Category: Sequence Risk

You Are Not a Monte-Carlo Simulation

On March 19, 2018

This commentary is available as a PDF download here.

Summary

Even when an investment has a positive expected average growth rate, the experience of most individuals may be catastrophic.
By focusing on the compound average growth rate, we can see the median realizations – which account for risk – are often more crucial decision points than ensemble averages, which are the focal point of Monte Carlo analysis.
These arguments also provide a simple explanation for investor behavior that avoids the need for utility theory concepts that have been used for the past 200+ years.
Since we can neither average our results with other investors nor average our results with potential copies of ourselves in infinite states of the world, the best we can do is try to average over time.
Because we all live in a multi-period world where we have a single investment portfolio that compounds over time, managing risk can help us maximize our long-term growth rate even if it seems foolish in hindsight.

Pretend we come to you offering a new investment strategy. Each week, you earn 0.65% (such that over a year you earn 40%), but there is a 1-in-200 chance that you lose -95%. Would you invest?

If we simulate out a single trial, we can see that within a year, we may lose most of our money.

Of course, just because things went wrong in our singular example does not mean that this is necessarily a bad investment. In fact, if we evaluate the prospects of this investment by looking at the average experience, we end up with something far more attractive (the “Ensemble,” which is essentially a Monte-Carlo simulation of the strategy).

The math here is simple: 99.5% of the time we make 1.0065x our money and 0.5% of the time, we end up with 0.05x our money. On average, then, we end up with 1.0017x, or 1.092x annualized. While the average experience is not the 40% annualized we sought, the 9.2% return after a year is still nothing to scoff at.

Of course, the average is not actually achievable. There are not infinite variations of this investment strategy for you to allocate your capital across, nor, we suspect, do you have access to infinite versions of you living in parallel universes who can pool their risk.

Rather, you are forced to diversify your risk over time. Here we end up with a different picture.

Another series of unfortunate events?

Not so fast. You see, when we move to diversifying over time, we need to look at a time-weighted average. It is not the arithmetic mean we are after, but rather the geometric mean which will account for the effects of compounding. Calculating the geometric mean – 1.0065^99.5% x 0.05^0.5% – leaves us with a value of 0.9915, i.e. our wealth is expected to decay over time.

Wait.

How is it possible that on average the strategy is a winner if each and every path is expected to decay over time?

The simple answer: A few fortunate outliers make up for all decaying paths.

The slightly more complex answer: In this investment, our wealth can never go below $0 but we can theoretically make an infinite amount of money. Thus, over time, the average is dragged up.

The Misleading Mean

In many cases, the average experience can be entirely misleading for the experience you can expect. In the world of bell-curves and normal distributions, we typically expect experiences to be clustered around the average. For example, there are more people close to the average height than there are far away.

However, when other distributions apply, the average can be unlikely. Wealth distribution is a perfect example of this. In 2013 in the United States, the top 10% of families held 76% of the wealth while the bottom 50% held 1%. Using 2017 figures, if we divided net worth among the U.S. population – i.e. the “average” household wealth – it would come out to around $760,000 per family. The bottom 50%, however, have a net worth closer to $11,000 per family.

In other words, if you pick a random person off the street, their experience is likely much closer to $11,000 than $760,000. It’s the wealthy outliers that are pulling the average up.

A more applicable metric, in this case, might be the median, which will say, “50% of experiences are below this level and 50% are above.”

The Role of Risk

As it turns out, the median is important for those of us diversifying over time as well. If we consider our hypothetical investment strategy above, our intuition is that the median result is probably not great. Eventually, it feels like, everyone goes practically bankrupt. If we plot the median result, we see almost exactly that.

(As a side note, if you’re wondering why the median result exhibits a sawtooth pattern rather than the smoother results of the mean, the answer is the median is the actual result that sits at the 50^th percentile. Knowing that the probability of losing 95% of our wealth is 1-in-200, it takes time for enough individuals to experience a poor result for the median to drop.)

In fact, if we model investment wealth as a Geometric Brownian Motion (a commonly used stochastic process for modeling stock prices), then over the long run an investor’s compound growth rate approaches the median, not the mean.[1] The important difference between the two is that while volatility does not affect the expected level of wealth, it does drive the mean and median further apart. In fact, the median growth rate is the mean growth rate minus half the volatility squared (which you might recognize as being the common approximation for – drum roll please – the geometric growth rate).

In other words: volatility matters.

Most investors we speak with have an intuitive grasp of this concept. They know that when you lose 10% of your wealth, you need to gain 11.11% back to get to break even.

And when you lose 50%, and you need to earn 100% to get back to break even. Under compound results, feeling twice the pain from losses than the pleasure from gain makes complete sense. There are no individual and independent trials: results have consequences.

This is why taking less risk can actually lead to greater growth in wealth in the long run. If we take too little risk, we will will not participate, but too much risk can lead to ruin. For example, below we plot final wealth results after a 50% drop in market value and a 100% recovery depending on your capture ratio.

As an example of reading this graph, if we start with $1 and experience a 50% loss and a 100% gain, but are only 50% exposed to each of those movements (i.e. we lose 25% and then gain 50%), we end up with $1.125. At the far right of the graph, we can see that at 2x exposure, the first 50% move completely wipes out our capital.

Common Sense Utility Theory

What economists have found, however, is that even if we offer our investment as a one-off event – where the expected return is definitively positive – most would still forego it. To resolve this conundrum, economists have proposed utility theory.

The argument is that investors do not actually try to maximize their expected change in wealth, but rather try to maximize the expected utility of that change. The earliest formalization of this concept was in a paper written by Daniel Bernoulli in 1738, where he proposed a mathematical function that would correct the expected return to account for risk aversion.

Bernoulli’s originally proposed function was log-utility. And under log-utility, our investment strategy offering is no longer appealing: log(1.0065) x 99.5% + log(0.05) x 0.50% is a negative value. What’s interesting about log utility is that, due to the property of logarithms, it ends up creating the identical decision axiom as had we used our compound growth rate model.

log(1.0065) x 99.5% + log(0.05) x 0.50% = log(1.0065^99.5%) + log(0.05^0.5%) = log(1.0065^99.5% x 0.05^0.5%)

So while utility theory is supposed to correct for behavioral foibles like “risk aversion,” what it really does is take a single-period bet and turn it into a multi-period, compound bet.

Under the context of multi-period, compounding results, “risk aversion” is not so foolish. If we have our arm mauled off by a lion on the African veldt, we cannot simply “average” our experience with others in the tribe and end up with 97% of an arm. We cannot “average” our experience across the infinite universes of other potential outcomes where we were not necessarily mauled. Rather, our state is permanently altered for life.

Similarly, if we lose 50% of our money, we cannot just “average” our results with other investors. Nor can we average our results with all the potential infinite alternate universes where we did not lose 50%. The best we can do is try to average over time, which means that our compound growth rate matters. And, as we demonstrated above, so does risk.

Conclusion

Ex-post, managing risk can often feel foolish. Almost exactly 9 years after the bottom of the 2008-2009 bear market, the S&P 500 has returned more than 380%. Asset class, geographic, and process diversification largely proved foolish relative to simple buy-and-hold.

Ex-ante, however, few would forgo risk management. Ask yourself this: would you sell everything today to buy only U.S. large-cap stocks? If not, then there is little to regret about not having done it in the past. While the narratives we spin often make realized results seem obvious in hindsight, the reality is that our collective crystal balls were just as cloudy back then as they are today.

Few lament that their house did not burn down when they buy fire insurance. We buy insurance “in case,” not because we want the risk to materialize.

We all live in a multi-period world where we have a single investment portfolio that compounds over time. In such a world, risk matters tremendously. A single, large loss can take us permanently off plan. Even small losses can put us off course when compounded in a streak of bad luck. While a focus on risk aversion may seem foolish in hindsight when risk does not materialize, going forward we know that managing risk can help us maximize our long-term growth rate.

[1] Derivations for this result can be found in our commentary Growth Optimal Portfolios

Should You Dollar-Cost Average?

