Robert Arnott in “What is Wealth?” explores “what is wealth?” and he concludes that the most useful definitions may be “the inflation indexed real income that our assets could sustain over time”. He then adds that “a closely related goal is to avoid shocks that jeopardize that future real spending”.
Robert Merton in “Observations on innovation in pension fund management in the impending future” appears to agree. “What matters to people, particularly in the context of the retirement part of the life cycle, is not how much wealth they have but the standard of living they can en¬joy. The standard of living is much better represented as a lifetime flow or perpetuity than as a stock of wealth. What we see is another dimension of risk in addition to wealth—changes in what you can earn with that wealth, described by changes in the investment opportunity set of risk and return, including the interest rate. From the per-spective of what really matters to people—their standard of living—what is the “risk-free” asset? It is not a Treasury bill. It is an inflation-protected life annuity whose mark-to-market value can fluctuate substantially as real interest rates change.”
Richard Croft in the Financial Post defined wealth as “From a long-term perspective, wealth is all about accumulating a large enough asset base to spin off sufficient income to allow us to live a comfortable lifestyle without having to work. Only you can define the cost of a comfortable lifestyle.”
So we could think of wealth as the capability for sustainable real spending .This would be changing every year and would be based on the residual asset base each year, after including the return on assets (positive or negative) less spending for that year.. So long as the return on assets exceeds impact of inflation plus actual spending, one’s wealth will not have diminished from previous year. Still it is reasonable to expect that different individuals would put different emphasis on spending rate during retirement and desire to leave an estate of a certain size. (One may even think of (all or part of) the estate reserve as a form of longevity insurance).
But perhaps to fully evaluate an annuity in the context of an asset allocation one would need to consider the multigenerational impact. With annuities as part of the overall asset allocation the immediate question that comes up is the trade-off between cash flow to investor/annuitizer and residual assets left to the estate (or multigenerational real income derivable over time). In fact Paul Kaplan in “Asset Allocation with Annuities for Retirement Income Management” uses Monte Carlo simulation to calculate “the trade-off curve between income level and success probability” (defined as “how likely you are not to run out of assets before dying”). He allows that “success probability may not be the only criterion for selecting a withdrawal and investment strategy. Potential future wealth, which becomes the estate value at death, may also be a criterion. So for a given income level, we also calculate median estate values as well as the success probability for various combinations of annuitization and asset mixes to find the trade-off between success probability and potential estate size under one of our inflation models”.
So for a given withdrawal (or spending) strategy and a horizon, we could then use two parameters to measure outcomes associated with different (additional cash flows like pensions/annuities,) inflation and return scenarios; these are (1) probability of success and (2) residual net-assets.