Category: Risk Management Page 4 of 11

Dynamic Spending in Retirement Monte Carlo

On July 15, 2019

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

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

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

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

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

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

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

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

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

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

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

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

The Initial Plan

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

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

The financial plan is complete.

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

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

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

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

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

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

Aligning the Plan with Reality

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

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

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

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

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

Source: Global Financial Data. Calculations by Newfound.

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

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

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

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

Source: Global Financial Data. Calculations by Newfound.

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

Dynamic Spending Rules

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

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

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

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

Source: Global Financial Data. Calculations by Newfound.

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

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

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

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

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

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

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

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

Source: Global Financial Data. Calculations by Newfound.

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

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

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

Source: Global Financial Data. Calculations by Newfound.

Conclusion

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

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

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

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

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

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

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

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

The Path-Dependent Nature of Perfect Withdrawal Rates

By Nathan Faber

On April 22, 2019

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary

The Perfect Withdrawal Rate (PWR) is the rate of regular portfolio withdrawals that leads to a zero balance over a given time frame.
4% is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history and the actual risk investors take on by using this number may be uncertain.
Using simulation techniques, we aim to explore how different assumptions match the historical experience of retirement portfolios.
We find that simple assumptions commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR.
Including more stress testing and utilizing richer simulation methods may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Financial planning for retirement is a combination of art and science. The problem is highly multidimensional, requiring estimates of cash flows, investment returns and risk, taxation, life events, and behavioral effects. Reduction along the dimensions can simplify the analysis, but introduces consequences in the applicability and interpretation of the results. This is especially true for investors who are close to the line between success and failure.

One of the primary simplifying assumptions is the 4% rule. This heuristic was derived using worst-case historical data for portfolio withdrawals under a set of assumptions, such as constant inflation adjusted withdrawals, a fixed mix of stock and bonds, and a set time horizon.

Below we construct a monthly-rebalanced, fixed-mix 60/40 portfolio using the S&P 500 index for U.S. equities and the Dow Jones Corporate Bond index for U.S. bonds. Using historical data from 12/31/1940 through 12/31/2018, we can evaluate the margin for error the 4% rule has historically provided and how much opportunity for higher withdrawal rates was sacrificed in “better” market environments.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

But the history is only a single realization of the world. Risk is hard to gauge.

Perfect Withdrawal Rates

The formula (in plain English) for the perfect withdrawal rate (“PWR”) in a portfolio, assuming an ending value of zero, is relatively simple since it is just a function of portfolio returns:

The portfolio value in the numerator is the final value of the portfolio over the entire period, assuming no withdrawals. The sequence risk in the denominator is a term that accounts for both the order and magnitude of the returns.

Larger negative returns earlier on in the period increase the sequence risk term and therefore reduce the PWR.

From a calculation perspective, the final portfolio value in the equation is typically described (e.g. when using Monte Carlo techniques) as a log-normal random variable, i.e. the log-returns of the portfolio are assumed to be normally distributed. This type of random variable lends itself well to analytic solutions that do not require numerical simulations.

The sequence risk term, however, is not so friendly to closed-form methods. The path-dependent, additive structure of returns within the sequence risk term means that we must rely on numerical simulations.

To get a feel for some features of this equation, we can look at the PWR in the context of the historical portfolio return and volatility.

The relationship is difficult to pin down.

As we saw in the equation shown before, the –annualized return of the portfolio– does appear to impact the –PWR– (correlation of 0.51), but there are periods (e.g. those starting in the 1940s) that had higher PWRs with lower returns than in the 1960s. Therefore, investors beginning withdrawals in the 1960s must have had higher sequence risk.

Correlation between –annualized volatility– and –PWR– was slightly negative (-0.35).

The Risk in Withdrawal Rates

Since our goal is to assess the risk in the historical PWR with a focus on the sequence risk, we will use the technique of Brownian Bridges to match the return of all simulation paths to the historical return of the 60/40 portfolio over rolling 30-year periods. We will use the historical full-period volatility of the portfolio over the period for the simulation.

This is essentially a conditional PWR risk based on assuming we know the full-period return of the path beforehand.

To more explicitly describe the process, consider a given 30-year period. We begin by computing the full-period annualized return and volatility of the 60/40 portfolio over that period. We will then generate 10,000 simulations over this 30-year period but using the Brownian Bridge technique to ensure that all of the simulations have the exact same full-period annualized return and intrinsic volatility. In essence, this approach allows us to vary the path of portfolio returns without altering the final return. As PWR is a path-dependent metric, we should gain insight into the distribution of PWRs.

The percentile bands for the simulations using this method are shown below with the actual PWR in each period overlaid.

From this chart, we see two items of note: The percentile bands in the distribution roughly track the historical return over each of the periods, and the actual PWR fluctuates into the left and right tails of the distribution rather frequently. Below we plot where the actual PWR actually falls within the simulated PWR distribution.

The actual PWR is below the 5^th percentile 12% of the time, below the 1^st percentile 4% of the time, above the 95^th percentile 11% of the time, and above the 99^th percentile 7% of the time. Had our model been more well calibrated, we would expect the percentiles to align; e.g. the PWR should be below the 5^th percentile 5% of the time and above the 99^th percentile 1% of the time.

This seems odd until we realize that our model for the portfolio returns was likely too simplistic. We are assuming Geometric Brownian Motion for the returns. And while we are fixing the return over the entire simulation path to match that of the actual portfolio, the path to get there is assumed to have constant volatility and independent returns from one month to the next.

In reality, returns do not always follow these rules. For example, the skew of the monthly returns over the entire history is -0.36 and the excess kurtosis is 1.30. This tendency toward larger magnitude returns and returns that are skewed to the left can obscure some of the risk that is inherent in the PWRs.

Additionally, returns are not totally independent. While this is good for trend following strategies, it can lead to an understatement of risk as we explored in our previous commentary on Accounting for Autocorrelation in Assessing Drawdown Risk.

Over the full period, monthly returns of lags 1, 4, and 5 exhibit autocorrelation that is significant at the 95% confidence level.

To incorporate some of these effects in our simulations, we must move beyond the simplistic assumption of normally distributed returns.

First, we will fit a skewed normal distribution to the rolling historical data and use that to draw our random variables for each period. This is essentially what was done in the previous section for the normally distributed returns.

Then, to account for some autocorrelation, we will use the same adjustment to volatility as we used in the previously reference commentary on autocorrelation risk. For positive autocorrelations (which we saw in the previous graphs), this results in a higher volatility for the simulations (typically around 10% – 25% higher).

The two graphs below show the same analysis as before under this modified framework.

The historical PWR now fall more within the bounds of our simulated results.

Additionally, the 5^th percentile band now shows that there were periods where a 4% withdrawal rule may not have made the cut.

Conclusion

Heuristics can be a great way to distill complex data into actionable insights, and the perfect withdrawal rate in retirement portfolios is no exception.

The 4% rule is a classic example where we may not be aware of the risk in using it. It is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history.

The actual risk investors take on by using this number may be uncertain.

Using simulation techniques, we explored how different assumptions match the historical experience of retirement portfolios.

The simple assumptions (expected return and volatility) commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR. Therefore, relying on these assumptions can be risky for investors who are close to the “go-no-go” point; they do not have much room for failure and will be more likely to have to make cash flow adjustments in retirement.

Utilizing richer simulation methods (e.g. accounting for negative skew and autocorrelation like we did here or using a downside shocking method like we explored in A Shock to the Covariance System) may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Having a number to base planning calculations on makes life easier in the moment, but knowing the risk in using that number makes life easier going forward.

Trend Following in Cash Balance Plans

By Nathan Faber

On March 18, 2019

This post is available as a PDF download here.

Summary

Cash balance plans are retirement plans that allow participants to save higher amounts than in traditional 401(k)s and IRAs and are quickly becoming more prevalent as an attractive alternative to defined benefit retirement plans.
The unique goals of these plans (specified contributions and growth credits) often dictate modest returns with a very low volatility, which often results in conservative allocations.
However, at closely held companies, there is a balance between the tax-deferred amount that can be contributed by partners and the returns that the plan earns. If returns are too low, the company must make up the shortfall, but if the returns are too high the partners cannot maximize their tax-deferred contributions.
By allocating to risk-managed strategies like trend equity, a cash balance plan can balance the frequency and size of shortfalls based on how the trend following strategy is incorporated within the portfolio.
Trend following strategies have historically reduced the exposure to large shortfalls in exchange for more conservative performance during periods where the plan is comfortably hitting its return target.

Retirement assets have grown each year since the Financial Crisis, exhibiting the largest gains in the years that were good for the market such as 2009, 2013, and 2017.

Source: Investment Company Institute (ICI).

With low interest rates, an aging workforce, and continuing pressure to reduce expected rates of return going forward, many employers have shifted from the defined benefit (DB) plans used historically to defined contribution (DC) models, such as 401(k)s and 403(b)s. While assets within DB plans have still grown over the past decade, the share of retirement assets in IRAs and DC plans has grown from around 50% to 60%.

But even with this shift toward more employee directed savings and investment, there is a segment of the private DB plan space that has seen strong growth since the early 2000s: cash balance plans.

Source: Kravitz. 2018 National Cash Balance Research Report.

What is a cash balance plan?

It’s sort of a hybrid retirement plan type. Employers contribute to it on behalf of their employees or themselves, and each participant is entitled to those assets plus a rate of return according to a prespecified rule (more on that in a bit).

Like a defined contribution plan, participants have an account value rather than a set monthly payment.

Like a defined benefit plan, the assets are managed professionally, and the actual asset values do not affect the value of the participant benefits. Thus, as with any liability-driven outcome, the plan can be over- or under-funded at a given time.

What’s the appeal?

According to Kravitz, (2018)¹ over 90% of cash balance plans are in place at companies with fewer than 100 participants. These companies tend to be white-collar professionals, where a significant proportion of the employees are highly compensated (e.g. groups of doctors, dentists, lawyers, etc.).

Many of these professionals likely had to spend a significant amount of time in professional school and building up practices. Despite higher potential salaries, they may have high debt loads to pay down. Similarly, entrepreneurs may have deferred compensating themselves for the sake of building a successful business.

Thus, by the time these professionals begin earning higher salaries, the amount of time that savings can compound for retirement has been reduced.

Source: Kravitz. 2018 National Cash Balance Research Report.

One option for these types of investors is to simply save more income in a traditional brokerage account, but this foregoes any benefit of deferring taxes until retirement.

Furthermore, even if these investors begin saving for retirement at the limit for 401(k) contributions, it is possible that they could end up with a lower account balance than a counterpart saving half as much per year but starting 10 years earlier. Time lost is hard to make up.

This, of course, depends on the sequence and level of investment returns, but an investor who is closer to retirement has less ability to bear the risk of failing fast. Not being able to take as much investment risk necessitates having a higher savings rate.

Cash balance plans can help solve this dilemma through significantly higher contribution limits.

Source: Kravitz.

An extra $6,000 in catch-up contributions starting for a 401(k) at age 50 seems miniscule compared to what a cash balance plan allows.

Now that we understand why cash balance plans are becoming more prevalent in the workplace, let’s turn to the investment side of the picture to see how a plan can make good on its return guarantees.

The Return Guarantee

Aside from the contribution schedule for each plan participant, the only other piece of information needed to determine the size of the cash balance plan liability in a given year is the annual rate at which the participant accounts grow.² There are a few common ways to set this rate:

A fixed rate of return per year, between 2% and 6%.
The 30-year U.S. Treasury rate.
The 30-year U.S. Treasury rate with a floor of between 3% and 5%.
The actual rate of return of the invested assets, often with a ceiling between 3% and 6%.

The table below shows that of the plans surveyed by Kravitz (2018), the fixed rate of return was by far the most common and the actual rate of return credit was the least common.

The Actual Rate of Return option is actually becoming more popular, especially with large cash balance plans, now that federal regulations allow plan sponsors to offer multiple investments in a single plan to better serve the participants who may have different retirement goals. This return option removes much of the investment burden from the plan sponsor since what the portfolio earns is what the participants get, up to the ceiling. Anything earned above the ceiling increases the plan’s asset value above its liabilities. Actual rate of return guarantees make it so that there is less risk of a liability shortfall when large stakeholders in the cash balance plan leave the company unexpectedly.

In this commentary, we will focus on the cases where the plan may become underfunded if it does not hit the target rate of return.

We often say, “No Pain, No Premium.” Well, in the case of cash balance plans, plan sponsors typically only want to bear the minimal amount of pain that is necessary to hit the premium.

With large firms that can rely more heavily on actuarial assumptions for participant turnover, much of this risk can be borne over multiyear periods. A shortfall in one year can be replenished by a combination of extra contributions from the company according to IRS regulations and (hopefully) more favorable portfolio gains in subsequent years. Any excess returns can be used to offset how much the company must contribute annually for participants.

In the case of closely held firms, things change slightly.

At first glance, it should be a good thing for a plan sponsor to earn a higher rate of return than the committed rate. But when we consider that many cash balance plans are in place at firms where the participants desire to contribute as much as the IRS allows to defer taxation, then earning more than the guaranteed rate of return actually represents a risk. At closely held firms, “the company” and “the participants” are essentially one in the same. The more the plan earns, the less you can contribute.

And with higher return potential comes a higher risk of earning below the guaranteed rate. When a company is small, making up shortfalls out of company coffers or stretching for higher returns in subsequent years may not be in the company’s best interest.

Investing a Cash Balance Plan

Because of the aversion to both high returns and high risk, many cash balance plans are generally invested relatively conservatively, typically in the range of a 20% stock / 80% bond portfolio (20/80) to a 40/60.

To put some numbers down on paper, we will examine the return profile of three different portfolios: a 20/80, 30/70, and 40/60 fixed mix of the S&P 500 and a constant maturity 10-year U.S. Treasury index.

We will also calculate the rate of return guarantees described above each year from 1871 to 2018.

Starting each January, if the return of one of the portfolio profiles meets hits the target return for the year, then we will assume it is cashed out. Otherwise, the portfolio is held the entire year.

As the 30-year U.S. Treasury bond came into inception in 1977 and had a period in the 2000s where it was not issued, we will use the 10-year Treasury rate as a proxy for those periods.

The failure rate for the portfolios are shown below.³

Source: Robert Shiller Data Library, St. Louis Fed. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. This does not reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.

We can see that as the rate of return guarantee increases, either through the fixed rate or the floor on the 30-year rate, the rate of shortfall increases for all allocations, most notably for the conservative 20/80 portfolio.

In these failure scenarios, the average shortfall and the average shortfall in the 90% of the worst cases (similar to a CVaR) are relatively consistent.

These shortfall numbers may not be a big deal for new plans when the contributions represent a significant percentage of the asset base. For example, for a $1M plan with $500k in contributions per year, a 15% shortfall is only $150k, which can be amortized over a number of years. Higher returns in the subsequent years can offset this, or partners could agree to reduce their personal contributions so that the company can have free cash to make up for the shortfall.

The problem is more pressing for plans where the asset base is significantly larger than the yearly contributions. For a $20M plan with $500k in yearly contributions, a 15% shortfall is $3M. Making up this shortfall from company assets may be more difficult, even with amortization.

Waiting for returns from the market can also be difficult in this case when there have been historical drawdowns in the market lasting 2-3 years from peak to trough (e.g. 1929-32, 2000-02, and 1940-42).

Risk-managed strategies can be a natural way to mitigate these shortfalls, both in their magnitude and frequency.

Using Trend Following in a Cash Balance Plan

Along the lines of our Three Uses of Trend Equity, we will look at adding a 20% allocation to a simple trend-following equity (“trend equity”) strategy in a cash balance plan. By taking the allocation either from all equities, all bonds, or an equal share of each.

For ease of illustration, we will only look at the 20/80 and 40/60 portfolios. The following charts show the benefit (i.e. reduction in shortfall) or detriment (i.e. increase in shortfall) of adding the 20% trend equity sleeve to the cash balance plan based on the metrics from the previous section.

For most of these return guarantees, substituting a greater proportion of bonds for trend equity reduced the frequency of shortfalls. This makes sense over a period where equities generally did well and a trend equity strategy increased participation during the up-markets.

Substituting in trend equity solely from the equity allocation was detrimental for a few of the return guarantees, especially the higher ones.

But the frequency of shortfalls is only one part of the picture.

Many of the cases that showed a benefit from a frequency of shortfall perspective sacrifice the average shortfall or average shortfall in the most extreme scenarios. Conversely, case that sacrifice on the frequency of shortfalls generally saw a meaningful reduction in the average shortfalls.

This is in line with our philosophy that risks are not destroyed, only transformed.

So which risks should a cash balance plan bear?

This can be answered by determining the balance of the plan to be exposure to failing fast and failing slow.

If a cash balance plan is large, even a moderate shortfall can be very large in dollar terms. These plans are at risk of failing fast. Mitigating the size of the shortfalls is definitely a primary concern.

If a cash balance plan is new or relatively small, it is somewhat like an investor early in their working career. Larger losses from a percentage perspective are smaller in dollar terms compared to a larger plan. These plans can stand to have larger shortfalls. If the shortfalls occur less frequently, there is the ability to generate higher returns in years after a loss to recoup some of the losses.

However, these small plans should still be concerned mostly about fast failure. The yearly reckoning of the liability to the participants skews the risks more heavily in the direction of fast failure. This is especially true when we factor in the demographic of the workforce. When employees leave, they are entitled to their account value based on the guaranteed return, not the underlying asset value. If a participant cashes out at a time when the assets are down, then the remaining participant are less funded based on the assets that are left.

Therefore, allocating to the trend strategy out of the equity sleeve or an equal split between equities and bonds is likely more in line with the goals of a cash balance plan.

Conclusion

Cash balance plans are quickly becoming more prevalent as an attractive alternative to defined benefit retirement plans. They are desirable both from an employer and employee perspective and can be a way to accelerate retirement savings, especially for highly compensated workers at small companies.

The unique goals of these plans (e.g. guaranteed returns, maximizing tax-deferred contributions, etc.) often dictate modest returns with a very low volatility. Since some risk must be borne in order to generate returns, these portfolios are typically allocated very conservatively.

Even so, there is a risk they will not hit their return targets.

By allocating to risk-managed strategies like trend equity, a cash balance plan can balance the frequency and size of shortfalls based on how the trend following strategy is incorporated within the portfolio.

Allocating to a trend equity strategy solely from bonds can reduce the frequency of shortfalls in exchange for larger average shortfalls. Allocating to a trend following equity strategy solely from equities can increase the frequency of shortfalls but reduce the average size of shortfalls and the largest shortfalls.

The balance for a specific plan depends on its size, the demographic of the participants, the company’s willingness and ability to cover shortfalls, and the guaranteed rate of return.

As with most portfolio allocation problems the solution exists on a sliding scale based on what risks the portfolio is more equipped to bear. For cash balance plans, managing the size of shortfalls is likely a key issue, and trend following strategies can be a way to adjust the exposure to large shortfalls in exchange for more conservative performance during periods where the plan is comfortably hitting its return target.

The Monsters of Investing: Fast and Slow Failure

By Corey Hoffstein

On March 11, 2019

In Risk Management, Trend

This post is available as a PDF download here.

Summary

Successful investing requires that investors navigate around a large number of risks throughout their lifecycle. We believe that the two most daunting risks investors face are the risk of failing fast and the risk of failing slow.
Slow failure occurs when an investor does not grow their investment capital sufficiently over time to meet future real liabilities. This often occurs because they fail to save enough or because they invest too conservatively.
Fast failure occurs when an investor – often those who are living off of portfolio withdrawals and for whom time is no longer an ally – suffers a significant drawdown that permanently impairs their portfolio.
We believe that sensitivity to these risks should dictate an investor’s allocation profile. Investors sensitive to slow failure should invest more aggressively and bear more risk in certain bad states of the world for the potential to earn excess returns in good states. On the other hand, investors sensitive to fast failure should invest more conservatively, sacrificing returns in order to avoid catastrophe.
We believe this framework can also be used to inform how investors can fund an allocation from their strategic policy to trend equity strategies.

Homer’s Odyssey follows the epic ten-year journey of Odysseus and his men as they try to make their way home after the fall of Troy. Along the way, the soldiers faced a seemingly endless string of challenges, including a cyclops who ate them alive, a sorceress who turned them into pigs, and sirens that would have lured them to their deaths with a song had they not plugged their ears with beeswax.

In one trial, the men had to navigate the Strait of Messina between the sea monsters Scylla and Charybdis. With her six serpentine heads, each with a triple row of sharp teeth, Scylla haunted the cliffs that lined one edge of the strait. Ships that came too close would immediately lose six sailors to the ravenous monster. Living under a rock on the other side of the strait was Charybdis. A few times a day, this monster would swallow up large amounts of water and belch it out, creating whirlpools that could sink an entire ship.

The strait was so narrow that the monsters lived within an arrow’s range of one another. To safely avoid one creature meant almost necessarily venturing too close to the other. On the one hand was almost certain, but limited, loss; on the other, the low probability of complete catastrophe.

Investors, similarly, must navigate between two risks: what we have called in the past the risks of failing slow and failing fast.

Slow failure results from taking too little risk, often from investors allocating too conservatively or holding excessive cash. In doing so, they fail to grow their capital at a sufficient rate to meet future real liabilities. Failure in this arena does not show up as a large portfolio drawdown: it creeps into the portfolio over time through opportunity cost or the slow erosion of purchasing power.

Fast failure results from the opposite scenario: taking too much risk. By allocating too aggressively (either to highly skewed or highly volatile investments), investors might incur material losses in their portfolios at a time when they cannot afford to do so.

We would argue that much of portfolio design is centered around figuring out which risk an investor is most sensitive to at a given point in their lifecycle and adjusting the portfolio accordingly.

Younger investors, for example, often have significant human capital (i.e. future earning potential) but very little investment capital. Sudden and large losses in their portfolios, therefore, are often immaterial in the long run, as both time and savings are on their side. Investing too conservatively at this stage in life can rely too heavily on savings and fail to exploit the compounding potential of time.

Therefore, younger, growth-oriented investors should be willing to bear the risk of failing fast to avoid the risk of failing slow. In fact, we would argue that it is the willingness to bear the risk of failing fast that allows these investors to potentially earn a premium in the first place. No pain, no premium.

Over time, investors turn their human capital into investment capital through savings and investment. At retirement, investors believe that their future liabilities are sufficiently funded, and so give-up gainful employment to live off of their savings and investments. In other words, the sensitivity to slow failure has significantly declined.

However, with less time for the potential benefits of compounding and no plan on replenishing investments through further savings, the sensitivity to the risk of fast failure is dramatically heightened, especially in the years just prior to and just after retirement. This is further complicated by the fact that withdrawals from the portfolio can heighten the impact of sustained and large drawdowns.

Thus, older investors tend shift from riskier stocks to safer bonds, offloading their fast failure risk to those willing to bear it. Yet we should be hesitant to de-risk entirely; we must also acknowledge longevity risk. Too conservative a profile may also lead to disaster if an investor outlives their nest-egg.

As we balance the scales of failing fast and slow, we can see why trying to invest a perpetual endowment is so difficult. Consistent withdrawals invite the risk of failing fast while the perpetual nature invites the risk of failing slow. A narrow strait to navigate between Scylla and Charybdis, indeed!

We would be remiss if we did not acknowledge that short-term, high quality bonds are not a panacea for fail fast risk. Inflation complicates the calculus and unexpected bouts of inflation (e.g. the U.S. in the 1970s) or hyper-inflation (e.g. Brazil in the 1980s, Peru from 1988-1991, or present-day Venezuela) can cause significant, if not catastrophic, declines in real purchasing power if enough investment risk is not borne.

Purchasing seemingly more volatile assets may actually be a hedge here. For example, real estate, when marked-to-market, may exhibit significant relative swings in value over time. However, as housing frequently represents one the largest real liabilities an investor faces, purchase of a primary residence can lock in the real cost of the asset and provide significant physical utility. Investors can further reduce inflation risk by financing the purchase with a modest amount of debt, a liability which will decline in real value with unexpected positive inflation shocks.

The aforementioned nuances notwithstanding, this broad line of thinking invites some interesting guidance regarding portfolio construction.

Investors sensitive to fast failure should seek to immunize their real future liabilities (e.g. via insurance, real asset purchases, cash-flow matching, structured products, et cetera). As they survey the infinite potential of future market states, they should be willing to give up returns in all states to avoid significant failure in any given one of them.

Investors sensitive to slow failure should seek to bear a diversified set of risk premia (e.g. equity risk premium, bond risk premium, credit premium, value, momentum, carry, et cetera) that allows their portfolios to grow sufficiently to meet future real liabilities. These investors, then, are willing to pursue higher returns in the vast majority of future market states, even if it means increased losses in a few states.

I personally imagine this as if the investor sensitive to failing slow has piled up all their risk – like a big mound of dough – in the bad outcome states of the world. For their willingness to bear this risk, they earn more return in the good outcome states. The investor sensitive to failing fast, on the other hand, smears that mound of risk across all the potential outcomes. In their unwillingness to bear risk in a particular state, they reduce return potential across all states, but also avoid the risk of catastrophe.

Source: BuzzFeed

Quantitatively, we saw exactly this trade-off play out in our piece The New Glide Path, where we attempted to identify the appropriate asset allocation for investors in retirement based upon their wealth level. We found that:

Investors who were dramatically under-funded – i.e. those at risk of failing slow – relative to real liabilities were allocated heavily to equities.
Investors who were near a safe funding level – i.e. those at risk of failing fast – were tilted dramatically towards assets like Treasury bonds in order to immunize their portfolio against fast failure.
The fortunate few investors who were dramatically over-funded could, pretty much, allocate however they pleased.

We believe this same failing slow and failing fast framework can also inform how trend equity strategies – like those we manage here at Newfound Research – can be implemented by allocators.

In our recent commentary Three Applications of Trend Equity we explored three implementation ideas for trend equity strategies: (1) as a defensive equity sleeve; (2) as a tactical pivot; or (3) as an alternative. While these are the most common approaches we see to implementing trend equity, we would argue that a more philosophically consistent route might be one that incorporates the notions of failing fast and failing slow.

In Risk Ignition with Trend Following we examined the realized efficient frontier of U.S. stocks and bonds from 1962-2017 and found that an investor who wanted to hold a portfolio targeting an annualized volatility of 10% would need to hold between 40-50% of their portfolio in bonds. If we were able to magically eliminate the three worst years of equity returns, at the cost of giving up the three best, that number dropped to 20-30%. And if we were able to eliminate the worst five at the cost of giving up the best five? Just 10%.

One interpretation of this data is that, with the benefit of hindsight, a moderate-risk investor would have had to carry a hefty allocation to bonds for the 55 years just to hedge against the low-probability risk of failing fast. If we believe the historical evidence supporting trend equity strategies, however, we may have an interesting solution at hand:

A strategy that has historically captured a significant proportion of the equity risk premium.
A strategy that has historically avoided a significant proportion of prolonged equity market declines.

Used appropriately, this strategy may help investors who are sensitive to failing slowly tactically increase their equity exposure when trends are favorable. Conversely, trend equity may help investors who are sensitive to failing fast de-risk their portfolio during negative trend environments.

To explore this opportunity, we will look at three strategic profiles: an 80% U.S. equity / 20% U.S. bond mix, a 50/50 mix, and a 20/80 mix. The first portfolio represents the profile of a growth investor who is sensitive to failing slow; the second portfolio represents a balanced investor, sensitive to both risks; the third represents a conservative investor who is sensitive to failing fast.

We will allocate a 10% slice of each portfolio to a naïve trend equity strategy in reverse proportion to the stock/bond mix. For example, for the 80/20 portfolio, 2% of the equity position and 8% of the bond position will be used to fund the trend equity position, creating a 78/12/10 portfolio. Similarly, the 20/80 will become an 12/78/10 and the 50/50 will become a 45/45/10.

We will use the S&P 500 index for U.S. equities, Dow Jones Corporate Bond index for U.S. bonds, and a 1-Year U.S. Government Note index for our cash proxy. The trend equity strategy will blend signals generated from trailing 6-through-12-month total returns, investing in the S&P 500 over the subsequent month in proportion to the number of positive signals. Remaining capital will be invested in the cash proxy. All portfolios are rebalanced monthly from 12/31/1940 through 12/31/2018.

Below we report the annualized returns, volatility, maximum drawdown, and Ulcer index (which seeks to simultaneously measure the duration and depth of drawdowns and can serve as a measure to a portfolio’s sensitivity to failing fast) for each profile.

	Fail Fast		Blend		Fail Slow
	20/ 80	12/ 78/ 10	50/ 50	45/ 45/ 10	80/ 20	78/ 12/ 10
Annualized Return	7.9%	8.0%	9.4%	9.6%	10.7%	11.0%
Annualized Volatility	5.8%	5.6%	8.4%	8.4%	11.9%	12.4%
Maximum Drawdown	16.9%	16.6%	28.8%	26.6%	42.9%	42.5%
Ulcer Index	0.025	0.025	0.045	0.044	0.083	0.087

Source: Global Financial Data. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

For conservative investors sensitive to the risk of failing fast, we can see that the introduction of trend equity not only slightly increased returns, but it reduced the maximum drawdown and Ulcer index profile of the portfolio. Below we plot the actual difference in portfolio drawdowns between a 12/78/10 mix and a 20/80 mix over the backtested period.

While we can see that there are periods where the 12/78/10 mix exhibited higher drawdowns (i.e. values below the 0% line), during major drawdown periods, the 12/78/10 mix historically provided relative relief. This is in line with our philosophy that risk cannot be destroyed, only transformed: the historical benefits that trend following has exhibited to avoiding significant and prolonged drawdowns have often come at the cost of increased realized drawdowns due to a slightly increased average allocation to equities as well as self-incurred drawdowns due to trading whipsaws.

On the opposite end of the spectrum, we can see that those investors sensitive to failing slowly were able to increase annualized returns without a significant increase to maximum drawdown. We should note, however, an increase in the Ulcer index, indicating more frequent and deeper drawdowns.

This makes sense, as we would expect the 78/12/10 mix to be on average over-allocated to equities, making it more sensitive to quick and sudden declines (e.g. 1987). Furthermore, the most defensive the mix can tilt is towards a 78/22 blend, leaving little wiggle-room in its ability to mitigate downside exposure. Nevertheless, we can see below that during periods of more prolonged drawdowns (e.g. 1975, 1980, and 2008), the 78/12/10 mix was able to reduce the drawdown profile slightly.

In these backtests we see that investors sensitive to failing fast can fund a larger proportion of trend equity exposure from their traditional equity allocation in an effort to reduce risk while maintaining their return profile. Conversely, investors sensitive to failing slow can fund a larger proportion of their trend equity exposure from bonds, hoping to increase their annualized return while maintaining the same risk exposure.

Of course, long-term annualized return statistics can belie short-term experience. Examining rolling return periods, we can gain a better sense as to our confidence as to the time horizon over which we might expect, with confidence, that a strategy should contribute to our portfolio.

Below we plot rolling 1-to-10-year annualized return differences between the 78/12/10 and the 80/20 mixes.

We can see that in the short-term (e.g. 1-year), there are periods of both significant out- and under-performance. Over longer periods (5- and 10-years), which tend to capture “full market cycles,” we see more consistent out-performance.

Of course, this is not always the case: the 78/12/10 mix underperformed the 80/20 portfolio for the 10 years following the October 1987 market crash. Being over-allocated to equities at that time had a rippling effect and serves to remind us that our default assumption should be that “risk cannot be destroyed, only transformed.” But when we have the option to adjust our exposure to these risks, the benefit of avoiding slow failure may outweigh the potential to underperform slightly.

This evidence suggests that funding an allocation to trend equity in a manner that is in line with an investor’s risk sensitivities may be beneficial. Nevertheless, we should also acknowledge that the potential benefits are rarely realized in a smooth, continuous manner and that the implementation should be considered a long-term allocation, not a trade.

