Retirement Income Scenario Matrices
Stress-test retirement choices across mortality, markets, and inflation
- Difficulty
- Expert
- Time to result
- ~months to results
- Steps
- 6
- Confidence
- 99%
Sharpe's retirement-income method represents uncertain futures as linked matrices. Each row is one possible multi-decade scenario and each column is a year. Separate matrices model household survival states, global market returns, inflation, inflation-protected securities, Social Security, and income produced by candidate withdrawal or annuity strategies. The matrices are then combined to show the range of income paths available to a household under each strategy. Analysts can inspect distributions over time, split results by whether both spouses or one spouse is alive, and diagnose whether a strategy is inefficient. Sharpe does not claim a universal optimum because households do not supply the required multidimensional utility functions. Instead, the framework compares feasible outcomes, identifies dominated choices, and reveals the preferences an efficient choice appears to imply.
Origin
Sharpe developed the public-domain retirement project after shifting his research from institutional portfolios and accumulation toward the harder individual decumulation problem.
Core principles
- 01Retirement is a multi-period problem with an uncertain ending date.
- 02Mortality, returns, inflation, income, and spending interact rather than resolve independently.
- 03A strategy should be judged across many possible futures, not one average forecast.
- 04Efficiency comparisons can reject inferior strategies even when no universal optimum exists.
How to run it
- 1
Define household states
Specify the household members, their ages, and the personal states that matter, such as both alive, one survivor, or the estate. Use actuarial information to generate many possible state paths.
Pro tip Model survivor states separately because annuity and Social Security payments can change after a death.
Watch out A fixed planning horizon hides the uncertainty of how long retirement will last.
- 2
Generate economic scenarios
Create year-by-year paths for the global market portfolio, inflation, and inflation-protected securities. Use enough rows to represent a wide range of plausible combinations.
Pro tip Keep inflation explicit because purchasing power, not nominal income alone, drives retirement welfare.
Watch out A single average-return path cannot represent sequence risk.
- 3
Model income sources
Build matrices for Social Security, annuities, and each candidate withdrawal rule or investment strategy. Express every source in the same year-by-scenario structure.
Pro tip Include how payments change when household status changes.
Watch out Do not assume a simple percentage rule is optimal merely because it is familiar.
- 4
Combine the matrices
Add the relevant strategy and income matrices for each scenario and year. Produce the household's full distribution of possible income paths rather than one projected balance.
Pro tip Retain the components so alternative strategy combinations can be tested quickly.
Watch out Aggregation can conceal which source creates a weak outcome unless the components remain traceable.
- 5
Visualise changing outcomes
Display income distributions year by year or use an income map that shows the full terrain of outcomes. Segment the display by relevant personal states when needed.
Pro tip Use a representation that clients can understand rather than exposing the raw matrix alone.
Watch out A sophisticated model is not automatically usable by an average retiree.
- 6
Diagnose efficiency
Compare strategies to determine whether one can deliver the same probability distributions more cheaply or improve outcomes without an offsetting sacrifice. For an efficient choice, inspect the implied utility preferences.
Pro tip Use dominance tests before attempting to infer subjective preferences.
Watch out Do not claim a universal optimum without a defensible multidimensional utility function.
In the wild
Sharpe's prototype follows Bob and Sue across scenarios in which both live for several years, one dies, the survivor continues, and the remaining estate is eventually distributed. That personal-state matrix is combined with market, inflation, Social Security, and strategy matrices.
→ The analysis captures how income needs and payments change as the household moves from two people to one and then to an estate.
A fixed real-withdrawal strategy takes a percentage in the first year and raises the amount with inflation until the household dies or the money runs out. The matrix approach tests that rule across mortality, return, and inflation paths rather than accepting it as a universal answer.
→ The rule's full distribution of income and depletion outcomes becomes visible and comparable with alternatives.
Common mistakes
Planning from one average path
One lifespan and one return forecast omit the interacting uncertainties that make decumulation difficult.
Declaring one rule optimal
Sharpe says an optimal strategy would require multidimensional utility functions that people do not actually provide.
Showing complexity without interpretation
The raw model is too complex for most retirees, so specialists must translate distributions into useful diagnostics.
Is it for you?
Best for
It is best for financial engineers and advisers comparing retirement-income strategies for a specific household.
Not ideal for
It is not ideal for someone seeking a quick universal withdrawal percentage or a simple consumer calculator.
From the transcript
“every row is a possible scenario for the next fifty years.”
“each column is a year.”
“You can get the same probability distributions cheaper if you do it more efficiently, so I can diagnose that.”
From the episode
Interview With William Sharpe: Masters in Business (Audio)
William Sharpe