By Nathan Faber

On February 12, 2018

In Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

Dollar-cost averaging (DCA) versus lump sum investing (LSI) is often a difficult decision fraught with emotion.
The historical and theoretical evidence contradicts the notion that DCA leads to better results from a return perspective, and only some measures of risk point to benefits in DCA.
Rather than holding cash while implementing DCA, employing a risk managed strategy can lead to better DCA performance even in a muted growth environment.
Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

Dollar-cost averaging (DCA) is the process of investing equal amounts into an asset or a portfolio over a period of time at regular intervals. It is commonly thought of as a way to reduce the risk of investing at the worst possible time and seeing your investment immediately decline in value.

The most familiar form of dollar-cost averaging is regular investment directed toward retirement accounts. A fixed amount is deducted from each paycheck and typically invested within a 401(k) or IRA. When the securities in the account decline in value, more shares are purchased with the cash, and over the long run, the expectation is to invest at a favorable average price.

For this type of dollar-cost averaging, there is not a lot of input on the investor’s part; the cash is invested as it arrives. The process is involuntary once it is initiated.

A slightly different scenario for dollar-cost averaging happens when an investor has a lump sum to invest: the choice is to either invest it at once (“lump-sum investing”; LSI) or spread the investment over a specified time horizon using DCA.

In this case, the investor has options, and in this commentary we will explore some of the arguments for and against DCA with a lump sum with the intention of reducing timing risk in the market.

The Historical Case Against Dollar-Cost Averaging

Despite the conventional wisdom that DCA is a prudent idea, investors certainly have sacrificed a fair amount of return potential by doing it historically.

In their 2012 paper entitle Dollar-Cost Averaging Just Means Taking Risk Later[1], Vanguard looked at LSI versus DCA in the U.S., U.K., and Australia over rolling 10-year periods and found that for a 60/40 portfolio, LSI outperformed DCA about 2/3 of the time in each market.

If we assume that a lump sum is invested in the S&P 500 in equal monthly amounts over 12-months with the remaining balance held in cash earning the risk-free interest rate, we see a similar result over the period from 1926 to 2017.

Why does dollar-cost averaging look so bad?

In our previous commentary on Misattributing Bad Behavior[2], we discussed how the difference between investment return – equivalent to LSI – and investor return – equivalent to DCA – is partly due to the fact that investors are often making contributions in times of positive market returns. Over this 92 year period from 1926 to 2017, the market has had positive returns over 74% of the rolling 12-month periods. Holding cash and investing at a later date means forgoing some of these positive returns. From a theoretical basis, this opportunity cost is the equity risk premium: the expected excess return of equities over cash.

In our current example where investors voluntarily choose to dollar-cost average, the same effect is experienced.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The average outperformance of the LSI strategy was 4.1%, and as expected, there is a strong correlation between how well the market does over the year and the benefit of LSI.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Surely DCA Worked Somewhere

If the high equity market returns in the U.S., and as the Vanguard piece showed in the U.K. and Australia, were the force behind the attractiveness of lump sum investing, let’s turn to a market where returns were not so strong: Japan. As of the end of 2017, the MSCI Japan index was nearing its high water mark set at the end of 1989: a drawdown of 38 years.

Under the same analysis, using the International Monetary Fund’s (IMF) Japanese discount rate as a proxy for the risk-free rate in Japan, DCA only outperforms LSI slightly more than half of the time over the period from 1970 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

Truncating the time frame to begin in 1989 penalizes DCA even more – perhaps surprisingly, given the negligible average return – with it now outperforming slightly under 50% of the time.

Over the entire time period, there is a similar relationship to the outperformance of LSI versus the performance of the Japanese equity index.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The Truth About Dollar-Cost Averaging

Given this empirical evidence, why is dollar-cost averaging still frequently touted as a superior investing strategy?

The claims – many of which come from media outlets – that dollar-cost averaging is predominantly beneficial from a return perspective are false. It nearly always sacrifices returns, and many examples highlighted in these articles paint pictures of hypothetical scenarios that, while grim, are very isolated and/or unrealistic given the historical data.

Moving beyond the empirical evidence, dollar-cost averaging is theoretically sub-optimal to lump sum investing in terms of expected return.

This was shown to be the case in a mean-variance framework in 1979 by George Constantinides.[6]

His argument was that rather than committing to a set investment schedule based on the initial information in the market, adopting a more flexible approach that adjusts the investment amount based on subsequent market information will outperform DCA.

In the years since, many other hypotheses have been put forward for why DCA should be beneficial – different investor utility functions, prospect theory, and mean reversion in equity returns, among others – and most have been shown to be inadequate to justify DCA.

More recently, Hayley (2012)[7] explains the flaw in many of the DCA arguments based on a cognitive error in assuming that the purchase at a lower average price increases the expected returns.

His argument is that since purchasing at the average price requires buying equal share amounts each period, you can only invest the total capital at the true average price of a security or portfolio with perfect foreknowledge of how the price will move. This leads to a lower average purchase price for DCA compared to this equal share investing strategy.

But if you had perfect foreknowledge of the future prices, you would not choose to invest equal share amounts in the first place!

Thus, the equal share investing plan is a straw man comparison for DCA.

We can see this more clearly when we actually dive into examples that are similar to ones generally presented in favor of DCA.

We will call the equal share strategy that invests the entire capital amount, ES Hypothetical. This is the strategy that uses the knowledge of the price evolution. The more realistic equal share investing strategy assumes that prices will remain fixed and purchases the same shares in each period as the DCA strategy purchases in the first period. The strategy is called ES Actual. Any remaining capital is invested in the final period regardless of whether it purchases more or fewer shares than desired, but the results would still hold if this amount were considered to still be held as cash (possibly borrowed if need be) since the analysis ends at this time step.

The following tables show the final account values for 4 simple market scenarios:

Downtrend
Uptrend
Down then up
Up then down

In every scenario, the DCA strategy purchases shares at a lower average cost than the ES Hypothetical strategy and ends up better off, but the true comparison is less clear cut.

The ES Actual and LSI strategies’ average purchase prices and final values may be higher or lower than DCA.

A Comparison of DCA to Equal Share Investing and LSI

Calculations by Newfound Research. All examples are hypothetical.

A More General Comparison of LSI and DCA

In these examples, DCA does outperform LSI half the time, but these examples are extremely contrived.

We can turn to simulations to get a better feel for how often LSI will outperform DCA and by how much under more realistic assumptions of asset price movements.

Using Monte Carlo, we can see how often LSI outperforms DCA for a variety of expected excess returns and volatilities over 12-month periods. Using expected excess returns allows us to neglect the return on cash.

For any positive expected return, LSI is expected to outperform more frequently at all volatility levels. The frequency increases as volatility decreases for a given expected return.

If the expected annual return is negative, then DCA outperforms more frequently.

Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

Turning now to the actual amount of outperformance, we see a worse picture for DCA.

For more volatile assets, the expected outperformance is in LSI’s favor even at negative expected returns. This is the case despite what we saw before about DCA outperforming more frequently for these scenarios.

As interest rates increase, DCA will benefit assuming that the expected return on equities remains the same (i.e. the expected excess return decreases). However, even if we assume that the cash account could generate an extra 200 bps, which is generous given that this would imply that cash rates were near 4%, for the 15% volatility and 5% expected excess return case, this would still mean that LSI would be expected to outperform DCA by 100 bps.

What About Risk?

It is clear that DCA does not generally outperform LSI from a pure return point-of-view, but what about when risk is factored in? After all, part of the reason DCA is so popular is because it is said to reduce the risk of investing at the worst possible time.

Under the same Monte Carlo setup, we can use the ulcer index to quantify this risk. The ulcer index measures the duration and severity of the drawdowns experienced in an investment, where a lower ulcer index value implies fewer and less severe drawdowns.

The chart below shows the median ratio of the LSI ulcer index and the DCA ulcer index. We plot the ratio to better compare the relative riskiness of each strategy.

As we would expect, since the DCA strategy linearly moves from cash to an investment, the LSI scheme takes on about twice the drawdown risk in many markets.

