A Sustainable Spending Rate without Simulation

Indeed the concept of a stochastic present value of a

This preview shows page 11 - 12 out of 12 pages.

Indeed, the concept of a stochastic present value of a retirement plan can be used beyond the limited scope of computing probabilities of ruin. For example, one can use this idea to investigate the impact of including payout annuities or nonlinear instruments in a retiree’s (or endowment’s) portfo- lio. Similarly, the SPV can be used to compare the relative tax efficiency of various asset location deci- sions for retirement income products and the role of life annuities in increasing the sustainability of a given spending rate. For example, we have found that including zero-cost collars in the retiree’s port- folio (i.e., selling out-of-the-money calls whose funds are then used to purchase out-of-the-money puts) shifts the SPV toward zero, which reduces the probability of ruin and increases the sustainability of the portfolio. In summary, we urge the financial industry to focus on designing products that max- imize income sustainability over a random retire- ment horizon. We would like to thank Jin Wang and Anna Abaimova for research assistance and Tom Salisbury and Kwok Ho, with whom we had very helpful discussions during the development of this research. Notes 1. The National Association of College and University Busi- ness Officers endowment survey conducted in 2004 showed that the median endowment spending rate in 2003 was 5.0 percent of assets, with the 10th percentile being 4.0 percent and the 90th percentile being 6.4 percent. 2. Using several free Web-based simulators, we ran some case studies and found wide variations in the suggested “nest egg” needed to support a comfortable retirement. A similar concern about the variation in simulation outcomes—which was misinterpreted as a criticism of the Monte Carlo method—was echoed recently by McCarthy (2002/2003). 3. The spreadsheet is available by selecting this article from the November/December contents page on the FAJ website at . 4. We provide an analysis of the effect of this assumption in an online technical appendix. 5. We discuss the question of reasonable return distribution assumptions later. 6. The more technically inclined readers might want more than simply a formula. A proof that Equation 8 is the proper distribution of the stochastic present value is based on moment-matching techniques and the partial differential equations for the probability of ruin based on Equation 2b. We believe that a variant of this result can be traced back to Merton. For more details, proofs, and restrictions, see Milevsky (1997), Browne (1999), or Milevsky (forthcoming 2006)—specifically, the actuarial, financial, and insurance references contained in this last article.
Image of page 11

Subscribe to view the full document.

Financial Analysts Journal 100 pubs .org ©2005, CFA Institute 7. For those readers who remain unconvinced that what is effectively the “sum of lognormals” can converge to the inverse of a gamma distribution, we suggest they simulate the SPV for a reasonably long horizon and conduct a Kolmogorov–Smirnov goodness-of-fit test of the inverse of
Image of page 12

{[ snackBarMessage ]}

Get FREE access by uploading your study materials

Upload your study materials now and get free access to over 25 million documents.

Upload now for FREE access Or pay now for instant access
Christopher Reinemann
"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

Ask a question for free

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern