*This *post is* available as a PDF download here.*

# Summary

- Many retirement planning analyses rely on Monte Carlo simulations with static assumptions for withdrawals.
- Incorporating dynamic spending rules can more closely align the simulations with how investors would likely behave during times when the plan looked like it was on a path to failure.
- Even a modest reduction in withdrawals (e.g. 10%) can have a meaningful impact on reducing failure rates, nearly cutting it in half in a sample simulation.
- Combining dynamic spending rules with other marginal improvements, such as supplemental income and active risk management, can lead to more robust retirement plans and give investors a better understanding of the variables that are within their realm of control.

Monte Carlo simulations are a prevalent tool in financial planning, especially pertaining to retirement success calculations.

Under a typical framework of normally distributed portfolio returns and constant inflation-adjusted withdrawals, calculating the success of a given retirement portfolio is straightforward. But as with most tools in finance, the art lies both in the assumptions that go into the calculation and in the proper interpretation of the result.

If a client is told they have a 10% chance of running out of money over their projected retirement horizon, what does that mean for them?

They cannot make 9 copies of themselves to live out separate lives, with one copy (hopefully not the original) unfortunately burning through the account prematurely.

They also cannot create 9 parallel universes and ensure they do not choose whichever one does not work out.

We wrote previously how investors follow a single path (You Are Not a Monte-Carlo Simulation). If that path hits zero, the other hypothetical simulation paths don’t mean a thing.

A simulation path is only as valuable as the assumptions that go into creating it, and fortunately, we can make our simulations align more closely with investor behavior.

The best way to interpret the 10% failure rate is to think of it as a 10% chance of *having* to make an adjustment before it hits zero. Rarely would an investor stand by while their account went to zero. There are circumstances that are entirely out of investor control, but to the extent that there was something they could do to prevent that event, they would most likely do it.

Derek Tharp, on Michael Kitces’ blog, wrote a post a few years ago weighing the relative benefit of implementing small but permanent adjustments vs. large but temporary adjustments to retirement withdrawals and found that making small adjustments and leaving them in place led to greater likelihoods of success over retirement horizons (Dynamic Retirement Spending Adjustments: Small-But-Permanent Vs Large-But-Temporary).

In this week’s commentary, we want to dig a little deeper into some simple path dependent modifications that we can make to retirement Monte-Carlo simulations with the hope of creating a more robust toolset for financial planning.

**The Initial Plan**

Suppose an investor is 65 and holds a moderate portfolio of 60% U.S. stocks and 40% U.S. Treasuries. From 1871 until mid-2019, this portfolio would have returned an inflation-adjusted 5.1% per year with 10.6% volatility according to Global Financial Data.

Sticking with the rule-of-thumb 4% annual withdrawal of the initial portfolio balance and assuming a 30-year retirement horizon, this yields a predicted failure rate of 8% (plus or minus about 50 bps).

The financial plan is complete.

If you start with $1,000,000, simply withdraw $3,333/month and you should be fine 92% of the time.

But what if the portfolio drops 5% in the first month? (It almost did that in October 2018).

The projected failure rate over the next 29 years and 11 months has gone up to 11%. That violates a 10% threshold that may have been a target in the planning process.

Or what if it drops 30% in the first 6 months, like it would have in the second half of 1931?

Now the project failure rate is a staggering 46%. Retirement success has been reduced to a coin flip.

Admittedly, these are trying scenarios, but these numbers are a key driver for financial planning. If we can better understand the risks and spell out a course of action beforehand, then the risk of making a rash emotion-driven decision can be mitigated.

**Aligning the Plan with Reality**

When the market environment is challenging, investors can benefit by being flexible. The initial financial plan does not have to be jettisoned; agreed upon actions within it are implemented.

One of the simplest – and most impactful – modifications to make is an adjustment to spending. For instance, an investor might decide at the outset to scale back spending by a set amount when the probably of failure crosses a threshold.*Source: **Global Financial Data**. Calculations by Newfound.*

This reduction in spending would increase the probability of success going forward through the remainder of the retirement horizon.

And if we knew that this spending cut would likely happen if it was necessary, then we can quantify it as a rule in the initial Monte Carlo simulation used for financial planning.

Graphically, we can visualize this process by looking at the probabilities of failure for varying asset levels over time. For example, at 10 years after retirement, the orange line indicates that a portfolio value ~80% of the initial value would have about a 5% failure rate.

*Source: **Global Financial Data**. Calculations by Newfound.*

As long as the portfolio value remains above a given line, no adjustment would be needed based on a standard Monte Carlo analysis. Once a line is crossed, the probability of success is below that threshold.

This chart presents a good illustration of sequence risk: the lines are flatter initially after retirement and the slope progressively steepens as the time progresses. A large drawdown initially puts the portfolio below the threshold for making and adjustment.

For instance, at 5 years, the portfolio has more than a 10% failure rate if the value is below 86%. Assuming zero real returns, withdrawals alone would have reduced the value to 80%. Positive returns over this short time period would be necessary to feel secure in the plan.

Looking under the hood along the individual paths used for the Monte Carlo simulation, at 5 years, a quarter of them would be in a state requiring an adjustment to spending at this 10% failure level.

*Source: **Global Financial Data**. Calculations by Newfound.*

This belies the fact that some of the paths that would have crossed this 10% failure threshold prior to the 5-year mark improved before the 5-year mark was hit. 75% of the paths were below this 10% failure rate at some point prior to the 5-year mark. Without more appropriate expectations of a what these simulations mean, under this model, most investors would have felt like their plan’s failure rate was uncomfortable at some point in the first 5 years after retirement!

**Dynamic Spending Rules**

If the goal is ultimately not to run out of funds in retirement, the first spending adjustment case can substantially improve those chances (aside from a large negative return in the final periods prior to the last withdrawals).

Each month, we will compare the portfolio value to the 90% success value. If the portfolio is below that cutoff, we will size the withdrawal to hit improve the odds of success back to that level, if possible.

The benefit of this approach is greatly improved success along the different paths. The cost is forgone income.

But this can mean forgoing a lot of income over the life of the portfolio in a particularly bad state of the world. The worst case in terms of this total forgone income is shown below.

*Source: **Global Financial Data**. Calculations by Newfound.*

The portfolio gives up withdrawals totaling 74%, nearly *19 years’ worth*. Most of this is given up in consecutive periods during the prolonged drawdown that occurs shortly after retirement.

This is an extreme case that illustrates how large of income adjustments could be required to ensure success under a Monte Carlo framework.

The median case foregoes 9 months of total income over the portfolio horizon, and the worst 5% of cases all give up 30% (7.5 years) of income based off the initial portfolio value.

That is still a bit extreme in terms of potential cutbacks.

As a more realistic scenario that is easier on the pocketbook, we will limit the total annual cutback to 30% of the withdrawal in the following manner:

- If the current chance of failure is greater than 20%, cut spending by 30%. This equates to reducing the annual withdrawal by $12,000 assuming a $1,000,000 initial balance.
- If the current chance of failure is between 15% and 20%, cut spending by 20%. This equates to reducing the annual withdrawal by $8,000 assuming a $1,000,000 initial balance.
- If the current chance of failure is between 10% and 15%, cut spending by 10%. This equates to reducing the annual withdrawal by $4,000 assuming a $1,000,000 initial balance.

These rules still increase the success rate to 99% but substantially reduce the amount of reductions in income.

Looking again at the worst-case scenario, we see that this case still “fails” (even though it lasts another 4.5 years) but that its reduction in come is now less than half of what it was in the extreme cutback case. This pattern is in line with the “lower for longer” reductions that Derek had looked at in the blog post.

*Source: **Global Financial Data**. Calculations by Newfound.*

On the 66% of sample paths where there was a cut in spending at some point, the average total cut amounted to 5% of the portfolio (a little over a year of withdrawals spread over the life of the portfolio).

Even moving to an even less extreme reduction regime where only 10% cuts are ever made if the probability of failure increases above 10%, the average reduction in the 66% of cases that required cuts was about 9 months of withdrawals over the 30-year period.

In these scenarios, the failure rate is reduced to 5% (from 8% with no dynamic spending rules).

*Source: **Global Financial Data**. Calculations by Newfound.*

**Conclusion**

Retirement simulations can be a powerful planning tool, but they are only as good as their inputs and assumptions. Making them align as closes with reality as possible can be a way to quantify the impact of dynamic spending rules in retirement.

While the magnitude of spending reductions necessary to guarantee success of a retirement plan in all potential states of the world is prohibitive. However, small modifications to spending can have a large impact on success.

For example, reducing withdrawal by 10% when the forecasted failure rate increases above 10% nearly cut the failure rate of the entire plan in half.

But dynamic spending rules do not exist in a vacuum; they can be paired with other marginal improvements to boost the likelihood of success:

- Seek out higher returns – small increases in portfolio returns can have a significant impact over the 30 -ear planning horizon.
- Supplement income – having supplements to income, even small ones, can offset spending during any market environment, improving the success rate of the financial plan.
- Actively manage risk – managing risk, especially early in retirement is a key factor to now having to reduce withdrawals in retirement.
- Plan for more flexibility – having the ability to reduce spending when necessary reduces the need to rely on the portfolio balance when the previous factors are not working.

While failure is certainly possible for investors, a “too big to fail” mentality is much more in line with the reality of retirement.

Even if absolute failure is unlikely, adjustments will likely be a requirement. These can be built into the retirement planning process and can shed light on stress testing scenarios and sensitivity.

From a retirement planning perspective, flexibility is simply another form of risk management.

Nathan is a Vice President at Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team.

Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software.

Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.

## Dynamic Spending in Retirement Monte Carlo

By Nathan Faber

On July 15, 2019

Thispost isavailable as a PDF download here.## Summary

Monte Carlo simulations are a prevalent tool in financial planning, especially pertaining to retirement success calculations.

Under a typical framework of normally distributed portfolio returns and constant inflation-adjusted withdrawals, calculating the success of a given retirement portfolio is straightforward. But as with most tools in finance, the art lies both in the assumptions that go into the calculation and in the proper interpretation of the result.

If a client is told they have a 10% chance of running out of money over their projected retirement horizon, what does that mean for them?

They cannot make 9 copies of themselves to live out separate lives, with one copy (hopefully not the original) unfortunately burning through the account prematurely.

They also cannot create 9 parallel universes and ensure they do not choose whichever one does not work out.

We wrote previously how investors follow a single path (You Are Not a Monte-Carlo Simulation). If that path hits zero, the other hypothetical simulation paths don’t mean a thing.

A simulation path is only as valuable as the assumptions that go into creating it, and fortunately, we can make our simulations align more closely with investor behavior.

The best way to interpret the 10% failure rate is to think of it as a 10% chance of

havingto make an adjustment before it hits zero. Rarely would an investor stand by while their account went to zero. There are circumstances that are entirely out of investor control, but to the extent that there was something they could do to prevent that event, they would most likely do it.Derek Tharp, on Michael Kitces’ blog, wrote a post a few years ago weighing the relative benefit of implementing small but permanent adjustments vs. large but temporary adjustments to retirement withdrawals and found that making small adjustments and leaving them in place led to greater likelihoods of success over retirement horizons (Dynamic Retirement Spending Adjustments: Small-But-Permanent Vs Large-But-Temporary).

In this week’s commentary, we want to dig a little deeper into some simple path dependent modifications that we can make to retirement Monte-Carlo simulations with the hope of creating a more robust toolset for financial planning.

The Initial PlanSuppose an investor is 65 and holds a moderate portfolio of 60% U.S. stocks and 40% U.S. Treasuries. From 1871 until mid-2019, this portfolio would have returned an inflation-adjusted 5.1% per year with 10.6% volatility according to Global Financial Data.

Sticking with the rule-of-thumb 4% annual withdrawal of the initial portfolio balance and assuming a 30-year retirement horizon, this yields a predicted failure rate of 8% (plus or minus about 50 bps).

The financial plan is complete.

If you start with $1,000,000, simply withdraw $3,333/month and you should be fine 92% of the time.

But what if the portfolio drops 5% in the first month? (It almost did that in October 2018).

The projected failure rate over the next 29 years and 11 months has gone up to 11%. That violates a 10% threshold that may have been a target in the planning process.

Or what if it drops 30% in the first 6 months, like it would have in the second half of 1931?

Now the project failure rate is a staggering 46%. Retirement success has been reduced to a coin flip.

Admittedly, these are trying scenarios, but these numbers are a key driver for financial planning. If we can better understand the risks and spell out a course of action beforehand, then the risk of making a rash emotion-driven decision can be mitigated.

Aligning the Plan with RealityWhen the market environment is challenging, investors can benefit by being flexible. The initial financial plan does not have to be jettisoned; agreed upon actions within it are implemented.

One of the simplest – and most impactful – modifications to make is an adjustment to spending. For instance, an investor might decide at the outset to scale back spending by a set amount when the probably of failure crosses a threshold.

Source:Global Financial Data. Calculations by Newfound.This reduction in spending would increase the probability of success going forward through the remainder of the retirement horizon.

And if we knew that this spending cut would likely happen if it was necessary, then we can quantify it as a rule in the initial Monte Carlo simulation used for financial planning.

Graphically, we can visualize this process by looking at the probabilities of failure for varying asset levels over time. For example, at 10 years after retirement, the orange line indicates that a portfolio value ~80% of the initial value would have about a 5% failure rate.

Source:Global Financial Data. Calculations by Newfound.As long as the portfolio value remains above a given line, no adjustment would be needed based on a standard Monte Carlo analysis. Once a line is crossed, the probability of success is below that threshold.

This chart presents a good illustration of sequence risk: the lines are flatter initially after retirement and the slope progressively steepens as the time progresses. A large drawdown initially puts the portfolio below the threshold for making and adjustment.

For instance, at 5 years, the portfolio has more than a 10% failure rate if the value is below 86%. Assuming zero real returns, withdrawals alone would have reduced the value to 80%. Positive returns over this short time period would be necessary to feel secure in the plan.

Looking under the hood along the individual paths used for the Monte Carlo simulation, at 5 years, a quarter of them would be in a state requiring an adjustment to spending at this 10% failure level.

Source:Global Financial Data. Calculations by Newfound.This belies the fact that some of the paths that would have crossed this 10% failure threshold prior to the 5-year mark improved before the 5-year mark was hit. 75% of the paths were below this 10% failure rate at some point prior to the 5-year mark. Without more appropriate expectations of a what these simulations mean, under this model, most investors would have felt like their plan’s failure rate was uncomfortable at some point in the first 5 years after retirement!

Dynamic Spending RulesIf the goal is ultimately not to run out of funds in retirement, the first spending adjustment case can substantially improve those chances (aside from a large negative return in the final periods prior to the last withdrawals).

Each month, we will compare the portfolio value to the 90% success value. If the portfolio is below that cutoff, we will size the withdrawal to hit improve the odds of success back to that level, if possible.

The benefit of this approach is greatly improved success along the different paths. The cost is forgone income.

But this can mean forgoing a lot of income over the life of the portfolio in a particularly bad state of the world. The worst case in terms of this total forgone income is shown below.

Source:Global Financial Data. Calculations by Newfound.The portfolio gives up withdrawals totaling 74%, nearly

19 years’ worth. Most of this is given up in consecutive periods during the prolonged drawdown that occurs shortly after retirement.This is an extreme case that illustrates how large of income adjustments could be required to ensure success under a Monte Carlo framework.

The median case foregoes 9 months of total income over the portfolio horizon, and the worst 5% of cases all give up 30% (7.5 years) of income based off the initial portfolio value.

That is still a bit extreme in terms of potential cutbacks.

As a more realistic scenario that is easier on the pocketbook, we will limit the total annual cutback to 30% of the withdrawal in the following manner:

These rules still increase the success rate to 99% but substantially reduce the amount of reductions in income.

Looking again at the worst-case scenario, we see that this case still “fails” (even though it lasts another 4.5 years) but that its reduction in come is now less than half of what it was in the extreme cutback case. This pattern is in line with the “lower for longer” reductions that Derek had looked at in the blog post.

Source:Global Financial Data. Calculations by Newfound.On the 66% of sample paths where there was a cut in spending at some point, the average total cut amounted to 5% of the portfolio (a little over a year of withdrawals spread over the life of the portfolio).

Even moving to an even less extreme reduction regime where only 10% cuts are ever made if the probability of failure increases above 10%, the average reduction in the 66% of cases that required cuts was about 9 months of withdrawals over the 30-year period.

In these scenarios, the failure rate is reduced to 5% (from 8% with no dynamic spending rules).

Source:Global Financial Data. Calculations by Newfound.ConclusionRetirement simulations can be a powerful planning tool, but they are only as good as their inputs and assumptions. Making them align as closes with reality as possible can be a way to quantify the impact of dynamic spending rules in retirement.

While the magnitude of spending reductions necessary to guarantee success of a retirement plan in all potential states of the world is prohibitive. However, small modifications to spending can have a large impact on success.

For example, reducing withdrawal by 10% when the forecasted failure rate increases above 10% nearly cut the failure rate of the entire plan in half.

But dynamic spending rules do not exist in a vacuum; they can be paired with other marginal improvements to boost the likelihood of success:

While failure is certainly possible for investors, a “too big to fail” mentality is much more in line with the reality of retirement.

Even if absolute failure is unlikely, adjustments will likely be a requirement. These can be built into the retirement planning process and can shed light on stress testing scenarios and sensitivity.

From a retirement planning perspective, flexibility is simply another form of risk management.

## Nathan Faber

Nathan is a Vice President at Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team.

Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software.

Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.