When the lump sum is invested, the whole investment is subject to the mercy of the market, but if DCA is used, the market exposure is only at its maximum in the last month.[8]

The illustration of this risk alone may be enough to convince investors that DCA meets its objective of smoothing out investment returns. However, at what cost?

Combining the expected outperformance and the risk embodied in the ulcer index shows that LSI is still expected to outperform on a risk adjusted basis between about 35% and 45% of the time.

While this is lower than it was from a pure return perspective, it should be taken with a grain of salt.

First, we know from the start that LSI will be more exposed to drawdowns. One possible solution would be treat a ratio of ulcer indices of 2 (instead of 1) as the base case.

Second, for an investor who is not checking their account monthly, the ulcer index may not mean much. If you only looked at the account value at the beginning and end of the year regardless of whether you did DCA or LSI, then LSI is generally expected to leave the account better off; the intermediate noise does not get “experienced.”

When Can DCA Work?

So now that we have shown that DCA is empirically and theoretically suboptimal to LSI , why might you still want to do it?

First, we believe there is still a risk reduction argument that makes sense when accounting for investor behavior. Most research has focused on risk in the form of volatility. We showed previously that focusing more on drawdown risk can lead to better risk-adjusted performance of DCA.

We could also look at the gain-to-pain ratio, defined here as the average outperformance divided by the average underperformance of the LSI strategy.

The following chart shows a sampling of asset classes expected returns and volatilities from Research Affiliates with indifference boundaries for different gain-to-pain ratios. Indifferences boundaries show the returns and volatilities with constant gain-to-pain ratios. For a given gain-to-pain ratio (e.g. 1.5 means that you will only accept the risk in LSI if its outperformance over DCA is 50% higher, on average), any asset class points that fall below that line are good candidates for DCA.

The table below shows which asset classes correspond to each region on the chart.

Source: Research Affiliates. Calculations by Newfound Research. Results assume Geometric Brownian Motion using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

As the indifference coefficient increases, the benefit of DCA from a gain-to-pain perspective becomes less. For volatile asset classes with lower expected returns (e.g. U.S. equities and long-term U.S. Treasuries), DCA may make sense. For less volatile assets like income focused funds and assets with higher expected growth like EM equities, LSI may be the route to pursue.

A second reason for using DCA is that there are also some market environments that are actually favorable to DCA. As we saw previously, down-trending markets lead to better absolute performance for DCA and volatility makes DCA more attractive from a drawdown risk perspective even in markets with positive expected returns.

Sideways markets are also good for DCA. So are markets that have a set final return.[9] The more volatility the better for DCA in these scenarios.

The chart below shows the return level below which DCA is favored. If you are convinced that the market will return less than -0.6% this year, then DCA is expected to outperform LSI.

Calculations by Newfound Research. Results assume Brownian Bridges using the given parameters and compare investing all capital at the beginning of 12 months to investing capital equally at the beginning of each month.

While a set final return may be an unrealistic hope – who knows where the market will be a year from now? – it allows us to translate beliefs for market returns into an investing plan with DCA or LSI.

However, even though the current high-valuation environment has historically low expected returns for stocks and bonds, the returns over the next year may vary widely. The appeal of DCA may be stronger in this environment even though it is sub-optimal to LSI.

Instead of using DCA on its own as a risk management tool – one that may sacrifice too much of the return to be had – we can pair it with other risk management techniques to improve its odds of outperforming LSI.

Finding a DCA Middle Ground

One of the primary drags on DCA performance is the fact that much of the capital is sitting in cash for most of the time.

Is there a way to reduce this cost of waiting to invest?

One initial alternative to cash is to hold the capital in bonds. This is in line with the intuitive notion of beginning in a low risk profile and moving gradually to a higher one. While this improves the frequency of outperformance of DCA historically, it does little to improve the expected outperformance.

Another option is to utilize a risk managed sleeve that is designed to protect capital during market declines and participate in market growth. Using a simple tactical strategy that holds stocks when they are above their 10-month SMA and bonds otherwise illustrates this point, boosting the frequency of outperformance for DCA from 32% to 71%.

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The tactical strategy narrows the distribution of expected outperformance much more than bonds.

Since we know that the tactical strategy did well over this historical period with the benefit of hindsight, we can also look at how it would have done if returns on stocks and bonds were scaled down to match the current expectations from Research Affiliates.[10]

Source: Kenneth French Data Library and Robert Shiller Data Library. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results.

The frequency of outperformance is still in favor of the tactical strategy, and the distribution of outperformance exhibits trends similar to using the actual historical data.

Going back to the Japanese market example, we also see improvement in DCA using the tactical strategy. The benefit was smaller than in the U.S, but it was enough to make both the frequency and expected outperformance swing in favor of DCA, even for the period from 1989 to 2017.

Source: MSCI and Federal Reserve of St. Louis. Calculations by Newfound Research. Results are hypothetical. Past performance does not guarantee future results. Data from 1970 to 2017.

Deploying cash immediately into a risk-managed solution does not destroy the risk of DCA underperforming if it uses cash. The cost of using this method is that a tactical strategy can be exposed to whipsaw.

One way to mitigate the cost of whipsaw is to use a more diversified (in terms of process and assets) risk management sleeve.

Conclusion

Dollar-cost averaging verses lump sum investing is often a difficult decision fraught with emotion. Losing 10% of an investment right off the bat can be a hard pill to swallow. However, the case against DCA is backed up by empirical evidence and many theoretical arguments.

If a portfolio is deemed optimal based on an investor’s risk preferences and tolerances, then anything else would be suboptimal. But what is optimal on paper is not always the best for an investor who cannot stick with the plan.

Because of this, there are times when DCA can be beneficial. Certain measures of risk that account for drawdowns or the asymmetric psychological impacts of gains and losses point to some benefits for DCA over LSI.

Given that even in this low expected return market environment, the expected return on cash is still less than that on equities and bonds, deploying cash in a risk-managed solution or a strategy that has higher expected returns for the amount of risk it takes may be a better holding place for cash while implementing a DCA scheme.

It is important to move beyond a myopic view, commonly witnessed in the market, that DCA is best for every situation. Even though LSI may feel like market timing, DCA is simply another form of market timing. With relatively small balances, DCA can also increase commission costs and possibly requires more oversight or leads to higher temptation to check in on a portfolio, resulting in rash decisions.

Ultimately, the best solution is the one that gets an investor into an appropriate portfolio, encourages them to stay on track for their long term financial goals, and appropriately manages any behavioral consequences along the way.

[1] https://personal.vanguard.com/pdf/s315.pdf

[2] https://blog.thinknewfound.com/2017/02/misattributing-bad-behavior/

[3] A Note on the Suboptimality of Dollar-Cost Averaging as an Investment Policy, https://faculty.chicagobooth.edu/george.constantinides/documents/JFQA_1979.pdf

[4] Dollar-Cost Averaging: The Role of Cognitive Error, https://www.cass.city.ac.uk/__data/assets/pdf_file/0008/128384/Dollar-Cost-Averaging-09052012.pdf

[5] This is a form of sequence risk. In DCA, the initial returns on the investment do not have the same impact as the final period returns.

[6] Milevsky, Moshe A. and Posner, Steven E., A Continuous-Time Re-Examination of the Inefficiency of Dollar-Cost Averaging (January 1999). SSBFIN-9901. Available at SSRN: https://ssrn.com/abstract=148754

[7] Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates. These capital market assumptions account 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 3.3%, respectively.

Addressing Low Return Forecasts in Retirement with Tactical Allocation

By Nathan Faber

On September 25, 2017

In Risk Management, Sequence Risk, Weekly Commentary

This post is available for download as a PDF here.

Summary

The current return expectations for core U.S. equities and bonds paint a grim picture for the success of the 4% rule in retirement portfolios.
While varying the allocation to equities throughout the retirement horizon can provide better results, employing tactical strategies to systematically allocate to equities can more effectively reduce the risk that the sequence of market returns is unfavorable to a portfolio.
When a tactical strategy is combined with other incremental planning and portfolio improvements, such as prudent diversification, more accurate spending assessments, tax efficient asset location, and fee-conscious investing, a modest allocation can greatly boost likely retirement success and comfort.

