A Sustainable Spending Rate without Simulation

# We link these three factors in one parsimonious

• Notes
• 12

This preview shows page 2 - 4 out of 12 pages.

by gender and age). We link these three factors in one parsimonious manner by using the “probabil- ity of retirement ruin,” where “ruin” is defined as outliving one’s resources, as a risk metric to gauge the relative impact of each factor and trade-offs between them. We evaluate the stochastic present value of a given spending plan at a given age under a given portfolio allocation at the initial level of wealth to determine the probability that the plan is sustain- able. Increasing the age of the retiree at retirement, reducing the spending rate, or increasing the port- folio return will each shift the mass of the SPV closer to zero (which means reducing the area inside the triangle) and thus generate a higher probability that an initial nest egg will be enough to sustain the plan. Reducing the age at retirement, increasing the spending rate, or reducing the portfolio return will shift the mass of the SPV away from zero— increasing the area inside the triangle—and will thus increase the probability of ruin. Stochastic Present Value of Spending The SPV concept is borrowed from actuaries in the insurance industry, who use a similar idea to compute the distribution of the present value of mortality-contingent liabilities, such as pension annuities and life insurance policies. At any given time, an insurance company is thus able to quan- tify the amount of reserves needed today to fulfill all future liabilities with 99 percent or 95 percent certainty. The same idea can be applied to retirement planning. Retirees can use an SPV model to com- pute the size of the retirement portfolio they need in order to draw down a specified annual amount while not incurring more than a specified probabil- ity of running out of money during their lifetime. Figure 1. Retirement Finances Triangle Heal t h, A g e, a n d Mor t al it y S pe n d ing a n d Co n s u mp ti o n Probab i l it y of Re ti reme nt R uin Asse t Alloca ti o n a n d I n ves t me nt s

Subscribe to view the full document.

A Sustainable Spending Rate without Simulation November/December 2005 pubs .org 91 In the language of stochastic calculus, the prob- ability that a diffusion process that starts at a value of w will hit zero prior to an independent “killing time” can be represented as the probability that a suitably defined SPV is greater than the same w . Imagine that you invest a lump sum of money in a portfolio earning a real (after-inflation) rate of return of R percent a year and you plan to consume/spend a fixed real dollar each and every year until some horizon denoted by T . If the horizon and investment rate of return are certain, the present value (PV) of your consumption at initial time zero, t 0 , is (1) which is the textbook formula for an ordinary simple annuity of \$1. In a deterministic world, if you start retirement with a nest egg greater than the PV in Equation 1 times your desired annual consump- tion, your money will last for the rest of your T -year life. If you have less than this amount, you will be “ruined” at some age prior to death.

{[ snackBarMessage ]}

###### "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

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern