While valuation-based market timing is notoriously difficult, present and future retirees should prepare for muted U.S. stock and bond returns relative to historical experience.

High valuations suggest that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip.

This outlook is by no means a call for despair, but rather highlights the increasing need for taking control of one’s destiny by controlling both investment and non-investment factors that can improve the odds of successfully meeting one’s retirement goals.

We are always on the lookout for interesting data visualizations related to the financial markets. Recently, two such charts have come across our computer screens.

The Drumbeat of High Equity Valuations Grows Louder

The first chart is from a recent article from Goldman Sachs Asset Management (“GSAM”)[1]. It reinforces the importance of developing realistic forward-looking expectations for asset class returns. This is a topic that we have droned on and on about over the last couple of years and one that we feel is especially important today, when the valuation backdrop for many core asset classes are stretched by historical standards.

The clear takeaway, at least in GSAM’s eyes, is found in the blue text in the upper right: “In 99% of the time at current valuation levels, equity returns have been single digit or negative.”

Now, there are a few complicating factors with the chart and this conclusion:

There is some hindsight bias embedded in the chart. In December 1999, when the S&P 500 reached an all-time high Shiller CAPE of 44.2, there was no way of knowing with certainty that valuations weren’t going even higher. After all, for an example of higher than tech bubble valuations, we need look no further than Japan.

The median rolling 10-year return for the S&P 500 over this period was 8.5%, so be careful in drawing the following conclusion: Equity returns have been “bad” 99% of the time when we’ve been at or near current valuation levels. A better conclusion to draw would be something like: Equity returns have tended to be average to below average when we’ve been at or near current valuation levels. When S&P 500 valuations were between the 75^{th} and 100^{th} percentile, subsequent 10-year returns were below the median of 8.5% approximately 80% of the time. The odds of a negative 10-year return, even at these valuation levels, is a pretty modest one in eight.

Mean reversion in valuations can take a very, very long time. For those looking to sell high and buy low (or vice-versa), the path to success can be terribly frustrating, requiring Buffett-like discipline to capture the eventual rewards. For example, Shiller’s CAPE rose above the 75^{th} percentile in January 1992. From this already high point, equities rallied another 300%+ before valuations peaked in late 1999. CAPE would not fall below the January 1992 value of 19.8 until October 2008.

There is a strong argument that valuations are driven by behavioral factors. For example, Jeremy Grantham discussed such a behavioral model in GMO’s most recent quarterly letter. He argues that the two factors most important in explaining high valuations are high profit margins and low inflation volatility. Viewed in this way, mean reversion would require one or both of these conditions to reverse course.

Visualizing Retirement Success and Failure

The second visualization comes from a recent post on Reddit; a news aggregation, web content rating, and discussion website; by a user going by the name zaladin. The graph shows the retirement wealth paths for various combinations of withdrawal rates and stock/bond splits.

However, before we start we want to point out that this is a highly simplified example. We only consider U.S. stocks and bonds, we don’t consider taxes or fees, etc.

In reality, the following factors can play a significant role in developing a retirement strategy: Alpha (investment performance vs. broadly diversified market portfolios), fees, taxes, desire to leave an inheritance to heirs, longevity/time horizon, diversification/risk management, spending flexibility, risk tolerance, valuation environment, etc.

Returning to our simplistic world, we’ve recreated the graph for a 4% inflation-adjusted withdrawal rate and a 60/40 stock/bond split below. In order to present data going back more than a century, we stick to U.S. equities for our stock exposure and 10-Year U.S. Treasuries for our bond exposure.

The horizontal (x-axis) represents the year when retirement starts. The vertical (y-axis) represents a given year in history. The coloring of each cell represents the savings balance at a given point in time. The meaning of each color as follows:

Green: Current account value greater than or equal to initial account value (e.g. an investor starting retirement with $1,000,000 has a current account balance that is at least $1,000,000).

Yellow: Current account value is between 75% and 100% of initial account value

Orange: Current account value is between 50% and 75% of the initial account value.

Red: Current account value is between 25% and 50% of the initial account value.

Dark Red: Current account value is between 0% and 25% of initial account value.

Black: Current account value is zero; the investor has run out of money.

The diagonal gray lines represent 20, 30, 40, and 50 years, respectively, after retirement.

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation

Source: Shiller Data Library. Calculations by Newfound Research. Credit to Reddit user zaladin for the graph format. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

One downside of the above visualization is that it only considers one withdrawal rate / portfolio composition combination. If we want the see results for withdrawal rates ranging from 1% to 10% in 1% increments and portfolio combinations ranging from 0/100 stocks/bonds to 100/0 stocks/bonds in 20% increments, we would need sixty graphs!

To distill things a bit more, we will look at the historical “success” of various investment and withdrawal strategies. We will evaluate success on three metrics:

Absolute Success Rate (“ASR”): The historical probability that an individual or couple will not run out of money before their retirement horizon ends.

Comfortable Success Rate (“CSR”): The historical probability that an individual or couple will have at least the same amount of money, in real terms, at the end of their retirement horizon compared to what they started with.

Ulcer Index (“UI”): The average pain of the wealth path over the retirement horizon where pain is measured as the severity and duration of wealth drawdowns relative to starting wealth. [Note: Normally, the Ulcer Index would be measured using true drawdown from peak, however, we believe that using starting wealth as the reference point may lead to a more accurate gauge of pain.]

We will evaluate these three metrics over a 30-year retirement horizon. Please feel free to reach out if you’d like to see the analysis for different horizon length.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

We see that withdrawal rates of 3% or less succeeded 95%+ of the time based on “ASR” regardless of asset allocation. A 4% withdrawal likewise succeeded with 90%+ historical probability as long as some equity exposure was incorporated into the portfolio. No stock/bond mix was able to support a withdrawal rate of 5% or more while succeeding at least nine times out of ten.

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

The results with “CSR” as our success measure largely mirror the “ASR” results. The only main differences are:

A 100% bond portfolio with a 3% withdrawal rate only leaves the investor with 100% of more of their initial wealth at the end of retirement in about two-thirds of scenarios. For an investor to achieve 90%+ CSR success with a 3% withdrawal rate, some equity is required.

Succeeding 90%+ of the time with a 4% withdrawal rate requires holding more stocks than bonds.

Ulcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns. The Ulcer Index is a measure of the duration and severity of drawdowns.

The Ulcer Index is a measure that summarizes the severity and duration of wealth drawdowns. We like this metric as it provides us some idea of how emotionally stressful a given market path is for investors. In our view, high investing stress not only is unenjoyable, but also raises the likelihood of making poor, emotionally-charged decisions.

Interpreting an individual Ulcer index alone can be difficult, but the relative values provide context. For example, for a 4% withdrawal rate, even though the portfolios with some equity had 90%+ ASRs, the 60/40 portfolio had the least stress, on average – even less than the slightly more successful (from a CSR standpoint) 80/20 portfolio.

So, what do these equity valuation and retirement visualizations have to do with one another?

For many investors, market returns are only the means to an end. Ultimately, investors are looking to achieve their financial goals. We certainly know that muted long-term returns in core stocks and bonds are not a good thing. But it can be hard to immediately understand what the true impact of such an outcome would be.

To see the effect of muted returns more clearly, we are going to recreate the retirement visualizations from earlier, but with one key modification: we adjust historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations given current valuation levels. We do this by subtracting the difference between the actual average log return and the forward-looking log return from each year’s return. By doing this, we reflect subdued average returns while retaining the peaks and valleys that we would expect in actual rolling 30-year periods.

Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates. These capital market assumptions assume that there is no valuation mean reversion (i.e. valuations stay the same going forward). The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.1%, respectively, compared to the historical values of 9.0% and 5.3%.

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation with Current Return Expectations

Source: Shiller Data Library. Calculations by Newfound Research. Credit to Reddit user zaladin for the graph format. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

With updated return assumptions, we see a dramatically different picture with a lot less green and a lot more of the dreaded black (i.e. fully exhausting one’s savings). The results are similar across withdrawal rates and asset allocations.

We see that only withdrawal rates of 2% or less would have achieved 90%+ success over thirty years regardless of asset allocation. High success rates can still be attained with a 3% withdrawal rate assuming investors are willing to bear the risk of moderate to aggressive equity allocations. Unfortunately, a 4% withdrawal rate no longer offers the safety that actual experience has suggested.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

In our example, passing on starting wealth to heirs at the end of retirement looks difficult except at withdrawal rates of less than 3%. The same can be said for investors looking for a stress-free journey as Ulcer Index values are much higher in this scenario for 3%+ withdrawal rates than what we saw using historical returns.

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

Ulcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon

Source: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns. The Ulcer Index is a measure of the duration and severity of drawdowns.

Conclusion: Taking Control of Retirement

High valuations of core assets in the U.S. suggest that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip. Unfortunately, we cannot control the returns of U.S. stocks or bonds (or any asset class returns for that matter).

But we can take control of the factors that we can influence.

For a current or future retiree, this means controlling to the extent possible factors like taxes, saving, and spending. From an investment perspective, it means:

Being strategic, not static: Have a thoughtful, forward-looking outlook when developing a strategic asset allocation. This means having a willingness to diversify U.S. stocks and bonds with the ever-expanding palette of complementary asset classes and strategies.

Directly address the role of behavioral finance by recognizing that an investor must have the willingness to stick with a plan in order to succeed (e.g. the journey is just as important as the destination).

Utilize a hybrid active/passive approach for core exposures given the increasing availability of evidence-based, factor-driven investment strategies.

Be fee-conscious, not fee-centric. For many exposures (e.g. passive and long-only core stock and bond exposure), minimizing cost is certainly appropriate. However, do not let cost considerations preclude the consideration of strategies or asset classes that can bring unique return generating or risk mitigating characteristics to the portfolio.

Look beyond fixed income for risk management given low interest rates.

Recognize that the whole can be more than the sum of its parts by embracing not only asset class diversification, but also strategy/process diversification.

Retirement success and muted future returns are not mutually exclusive. However, achieving financial goals in such an environment requires careful planning for factors that may have been safely ignored given the generous market tailwinds of prior decades.

[1] Goldman Sachs Asset Management, “The Synchronized Expansion.” https://www.gsam.com/content/gsam/us/en/advisors/market-insights/market-strategy/market-know-how/2017/Q32017.html#section-background_ebd2_background_moduletitle_874b

## Impact of High Equity Valuations on Safe Retirement Withdrawal Rates

By Justin Sibears

On August 14, 2017

In Sequence Risk, Weekly Commentary

This post is available as a PDF here.## Summary

We are always on the lookout for interesting data visualizations related to the financial markets. Recently, two such charts have come across our computer screens.

## The Drumbeat of High Equity Valuations Grows Louder

The first chart is from a recent article from Goldman Sachs Asset Management (“GSAM”)[1]. It reinforces the importance of developing realistic forward-looking expectations for asset class returns. This is a topic that we have droned on and on about over the last couple of years and one that we feel is especially important today, when the valuation backdrop for many core asset classes are stretched by historical standards.

The clear takeaway, at least in GSAM’s eyes, is found in the blue text in the upper right: “

In 99% of the time at current valuation levels, equity returns have been single digit or negative.”Now, there are a few complicating factors with the chart and this conclusion:

^{th}and 100^{th}percentile, subsequent 10-year returns were below the median of 8.5% approximately 80% of the time. The odds of a negative 10-year return, even at these valuation levels, is a pretty modest one in eight.^{th}percentile in January 1992. From this already high point, equities rallied another 300%+ before valuations peaked in late 1999. CAPE would not fall below the January 1992 value of 19.8 until October 2008.## Visualizing Retirement Success and Failure

The second visualization comes from a recent post on Reddit; a news aggregation, web content rating, and discussion website; by a user going by the name zaladin. The graph shows the retirement wealth paths for various combinations of withdrawal rates and stock/bond splits.

However, before we start we want to point out that this is a highly simplified example. We only consider U.S. stocks and bonds, we don’t consider taxes or fees, etc.

In reality, the following factors can play a significant role in developing a retirement strategy: Alpha (investment performance vs. broadly diversified market portfolios), fees, taxes, desire to leave an inheritance to heirs, longevity/time horizon, diversification/risk management, spending flexibility, risk tolerance, valuation environment, etc.

Returning to our simplistic world, we’ve recreated the graph for a 4% inflation-adjusted withdrawal rate and a 60/40 stock/bond split below. In order to present data going back more than a century, we stick to U.S. equities for our stock exposure and 10-Year U.S. Treasuries for our bond exposure.

The horizontal (x-axis) represents the year when retirement starts. The vertical (y-axis) represents a given year in history. The coloring of each cell represents the savings balance at a given point in time. The meaning of each color as follows:

Green:Current account value greater than or equal to initial account value (e.g. an investor starting retirement with $1,000,000 has a current account balance that is at least $1,000,000).Yellow:Current account value is between 75% and 100% of initial account valueOrange:Current account value is between 50% and 75% of the initial account value.Red:Current account value is between 25% and 50% of the initial account value.Dark Red:Current account value is between 0% and 25% of initial account value.Black: Current account value is zero; the investor has run out of money.The diagonal gray lines represent 20, 30, 40, and 50 years, respectively, after retirement.

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond AllocationSource: Shiller Data Library. Calculations by Newfound Research. Credit to Reddit user zaladin for the graph format. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

One downside of the above visualization is that it only considers one withdrawal rate / portfolio composition combination. If we want the see results for withdrawal rates ranging from 1% to 10% in 1% increments and portfolio combinations ranging from 0/100 stocks/bonds to 100/0 stocks/bonds in 20% increments, we would need sixty graphs!

To distill things a bit more, we will look at the historical “success” of various investment and withdrawal strategies. We will evaluate success on three metrics:

relative to starting wealth. [Note: Normally, the Ulcer Index would be measured using true drawdown from peak, however, we believe that using starting wealth as the reference point may lead to a more accurate gauge of pain.]We will evaluate these three metrics over a 30-year retirement horizon. Please feel free to reach out if you’d like to see the analysis for different horizon length.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. HorizonSource: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

We see that withdrawal rates of 3% or less succeeded 95%+ of the time based on “ASR” regardless of asset allocation. A 4% withdrawal likewise succeeded with 90%+ historical probability as long as some equity exposure was incorporated into the portfolio. No stock/bond mix was able to support a withdrawal rate of 5% or more while succeeding at least nine times out of ten.

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. HorizonSource: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

The results with “CSR” as our success measure largely mirror the “ASR” results. The only main differences are:

Ulcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. HorizonSource: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns. The Ulcer Index is a measure of the duration and severity of drawdowns.

The Ulcer Index is a measure that summarizes the severity and duration of wealth drawdowns. We like this metric as it provides us some idea of how emotionally stressful a given market path is for investors. In our view, high investing stress not only is unenjoyable, but also raises the likelihood of making poor, emotionally-charged decisions.

Interpreting an individual Ulcer index alone can be difficult, but the relative values provide context. For example, for a 4% withdrawal rate, even though the portfolios with some equity had 90%+ ASRs, the 60/40 portfolio had the least stress, on average – even less than the slightly more successful (from a CSR standpoint) 80/20 portfolio.

So, what do these equity valuation and retirement visualizations have to do with one another?For many investors, market returns are only the means to an end. Ultimately, investors are looking to achieve their financial goals. We certainly know that muted long-term returns in core stocks and bonds are not a good thing. But it can be hard to immediately understand what the true impact of such an outcome would be.

To see the effect of muted returns more clearly, we are going to recreate the retirement visualizations from earlier, but with one key modification: we adjust historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations given current valuation levels. We do this by subtracting the difference between the actual average log return and the forward-looking log return from each year’s return. By doing this, we reflect subdued average returns while retaining the peaks and valleys that we would expect in actual rolling 30-year periods.

Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates. These capital market assumptions assume that there is no valuation mean reversion (i.e. valuations stay the same going forward). The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.1%, respectively, compared to the historical values of 9.0% and 5.3%.

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation with Current Return ExpectationsSource: Shiller Data Library. Calculations by Newfound Research. Credit to Reddit user zaladin for the graph format. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

With updated return assumptions, we see a dramatically different picture with a lot less green and a lot more of the dreaded black (i.e. fully exhausting one’s savings). The results are similar across withdrawal rates and asset allocations.

We see that only withdrawal rates of 2% or less would have achieved 90%+ success over thirty years regardless of asset allocation. High success rates can still be attained with a 3% withdrawal rate assuming investors are willing to bear the risk of moderate to aggressive equity allocations. Unfortunately, a 4% withdrawal rate no longer offers the safety that actual experience has suggested.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. HorizonSource: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

In our example, passing on starting wealth to heirs at the end of retirement looks difficult except at withdrawal rates of less than 3%. The same can be said for investors looking for a stress-free journey as Ulcer Index values are much higher in this scenario for 3%+ withdrawal rates than what we saw using historical returns.

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. HorizonUlcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. HorizonSource: Shiller Data Library. Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends. Returns are hypothetical index returns and are gross of all fees and expenses. Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns. The Ulcer Index is a measure of the duration and severity of drawdowns.

Conclusion: Taking Control of RetirementHigh valuations of core assets in the U.S. suggest that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip. Unfortunately, we cannot control the returns of U.S. stocks or bonds (or any asset class returns for that matter).

But we can take control of the factors that we can influence.

For a current or future retiree, this means controlling to the extent possible factors like taxes, saving, and spending. From an investment perspective, it means:

These are all ideas that help form the foundation for our QuBe Model Portfolios.

Retirement success and muted future returns are not mutually exclusive. However, achieving financial goals in such an environment requires careful planning for factors that may have been safely ignored given the generous market tailwinds of prior decades.

[1] Goldman Sachs Asset Management, “The Synchronized Expansion.” https://www.gsam.com/content/gsam/us/en/advisors/market-insights/market-strategy/market-know-how/2017/Q32017.html#section-background_ebd2_background_moduletitle_874b