Over the past few weeks, we have written a number of posts on retirement withdrawal planning.

The first was about the potential impact that high core asset valuations – and the associated muted forward return expectations – may have on retirement.

The second was about the surprisingly large impact that small changes in assumptions can have on retirement success, akin to the Butterfly Effect in chaos theory. Retirement portfolios can be very sensitive to assumed long-term average returns and assumptions about how a retiree’s spending will evolve over time.

In the first post, we presented a visualization like the following:

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation
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 horizontal (x-axis) represents the year when retirement starts. The vertical (y-axis) represents the years post-retirement. 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.

We then recreated the visualization, but with one key modification: we adjusted the historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations[1] given current valuation levels. We did this by subtracting the difference between the actual average log return and the forward-looking long return from each year’s return. With this technique, we capture the effect of subdued average returns while retaining realistic behavior for shorter-term returns.

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. 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 visualizations is that they only consider 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 looked at the historical “success” of various investment and withdrawal strategies. We evaluated 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. [2]

As a quick refresher, below we present the ASR for various withdrawal rate / risk profile combinations over a 30-year retirement horizon first using historical returns and then using historical returns adjusted to reflect current valuation levels. The CSR and Ulcer Index table illustrated similar effects.

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

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

Overall, our analysis suggested that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip.

The combined conclusion of these two posts is that the near future looks pretty grim for retirees and that an assumption that is slightly off can make the outcome even worse.

Now, we are going to explore a topic that can both mitigate low growth expectations and adapt a retirement portfolio to reduce the risk of a bad planning assumption. But first, some history.

How the 4% Rule Started

In 1994, Larry Bierwirth proposed the 4% rule, and William Bengen expanded on the research in the same year.[3], [4]

In the original research, the 4% rule was derived assuming that the investor held a 50/50 stock/bond portfolio, rebalanced annually, withdrew a certain percentage of the initial balance, and increased withdrawals in line with inflation. 4% is the highest percentage that could be withdrawn without ever running out of money over an historical 30-year retirement horizon.

Graphically, the 4% rule is the minimum value shown below.

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon

Since its publication, the rule has become common knowledge to nearly all people in the field of finance and many people outside it. While it is a good rule-of-thumb and starting point for retirement analysis, we have two major issues with its broad application:

It assumes that not running out of money is the only goal in retirement without considering implications of ending surpluses, return paths that differ from historical values, or evolving spending needs.
It provides a false sense of security: just because 4% withdrawals never ran out of money in the past, that is not a 100% guarantee that they won’t in the future.

For example, if we adjust the stock and bond historical returns using the estimates from Research Affiliates (discussed previously) and replicate the analysis Bengen-style, the safe withdrawal rate is a paltry 2.6%.

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon using Current Return Estimates

Source: Shiller Data Library and Research Affiliates. 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.

While this paints a grim picture for retirement planning, it’s not likely how one would plan their financial future. If you were to base your retirement planning solely on this figure, you would have to save 54% more for retirement to generate the same amount of annual income as with the 4% rule, holding everything else constant.

In reality, even with the low estimates of forward returns, many of the scenarios had safe withdrawal rates closer to 4%. By putting a multi-faceted plan in place to reduce the risk of the “bad” scenarios, investors can hope for the best while still planning for the worst.

One aspect of a retirement plan can be a time-varying asset allocation scheme.

Temporal Risk in Retirement

Conventional wisdom says that equity risk should be reduced as one progresses through retirement. This is what is employed in many “through”-type target date funds that adjust equity exposure beyond the retirement age.

If we heed the “own your age in bonds” rule, then a retiree would decrease their equity exposure from 35% at age 65 to 5% at the end of a 30-year plan horizon.

Unfortunately, this thinking is flawed.

When a newly-minted retiree begins retirement, their success is highly dependent on their first few years of returns because that is when their account values are the largest. As they make withdrawals and are reducing their account values, the impact of a large drawdown in dollar terms is not nearly as large. This is known as sequence risk.

As a simple example, consider three portfolio paths:

Portfolio A: -30% return in Year 1 and 6% returns for every year from Year 2 – Year 30.
Portfolio B: 6% returns for every year except for Year 15, in which there is a -30% return.
Portfolio C: 6% returns for every year from Year 1 – Year 29 and a -30% return in Year 30.

These returns work about to the expected returns on a 60/40 portfolio using Research Affiliates’ Yield & Growth expectations, and the drawdown is approximately in line with the drawdown on a 60/40 portfolio over the past decade. We will assume 4% annual withdrawals and 2% annual inflation with the withdrawals indexed to inflation.

3 Portfolios with Identical Annualized Returns that Occur in Different Orders

Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with. Portfolio B makes it through, not as comfortably as Portfolio C but still with 61% of its starting wealth. Portfolio A, however, starts off stressful for the retiree and runs out of money in year 27.

Sequence risk is a big issue that retirement portfolios face, so how does one combat it with dynamic allocations?

The Rising Glide Path in Retirement

Kitces and Pfau (2012) proposed the rising glide path in retirement as a method to reduce sequence risk.[5] They argued that since retirement portfolios are most exposed to market risk at the beginning of the retirement period, they should start with the lowest equity risk and ramp up as retirement progresses.

Based on Monte Carlo simulations using both capital market assumptions in line with historical values and reduced return assumptions for the current environment, the paper showed that investors can maximize their success rate and minimize their shortfall in bad (5^th percentile) scenarios by starting with equity allocations of between 20% and 40% and increasing to 60% to 80% equity allocations through retirement.

We can replicate their analysis using the reduced historical return data, using the same metrics from before (ASR, CSR, and the Ulcer Index) to measure success, comfort, and stress, respectively.

Absolute Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Note that the main diagonal in the chart represents static allocations, above the main diagonal represents the decreasing glide paths, and below the main diagonal represents increasing glide paths.

Since these returns are derived from the historical returns for stocks and bonds (again, accounting for a depressed forward outlook), they capture both the sequence of returns and shifting correlations between stocks and bonds better than Monte Carlo simulation. On the other hand, the sample size is limited, i.e. we only have about 4 non-overlapping 30 year periods.

Nevertheless, these data show that there was not a huge benefit or detriment to using either an increasing or decreasing equity glide path in retirement based on these metrics. If we instead look at minimizing expected shortfall in the bottom 10% of scenarios, similar to Kitces and Pfau, we find that a glide path starting at 40% rising to around 80% performs the best.

However, it will still be tough to rest easy with a plan that has an ASR of around 60 and a CSR of around 30 and an expected shortfall of 10 years of income.

With these unconvincing results, what can investors do to improve their retirement outcomes through prudent asset allocation?

Beyond a Static Glide Path

There is no reason to constrain portfolios to static glide paths. We have said before that the risk of a static allocation varies considerably over time. Simply dictating an equity allocation based on your age does not always make sense regardless of whether that allocation is increasing or decreasing.

If the market has a large drawdown, an investor should want to avoid this regardless of where they are in the retirement journey. Missing drawdowns is always beneficial as long as enough upside is subsequently realized.

In recent papers, Clare et al. (2017 and 2017) showed that trend following can boost safe withdrawal rates in retirement portfolios by managing sequence risk. [6],[7]

The million-dollar question is, “how tactical should we be?”

The following charts show the ASR, CSR, and Ulcer index values for static allocations to stocks, bonds, and a simple tactical strategy that invests in stocks when they are above their 10-month simple moving average (SMA) and in bonds otherwise.

The charts are organized by the minimum and maximum equity exposures along the rows and columns. The charts are symmetric across the main diagonal so that they can be compared to both increasing and decreasing equity glide paths.

The equity allocation is the minimum of the row and column headings, the tactical strategy allocation is the absolute difference between the headings, and the bond allocation is what’s needed to bring the total allocation to 100%.

For example, the 20% and 50% column is a portfolio of 20% equities, 30% tactical strategy, and 50% bonds. It has an ASR of 75, a CSR of 40, and an Ulcer index of 22.

Absolute Success Rate for Various Tactical Allocation Bounds Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

These charts show that being tactical is extremely beneficial under these muted return expectations and that being highly tactical is even better than being moderately tactical.

So, what’s stopping us from going whole hog with the 100% tactical portfolio?

Well, this is a case where a tactical strategy can reduce the risk of not making it through the 30-year retirement at the risk of greatly increasing the ending wealth. It may sound counterintuitive to say that ending with too much extra money is a risk, but when our goal is to make it through retirement comfortably, taking undue risks come at a cost.

For instance, we know that while the tactical strategy may perform well over a 30-year time horizon, it can go through periods of significant underperformance in the short-term, which can lead to stress and questioning of the investment plan. For example, in 1939 and 1940, the tactical strategy underperformed a 50/50 portfolio by 16% and 11%, respectively.

These times can be trying for investors, especially those who check their portfolios frequently.[8] Even the best-laid plan is not worth much if it cannot be adhered to.

Being tactical enough to manage the risk of having to make a major adjustment in retirement while keeping whipsaw, tracking error, and the cost of surpluses in check is key.

Sizing a Tactical Sleeve

If the goal is having the smallest tactical sleeve to boost the ASR and CSR and reduce the Ulcer index to acceptable levels in a low expected return environment, we can turn back to the expected shortfall in the bad (10^thpercentile) scenarios to determine how large of a tactical sleeve to should include in the portfolio. The analysis in the previous section showed that being tactical could yield ASRs and CSRs in the 80s and 90s (dark green). This, however, requires a tactical sleeve between 50% and 70%, depending on the static equity allocation.

Thankfully, we do not have to put the entire burden on being tactical: we can diversify our approaches. In the previous commentaries mentioned earlier, we covered a number of topics that can improve retirement results in a low expected return environment.

Thoroughly examine and define planning factors such as taxes and the evolution of spending throughout retirement.
Be 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.
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.

While each modification might only result in a small, incremental improvement in retirement outcomes, the compounding effect can be very beneficial.

The chart below shows the required tactical sleeve size needed to minimize shortfalls/surpluses for a given improvement in the annual returns (0bp through 150bps).

Tactical Allocation Strategy Size Needed to Minimize 10% Expected Shortfall/Surplus with Average Stock and Bond Returns Equal to Current Expectations for a Range of Annualized Return Improvements – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

For a return improvement of 125bps per year over the current forecasts for static U.S. equity and bond portfolios, with a static equity allocation of 50%, including a tactical sleeve of 20% would minimize the shortfall/surplus.

This portfolio essentially pivots around a static 60/40 portfolio, and we can compare the two, giving the same 125bps bonus to the returns for the static 60/40 portfolio.

Comparison of a Tactical Allocation Enhanced Portfolio with a Static 60/40 Portfolio with Average Stock and Bond Returns Equal to Current Expectations + 125bps per year – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

In addition to the much more favorable statistics, the tactically enhanced portfolio only has a downside tracking error of 1.1% to the static 60/40 portfolio.

Conclusion: Being Dynamic in Retirement

From this historical analysis, high valuations of core assets in the U.S. suggest a grim outlook for the 4% rule. Predetermined dynamic allocation paths through retirement can help somewhat, but merely specifying an equity allocation based on one’s age loses sight of the changing risk a given market environment.

The sequence of market returns can have a large impact on retirement portfolios. If a drawdown happens early in retirement, subsequent returns may not be enough to provide the tailwind that they have in the past.

Investors who are able to be fee/expense/tax-conscious and adhere to prudent diversification may be able to incrementally improve their retirement outlook to the point where a modest allocation to a sleeve of tactical investment strategies can get their portfolio back to a comfortable success rate.

Striking a balance between shortfall/surplus risk and the expected experience during the retirement period along with a thorough assessment of risk tolerance in terms of maximum and minimum equity exposure can help dictate how flexible a portfolio should be.

In our QuBe Model Portfolios, we pair allocations to tactically managed solutions with systematic, factor based strategies to implement these ideas.

While long-term capital market assumptions are a valuable input in an investment process, adapting to shorter-term market movements to reduce sequence risk may be a crucial way to combat market environments where the low return expectations come to fruition.

[1] 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%.

[2] 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.

[3] Bierwirth, Larry. 1994. Investing for Retirement: Using the Past to Model the Future. Journal of Financial Planning, Vol. 7, no. 1 (January): 14-24.

[4] Bengen, William P. 1994. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning, vol. 7, no. 4 (October): 171-180.

[5] Pfau, Wade D. and Kitces, Michael E., Reducing Retirement Risk with a Rising Equity Glide-Path (September 12, 2013). Available at SSRN: https://ssrn.com/abstract=2324930

[6] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017). Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Available at SSRN: https://ssrn.com/abstract=3019089

[7] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017) Reducing Sequence Risk Using Trend Following and the CAPE Ratio. Financial Analysts Journal, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2764933

[8] https://blog.thinknewfound.com/2017/03/visualizing-anxiety-active-strategies/

The Butterfly Effect in Retirement Planning

By Justin Sibears

On September 5, 2017

In Sequence Risk, Weekly Commentary

This article is available for download as a PDF here.

Summary

The low current market outlook for stocks and bonds paints a gloomy picture for retirees under common retirement forecasting assumptions.
However, assumptions such as net investment returns and retirement spending can have a large impact on forecasted retirement success, even for small changes in parameters.
By boosting returns through a combination of broader asset class and strategy diversification, considering lower fee options for passive exposures, and nailing down how retirement spending will evolve over time, we can arrive at retirement success projections that are both more reflective of a retiree’s actual situation and more in line with historical experience.

A few weeks back, we wrote about the potential impact that high core asset valuations – and the associated muted forward return expectations – may have on retirement[1].

In the post, we presented the following visualization:

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 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 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.

We then recreated the visualization, but with one key modification: we adjusted the historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations[2] given current valuation levels. We did this by subtracting the difference between the actual average log return and the forward-looking long return from each year’s return. With this technique, we capture the effect of subdued average returns while retaining realistic behavior for shorter-term returns.

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

To distill things a bit more, we looked at the historical “success” of various investment and withdrawal strategies. We evaluated 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[3].

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

Source: Shiller Data Library. Calculations by Newfound Research. Analysis 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.

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

Overall, our analysis suggested that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip.

Over the coming weeks, we want to delve a bit deeper into this topic. Specifically, we are going to explore some key properties of distribution portfolios – portfolios from which investors take regular withdrawals to finance retirement spending – as well as some strategies that investors may consider in order to improve retirement outcomes.

This week we are going to focus on the high degree of sensitivity that retirement planning outcomes can have to initial assumptions. In upcoming weeks, we will explore other retirement investment topics, including:

The sequence of returns and risk management.
The impact of behavioral finance and investor emotions.
Finding the right portfolio risk profile through retirement.

The Butterfly Effect in Retirement Portfolios

Quoting from a great piece on distribution portfolio theory by James Sandidge[4]:

“The butterfly effect refers to the ability of small changes early in a process that lead to significant impact later. It gets its name from the idea that a butterfly flapping its wings in Brazil could trigger a chain of events that would culminate in the formation of a tornado in Texas[5]. The butterfly effect applies to distribution portfolios where even small changes early in retirement can have significant impact long-term.”

One example of the butterfly effect in the context of retirement planning is the impact of small changes in long-term average returns. These differences could arise from investment outperformance or underperformance, fees, expenses, or taxes.

In the example below, we consider 60/40 stock/bond investor with a 30-year investment horizon and a 4% target withdrawal rate, adjusted each year for inflation. We consider three scenarios:

Pessimistic Scenario: Average annual portfolio returns are 100bps below our long-term assumption (e.g. we picked bad managers, allocated assets poorly, paid high fees, etc.).
Base Case Scenario: Average annual portfolio returns are equal to our long-term assumption.
Optimistic Scenario: Average annual portfolio returns are 100bs above our long-term assumption (e.g. we picked good managers, nailed our asset allocation, paid lower than expected fees, etc.).

We see that varying our return assumption by just +/-100bps can swing our probability of fully funding retirement – without decreasing withdrawals below plan – from 48% to 74%. Similarly, the probability of ending retirement with our original nest egg fully intact ranges from 11% in the pessimistic scenario to 47% in the optimistic scenario.

In the optimistic scenario, the median ending wealth after 30 years is $800k for an initial investment of $1mm. Not outstanding but certainly nothing to complain about. In the pessimistic scenario, however, our median ending wealth is zero, meaning the most likely outcome is running out of money!

The Butterfly Effect and Changes to Average Long-Term Return Assumption:
30-Yr. Horizon, 60/40 Allocation, 4% Withdrawals

Below, we present one example that is particularly telling: an investor that retired in 1973[6]. We see that a 100bps difference in returns in either direction can literally be the difference between running out of funds (gray), sweating every dollar and cent (orange), or a relatively comfortable retirement (blue).

Camouflaged Butterflies: Assumptions in Spending Rate Changes

An example of a secondary input that sometimes may be glossed over, but nonetheless can have a large impact on outcomes is the assumption regarding how quickly withdrawals will increase relative to inflation. Again, we consider three scenarios:

Withdrawals increase at a rate that is 1% slower than inflation (i.e. spending will rise by 2% year-over-year when inflation is 3% – spending falls in real terms).
Withdrawals increase at the same rate of inflation (spending stays constant in real terms).
Withdrawals increase at a rate that is 1% faster than inflation (i.e. spending will rise by 4% year-over-year when inflation is 3% – spending rises in real terms). This is probably an unrealistic scenario, for reasons that we will discuss later, but it still helps illustrate the sensitivity of planning analysis to its inputs.

The Butterfly Effect and Changes to the Spending Growth Assumption:
30-Yr. Horizon, 60/40 Allocation, 4% Withdrawals

Overall, the results are very similar in magnitude to what we saw when we adjusted the return assumption.

Implications of the Butterfly Effect

The examples above provide clear evidence that retirement success is significantly impacted by both primary and secondary assumptions. But what does this mean for investors? We think there are two main implications.

Getting the details right is crucial.

First, it’s important to get the details right when planning for retirement. To highlight this, let’s return to the topic of spending. Many financial calculators assume that spending increases one-for-one with inflation through retirement. Put differently, this assumes that spending is constant after adjusting for inflation.

Data from the Employee Benefit Research Institute (“EBRI”) suggests that this is generally an erroneous assumption. Instead, spending tends to decline as retirees age. Specifically, EBRI found that on average spending declines 20% from age 50-64 to 65-79, 22% from age 65-79 to 80-89, and 12% from age 80-89 to 90+.

(Note: This is obviously a gross oversimplification of actual spending behavior. At the end of this commentary, we discuss a few interesting research pieces on this topic. They make clear the importance of customizing spending assumptions to each client’s situation and preferences.)

Source: “Adaptive Distribution Theory” by James B. Sandidge

Implementing more realistic spending assumptions makes a material difference in our Absolute Success Rate (“ASR”), Comfortable Success Rate (“CSR”), and Ulcer Index stats.

Below, we recreate our ASR, CSR, and Ulcer Index tables assuming that real spending declines by 1% per year. We also compare these measures across three scenarios for a 4% withdrawal rate:

Historical return assumptions and constant real spending
Current return assumptions and constant real spending
Current return assumptions and 1% per year decline in real spending

We see that our adjusted spending assumption helps to close the gap between the historical and forward-looking return scenarios. This is especially true when we look at the ASR.

For example, a 60/40 portfolio and 4% constant real withdrawal rate produced an ASR of 99% across all historical market scenarios. The success rate dropped all the way to 58% when we adjusted the historical stock and bond returns downward for our future expectations. Changing to the declining spending path increases the success rate from 58% to 75%.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Ulcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Incremental increases (decreases) in portfolio returns (spending) matter, a lot.

Reducing spending is a very personal topic, so we will focus on some potential ways to grind out some incremental portfolio gains. (Note: another important topic when constructing withdrawal portfolios is to manage sequence of return risk. We will address this topic in a future post).

First, it’s important to be strategic, not static. To us, this means having a thoughtful, forward-looking outlook when setting a strategic asset allocation. A big part of this is fighting the temptation of home-country bias.

Source: https://personal.vanguard.com/pdf/icrrhb.pdf

This tendency to prefer home-country assets not only leaves quite a bit of diversification on the table, but also puts U.S. investors on the wrong side current equity market valuations.

Source: https://personal.vanguard.com/pdf/icrrhb.pdf

Based upon a blended set of capital market assumptions sourced from J.P. Morgan, Blackrock, and BNY Mellon, we see that it’s possible to increase long-term expected returns by between 30bps and 50bps, depending on desired risk profile, by moving beyond U.S. stocks and bonds[7]. Last week we discussed the “weird portfolios” that may be best positioned for the future.

Source: J.P. Morgan, Blackrock, BNY Mellon, Newfound Research. Return forecasts are forward-looking statements based upon the reasonable beliefs of Newfound Research and are not a guarantee of future performance. Forecasts are not representative of any Newfound Research strategy or fund. Forward-looking statements speak only as of the date they are made and Newfound assumes no duty to and does not undertake to update forward-looking statements. Forward looking statements are subject to numerous assumptions, risks, and uncertainties, which change over time. Actual results may differ materially from those anticipated in forward-looking statements. Returns are presented gross of taxes and fees.

Second, we recommend using a hybrid active/passive approach for core exposures given the increasing availability of evidence-based, favor-driven investment strategies. Now this sounds great in theory, but with over 300 factors now identified across the global equity markets and the proliferation of “smart beta” ETFs, it is reasonable to wonder how in the world one can have a view of which factors will actually work going forward. To dig into this a bit deeper, let’s look at one of our favorite examples of factor-based investing.

This portfolio, suggested by Vanguard, buys companies whose tickers start with the letters S, M, A, R, or T. This is not a real portfolio that anyone should invest in; yet it has identified an anomalous outperformance pattern. On a backtested basis, the S.M.A.R.T. Beta portfolio nearly doubled the annualized return of the S&P 500.

In order to determine the validity of this so-called factor, we need to understand:

What is the theory that explains why the factor works (provides excess return)? Without a theory for why something works, we cannot possibly form an intelligent view as to whether or not it will world in the future.
How has the factor performed on an out-of-sample basis? This is math speak for the following types of questions: How as the factor performed after its discovery? How does the factor work with slightly alternative implementations? Does the factor perform well in other assets classes and geographies?

In the case of the S.M.A.R.T. Beta factor, these questions allow us to quickly dismiss it. There is obviously no good reason – at least no good reason we can think of off the top of our heads – for why the first letter in a stock’s ticker should drive returns[8]. While we have not tested S.M.A.R.T. Beta across asset classes and geographies, we know that this was simply a tongue-in-cheek example presented by Vanguard trying to get the point across that it’s easy to find something that works in the past, but much harder to find something that works in the future. We suspect that if we did test the strategy in other countries, as an example, that it would probably outperform in some cases and underperform in others. This lack of robustness would be a clear sign that our level of confidence in this factor going forward should be very low.

So, what factors do meet these criteria (in our view)? Only four that are applicable to stocks:

Value: Buy cheap stocks and sell expensive ones
Momentum: Buy outperforming securities and sell underperforming ones
Defensive: But lower risk/higher quality securities and sell higher risk/lower quality ones
Size/Liquidity: Buy smaller/less liquid companies and sell larger/more liquid ones[9]

Data Source: AQR, Calculations by Newfound Research. Value is the HML Devil factor. Momentum is the UMD factor. Defensive is a blend of the BAB and QMJ factors. Size is the SMB factor. Equal Weight is an equally weighted blend of all four factors, rebalanced monthly. Returns include the reinvestment of dividends and are gross of all fees and expenses. Past performance does not guarantee future results.

Going back to 1957, an equally-weighted blend of the four factors mentioned above would have generated in excess of 500bps of excess annualized return before fees and expenses. Even if we discount future performance by 50% for reduced strategy efficacy and fees, the equal weight factor portfolio could add nearly 160bps for a 60/40 investor[10].

Third, we recommend looking beyond fixed income for risk management. Broadly speaking, we divide asset classes and strategies into two categories: return generators and risk mitigators.

Over the last 30+ years, investors have been very fortunate that their primary risk mitigator – fixed income – happened to experience an historic bull market.

Unfortunately, our situation today is much different than the early 1980s. Current yields are very low by historical standards, implying that fixed income is likely to be a drag to portfolio performance especially after accounting for inflation. However, that does not mean that bonds should not still play a key role in all but the most aggressive portfolios. It simply means that the premium for using bonds as a form of portfolio insurance is high relative to historical standards. As a result, we advocate looking for complementary risk management tools.

One option here would be to employ a multi-strategy, unconstrained sleeve like we constructed in a recent commentary[11]. When constructed with the right objectives in mind, these types of portfolios can act as an effective buffer to equity market volatility without the cost of large fixed income positions in a low interest rate environment. Let’s take the Absolute Return strategy that we discussed in that piece. It was constructed by optimizing for an equal risk contribution across the following seven asset classes and strategies:

U.S. Treasuries: 25%
Low volatility equities: 8%
Trend-based tactical asset allocation: 9%
Value-based tactical asset allocation: 12%
Unconstrained fixed income: 25%
Risk Parity: 9%
Managed Futures: 12%

Now let’s consider our typical 60/40 investor. Historically, a 25% allocation to this unconstrained sleeve with 18.8% (3/4 of the 25%) taken from fixed income and 6.3% (1/4 of the 25%) taken from equities would have left the investor in the same place as the original 60/40 from a risk perspective. This holds true whether we measure risk as volatility or maximum drawdown.

When we regress the absolute return strategy on world equities and U.S. Treasuries, we get the following results (data for this analysis covers the period from January 1993 to June 2016):

A loading to global equities of 0.25
A loading to U.S. Treasuries of 0.49
Annualized alpha of approximately 2%
Annualized residual volatility of 2.2%.
An R-squared of around 0.77

From the relatively high R-squared, we can conclude that a decent way to think of the absolute return portfolio is as a combination of three positions: 1) a 25% allocation to world stocks, 2) a 49% allocation to U.S. Treasuries, and 3) a 100% allocation to an unconstrained long/short portfolio with historical performance characterized by a 2% excess return and 2.2% volatility.

Using this construct, we can get at least a very rough idea of what to expect going forward by plugging in our capital market assumptions for world equities and U.S. Treasuries and making a reasonable assumption for what the long/short portfolio can deliver going forward on a net-of-fee basis. Let’s assume as we did for the factor discussion that the long/short portfolio only captures around 50% of its historical performance after fees. This would still imply an expected forward-looking return of 4.1% compared to an average expected return of 2.5% for U.S. core bonds[15]. For the 60/40 investor, this could mean close to 25bps of incremental return.

Finally, we should seek to reduce fees, all else being equal. Four things that we think are worth mentioning here.

We need to consider fees holistically. This means looking beyond expense ratios and considering factors like execution costs (e.g. bid/ask spread), commissions, and ticket charges.
The “all else being equal” part is really important. We want to be fee-conscious, not fee centric. Just like you probably don’t always buy the cheapest home, clothes, and electronics, we don’t believe in defaulting to the lowest cost investment option in all cases. We want to find value in the investments we choose. If market-cap weighted equity exposure costs 5bps and we can get multi-factor exposure for 25bps, we will not eliminate the factor product from consideration just due higher fees if we believe it can offer more than 20bps in incremental value. Fortunately, the proliferation of passive investment vehicles effectively being offered for free has helped put downward pressure on products throughout the industry.
We have to remember that while there are many, many merits to a passive, market-cap weighted approach, the rise of this type of investing has largely coincided with upward trends in equity and bond valuations. In other words, the return pie has been very big and therefore the name of the game has been capturing as much of the pie as possible, usually by minimizing fees and staying disciplined (after all, a passive approach to investing, like any other approach, only works long-term if we can stick with it, and behavioral science and experience suggests there are real difficulties doing so especially when markets get volatile). Today, we are in a fundamentally different situation. The pie is nearly as small as it’s ever been. For many investors, even capturing 100% of the pie may not be enough. Instead, many must search out ways to expand the pie in order to meet their goals.
From a behavioral perspective, there is nothing wrong with channeling our inner Harry Markowitz and going with a hybrid active[13]/passive approach within the same portfolio. Markowitz, who helped revolutionize portfolio construction theory with his landmark paper “Portfolio Selection,” famously explained that when building his own portfolio he knew he should have “…computed the historical covariances of the asset classes and drawn an efficient frontier.” Instead, he said, “I visualized my grief if the stock market went way up and I wasn’t in it – or if it went way down and I was completely in it. So, I split my contributions 50/50 between stocks and bonds.” We are strong advocates for passive, just not for 100% concentration in passive.

Let’s say as an example that by using these techniques, we are able to improve returns by 150bps annually. What would the impact be on ASR, CSR, and Ulcer Index using our same framework? For this analysis, we retain our assumption from earlier that real spending declines by 1% per year.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations Plus 150bps and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Comfortable Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations Plus 150bps and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Ulcer Index for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations Plus 150bps and Real Spending Declining by 1% Per Year – 30 Yr. Horizon

Conclusion: The Sum of All Assumptions in Retirement

Retirement projections are based on many different assumptions including asset class returns, time horizon, allocation strategies, inflation, and how withdrawals evolve over time. Small changes in many of these assumptions can have a large impact on retirement success rates (the Retirement Butterfly Effect).

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. However, by focusing our efforts on refining the assumptions that go into retirement planning, we can arrive at results that do not spell doom and gloom for retirees.

While getting all the details right is ideal, there are specific areas that matter the most.

For returns, increasing net returns is what matters, which means there are many knobs to adjust. Incorporating factor based strategies and broader diversification are good initial starting points. Expanding the usage of international equity and unconstrained strategy exposure can be simple modifications to traditional U.S. equity and bond heavy portfolios that may give a boost to forward-looking returns.

Fees, expenses, and taxes can be other areas to examine as long as we keep in mind that it is best to be fee/expense/tax-conscious, not fee/expense/tax-centric. Slight fee or tax inefficiencies can cause a “guaranteed” loss of return, but these effects must be weighed against the potential upside.

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.

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

With spending, the assumption that retirees will track inflation with their withdrawals throughout a 30 year retirement is not applicable across the board. Nailing down spending is tough, but improved assumptions can have a big impact on retirement forecasts. A thorough conversation on housing, health care, travel, insurance, and general consumption is critical.

As with any model that produces a forecast, there will always be errors in retirement projections. When asset class returns are strong, as they have been in previous decades, we can comfortably brush many assumptions under the rug. However, with muted future returns, achieving financial goals requires a better understanding of model sensitivities and more diligent research into how to equip portfolios to thrive in such an environment.

Appendix: Retiree Spending Behavior

Estimating the True Cost of Retirement[14]

David Blanchett, Head of Retirement Research for Morningstar Investment Management, argues that the common assumptions of a generic replacement rate[15], constant real spending, and a fixed retirement horizon do not accurately capture the highly personalized nature of a retiree’s spending behavior.

