. As a result, investors often rely on relatively simple investment heuristics, most often age-based portfolio policies that rebalance the investor's portfolio as a function of age alone. We find that (i) the welfare losses associated with optimal age-based policies are often negligible, so that the trade-off between the first-best and these simpler policies likely favors the latter, and that (ii) not only do initial age-based portfolios display the same overall pattern as first-best portfolios but they are also always within the same order of magnitude.
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6. A Study of Inaction in Investment Games via the Early Exercise Premium Representation, with Doriana Ruffino (Submitted to Economic Modelling). Abstract: This paper examines strategic investment in the context of a duopolistic continuous-time real options game. Our contribution is twofold, economic and methodological. The former is the recognition that, under fixed costs of investment and time-to-build, the firm pays a fraction of the implicit strike price to its competitor in the form of transferred foregone consumer demand. The latter is the introduction of the early exercise premium representation as a valuable device for the characterization of optimal exercise policies in real options games. We find that positive capital depreciation, technology improvement, and harm effects to the low-technology producer are not sufficient to generate equilibria characterized by action.