arXiv subjects

Christopher J. Rook

Publications and source records attributed to Christopher J. Rook.

4 recordsLinked to original sources

arXiv2017

Multivariate Density Modeling for Retirement Finance

Prior to the financial crisis mortgage securitization models increased in sophistication as did products built to insure against losses. Layers of complexity formed upon a foundation that could not support it and as the foundation crumbled the housing market followed. That foundation was the Gaussian copula which failed to correctly model failure-time correlations of derivative securities in duress. In retirement, surveys suggest the greatest fear is running out of money and as retirement decumulation models become increasingly sophisticated, large financial firms and robo-advisors may guarantee their success. Similar to an investment bank failure the event of retirement ruin is driven by outliers and correlations in times of stress. It would be desirable to have a foundation able to support the increased complexity before it forms however the industry currently relies upon similar Gaussian (or lognormal) dependence structures. We propose a multivariate density model having fixed marginals that is tractable and fits data which are skewed, heavy-tailed, multimodal, i.e., of arbitrary complexity allowing for a rich correlation structure. It is also ideal for stress-testing a retirement plan by fitting historical data seeded with black swan events. A preliminary section reviews all concepts before they are used and fully documented C/C++ source code is attached making the research self-contained. Lastly, we take the opportunity to challenge existing retirement finance dogma and also review some recent criticisms of retirement ruin probabilities and their suggested replacement metrics.

q-fin.GN↗

arXiv2015

Approximating the Sum of Correlated Lognormals: An Implementation

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. Some approximation methods date back over 80 years and most take one of two approaches, either: 1) an approximate probability distribution is derived mathematically, or 2) the sum is approximated by a single lognormal random variable. In this research, we take the latter approach and review a fairly recent approximation procedure proposed by Mehta, Wu, Molisch, and Zhang (2007), then implement it using C++. The result is applied to a discrete time model commonly encountered within the field of financial economics.

q-fin.GN↗

arXiv2015

Optimal Equity Glidepaths in Retirement

Dynamic retirement glidepaths evolve over time based on some measure such as the retiree's funded status or current market valuations. Conversely, static glidepaths are fixed at a starting point and selected under the assumption that they will not change. In practice, new static glidepaths may be derived periodically making them more flexible. The optimal static retirement glidepath would be the one that performs better than all others with respect to some metric. When systematic withdrawals are made from a retirement portfolio, glidepaths are often assessed via the probability of ruin (or success). Our goal here is to derive the optimal static glidepath with respect to this metric. It is a result new to the literature and the shape will be of special interest to retirees, financial advisors, retirement researchers, and target-date fund providers.

q-fin.GN↗

arXiv2015

Minimizing the Probability of Ruin in Retirement

Retirees who exhaust their savings while still alive are said to experience financial ruin. These savings are typically grown during the accumulation phase then spent during the retirement decumulation phase. Extensive research into invest-and-harvest decumulation strategies has been conducted, but recommendations differ markedly. This has likely been a source of concern and confusion for the retiree. Our goal is to find what has heretofore been elusive, namely an optimal decumulation strategy. Optimality implies that no alternate strategy exists or can be constructed that delivers a lower probability of ruin, given a fixed inflation-adjusted withdrawal rate.

q-fin.GN↗