Key takeaways include:

From a category perspective, the main changes through retirement are a decline in relative spending on insurance and pensions and an increase in health care spending.
Source: Blanchett’s Estimating the True Cost of Retirement
Forecasts on spending by category can be used to determine a customized spending inflation rate for a given household. For example, Blanchett plots general inflation vs. medical inflation. Using this relationship, we can predict that 2% general inflation would lead to medical cost inflation of approximately 4%. One theme of many research papers on the topic of retirement spending is that health care planning should be accounted for in a separate line item. Not only does the future of the health care system have the potential to look much different from the past, but the actual financial impact of health care costs can differ greatly depending on each individual’s insurance situation. Blanchett also finds that health care spending does not differ materially across income levels.
Source: Blanchett’s Estimating the True Cost of Retirement
Blanchett finds that spending does decline through retirement and on average follows a “U” pattern whereby spending declines accelerate before age 75 and decelerate afterwards.
Source: Blanchett’s Estimating the True Cost of Retirement
Blanchett decomposed the population of his dataset into four groups based on spending and net worth. $30,000 was the threshold for separating spenders into high and low groups. $400,000 was the threshold for dividing the population by net worth. He found that households with “matched” spending and net worth (i.e. low spending and low net worth or high spending and high net worth) exhibited the “U” pattern that we saw with the full dataset. However, households with mismatched spending/net worth behaved differently. High net worth and low spending households saw spending increase through retirement, although the rate of this increase was faster earlier in retirement. Conversely, households with high spending and low net worth reduced their spending more aggressively than the other groups.
Source: Blanchett’s Estimating the True Cost of Retirement

How Does Household Expenditure Change with Age for Older Americans? [16]

The EBRI studied linked above also documents spending reductions through retirement. It presents very interesting data on the distribution of health care spending by age group. We see that the distribution widens out significantly over time with the largest increases occurring in the right tail (90^th and 95^th percentile of spending).

Source: EBRI

Spending in Retirement [17]

In this piece, J.P. Morgan analyzed retirement spending using a unique dataset of 613,000 households that utilize the Chase platform (debit cards, credit cards, mortgage payments, etc.) for the majority of their spending. The authors found the same general trend of declining spending as in the EBRI and Morningstar pieces.

Spending declines were largest in the transportation, apparel & services, and mortgage categories. The overall and category-specific patterns were generally consistent across wealth levels. The researchers were able to classify households into five categories: foodies, homebodies, globetrotters, health care spenders, and snowflakes. This categorization is relevant because each group can expect to see their spending needs evolve differently over time. Some key takeaways for each group are:

Foodies
1. Most common group
2. Generally frugal
3. Low housing expenses due to mortgages being paid off and low property tax bills
4. Tend to spend less as they get older and so an assumption of faster declines in real spending may be appropriate
Homebodies
1. High share of spending on mortgages, real estate taxes, and ongoing maintenance
2. May be prudent to assume that expenses track inflation
3. For planning purposes, it’s important to consider future plans related to housing
Globetrotters
1. Highest overall spending
2. More common among households with higher net worth
3. May be prudent to assume that expenses track inflation
Health care spenders
1. Medicare-related expenses were the largest share of spending for these households
2. These expenses may grow faster than inflation.
3. For further reading, see:
  1. Health care costs in retirement [18]
  2. Guide to Retirement [19]
Snowflakes
1. These households are more unique and do not fit into one of the other four categories.

[1] https://blog.thinknewfound.com/2017/08/impact-high-equity-valuations-safe-retirement-withdrawal-rates/

[2] 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%.

[3] 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.

[4] References to ideas similar to the butterfly effect date back as far as the 1800s. In academia, the idea is prevalent in the field of chaos theory.

[5] https://www.imca.org/sites/default/files/current-issues/JIC/JIC172_AdaptiveDistributionTheory.pdf

[6] We continue to adjust returns to account for current valuations. Therefore, this example takes the actual returns for U.S. stocks and bonds from 1973 to 2003 and then adjusts them downward based on the Research Affiliates’ long-term return assumptions.

[7] Potential increases in expected return, based upon the capital market assumptions of the three institutions listed, are actually larger than what we present here. This results from two aspects of the QuBe investment process. First, we utilize a simulation-based approach that incorporates downside shocks to the correlation matrix and that accounts for parameter estimate uncertainty. Second, we consider two behaviorally-based optimizations, one that attempts to smooth the absolute path of returns and another that attempts to smooth the path of returns relative to a common benchmark, which is tilted toward U.S. equities. Both of these techniques reduce the expected returns generated when we combine the resulting weights with the stated capital market assumptions.

[8] There actually has been research published suggesting evidence that stock tickers can be useful in picking stocks. For example, “Would a stock by any other ticker smell as sweet?” by Alex Head, Gary Smith, and Julia Wilson find evidence that stocks with “clever” tickers (e.g. Southwest’s choice of LUV to reflect its brand) outperform the broader market. Their results were robust to the Fama-French 3-factor model. As a rationale for these results, the authors posited that clever tickers might signal manager ability or that the memorable tickers feed into the behavioral biases of investors.

[9] The size premium is probably the most hotly debated of the four today. Recent research suggests that that size prospers once we control for quality (i.e. we want to buy small, high quality companies not just small companies).

[10] As we’ve written about in the past, factor portfolios do not have to generate excess returns to justify an allocation in equity portfolios. Even with zero to slightly negative premiums, moderate allocations to these strategies would have historically led to increased risk-adjusted returns due to the diversification that they provide to market-cap weighted portfolios.

[11] https://blog.thinknewfound.com/2017/07/building-unconstrained-sleeve/

[12] Again using data from J.P. Morgan, Blackrock, and BNY Mellon.

[13] When we say active, we usually (but not always) mean systematic strategies that are factor-based and implemented using a quantitative and rules-based investment process.

[14] Blanchett, David. 2013. Estimating the True Cost of Retirement. Working paper, Morningstar Investment Management. https://corporate.morningstar.com/ib/documents/MethodologyDocuments/ResearchPapers/Blanchett_True-Cost-of-Retirement.pdf

[15] Quoting from Blanchett, “The replacement rate is the percentage of household earnings need to maintain a similar standard of living during retirement.

[16] Banerjee, Sudipto. 2014. How Does Household Expenditure Change with Age for Older Americans? Employee Benefits Research Institute. Notes 35, no. 9 (September). https://www.ebri.org/pdf/notespdf/Notes.Sept14.EldExp-Only.pdf

[17] Roy, Katherine and Sharon Carson. 2015. Spending in Retirement. J.P. Morgan. https://am.jpmorgan.com/gi/getdoc/1383244966137.

[18] Carson, Sharon and Laurance McGrath. 2016. Health care costs in retirement. J.P. Morgan. https://am.jpmorgan.com/blob-gim/1383331734803/83456/RI_Healthcare%20costs_2016_r4.pdf?segment=AMERICAS_US_ADV&locale=en_US

[19] Roy, Katherine, Sharon Carson, and Lena Rizkallah. 2016. Guide to Retirement. J.P. Morgan. https://am.jpmorgan.com/blob-gim/1383280097558/83456/JP-GTR.pdf

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

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.

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

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

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

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

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

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

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

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.

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

Category: Sequence Risk

You Are Not a Monte-Carlo Simulation

Summary­

The Misleading Mean

The Role of Risk

Common Sense Utility Theory

Conclusion

Should You Dollar-Cost Average?

Summary­­

The Historical Case Against Dollar-Cost Averaging

Surely DCA Worked Somewhere

The Truth About Dollar-Cost Averaging

A More General Comparison of LSI and DCA

What About Risk?

When Can DCA Work?

Finding a DCA Middle Ground

Conclusion

Addressing Low Return Forecasts in Retirement with Tactical Allocation

Summary­­

How the 4% Rule Started

Temporal Risk in Retirement

The Rising Glide Path in Retirement

Beyond a Static Glide Path

Sizing a Tactical Sleeve

Conclusion: Being Dynamic in Retirement

The Butterfly Effect in Retirement Planning

Summary

The Butterfly Effect in Retirement Portfolios

Camouflaged Butterflies: Assumptions in Spending Rate Changes

Implications of the Butterfly Effect

Conclusion: The Sum of All Assumptions in Retirement

Appendix: Retiree Spending Behavior

Impact of High Equity Valuations on Safe Retirement Withdrawal Rates

Summary

The Drumbeat of High Equity Valuations Grows Louder

Visualizing Retirement Success and Failure

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

Conclusion: Taking Control of Retirement

Summary

Summary

Summary