Conclusion

Investors must navigate a significant number of risks throughout their lifecycle. At Newfound, we like to think of the two driving risks that investors face as the risk of failing fast and the risk of failing slow. Much like Odysseus navigating between Scylla and Charybdis, these risks are at direct odds with one another and trying to avoid one increases the risk of the other.

Fortunately, which of these risks an investor cares about evolves throughout their lifecycle. Young investors typically can afford to fail fast, as they have both future earning potential and time on their side. By not saving adequately, or investing too conservatively, however, a young investor can invite the risk of slow failure and find themselves woefully underfunded for future real liabilities. Hence investors at this stage or typically aggressively allocated towards growth assets.

As investors age, time and earning potential dwindle and the risk of fast failure increases. At this point, large and prolonged drawdowns can permanently impair an investor’s lifestyle. So long as real liabilities are sufficiently funded, the risk of slow failure dwindles. Thus, investors often de-risk their portfolios towards stable return sources such as high-quality fixed income.

We believe this dual-risk framework is a useful model for determining how any asset or strategy should fit within a particular investor’s plan. We demonstrate this concept with a simple trend equity strategy. For an investor sensitive to slow failure, we fund the allocation predominately from bond exposure; for an investor sensitive to fast failure, we fund the allocation predominately form equities.

Ultimately – and consistent with findings in our other commentaries – a risk-based mindset makes it obvious that allocation choices are really all about trade-offs in opportunity (“no pain, no premium”) and risk (“risk cannot be destroyed, only transformed.”)

G̷̖̱̓́̀litch

By Corey Hoffstein

On February 19, 2019

In Risk & Style Premia, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

Trend following’s simple, systematic, and transparent approach does not make it any less frustrating to allocate to during periods of rapid market reversals.
With most trend equity strategies exhibiting whipsaws in 2010, 2011, 2015-2016, and early 2018, it is tempting to ask, “is this something we can fix?”
We argue that there are three historically-salient features that make trend following attractive: (1) positive skew, (2) convexity, and (3) a positive premium.
We demonstrate that the convexity exhibited by trend equity strategies is both a function of the strategy itself (i.e. a fast- or slow-paced trend model) as well as the horizon we measure returns over.
We suggest that it may be more consistent to think of convexity as an element than can provide crisis beta, where the nature of the crisis is defined by the speed of the trend following system.
The failure of a long-term trend strategy to de-allocate in Q4 2018 or meaningfully re-allocate in Q1 2019 is not a glitch; it is encoded in the DNA of the strategy itself.

There’s an old saying in Tennessee – I know it’s in Texas, probably in Tennessee – that says, fool me once, shame on – shame on you. Fool me – you can’t get fooled again! — George W. Bush

It feels like we’ve seen this play before. It happened in 2010. Then again in 2011. More recently in 2015-2016. And who can forget early 2018? To quote Yogi Berra, “It’s déjà vu all over again.” We’re starting to think it is a glitch in the matrix.

Markets begin to deteriorate, losses begin to more rapidly accelerate, and then suddenly everything turns on a dime and market’s go on to recover almost all their losses within a few short weeks.

Trend following – like the trend equity mandates we manage here at Newfound – requires trends. If the market completely reverses course and regains almost all of its prior quarter’s losses within a few short weeks, it’s hard to argue that trend following should be successful. Indeed, it is the prototypical environment that we explicitly warn trend following will do quite poorly in.

That does not mean, however, that changing our approach in these environments would be a warranted course of action. We embrace a systematic approach to explicitly avoid contamination via emotion, particularly during these scenarios. Plus, as we like to say, “risk cannot be destroyed, only transformed.” Trying to eliminate the risk of whipsaw not only risks style pollution, but it likely introduces risk in unforeseen scenarios.

So, we have to scratch our heads a bit when clients ask us for an explanation as to our current positioning. After all, trend following is fairly transparent. You can probably pull up a chart, stand a few feet back, squint, and guess with a reasonable degree of accuracy as to how most trend models would be positioned.

When 12-month, 6-month, and 3-month returns for the S&P 500 were all negative at the end of December, it is a safe guess that we’re probably fairly defensively positioned in our domestic trend equity mandates. Despite January’s record-breaking returns, not a whole lot changed. 12-, 6-, and 3-month returns were negative, negative, and just slightly positive, respectively, entering February.

To be anything but defensively positioned would be a complete abandonment of trend following.

It is worth acknowledging that this may all just be Act I. Back when this show was screening in 2011 and 2015-2016, markets posted violent reversals – with the percent of stocks above their 50-day moving average climbing from less than 5% to more than 90% – only to roll over again and retest the lows.

Or this will be February 2018 part deux. We won’t know until well after the fact. And that can be frustrating depending upon your perspective of markets.

If you take a deterministic view, incorrect positioning implies an error in judgement. You should have known to abandon trend following and buy the low on December 24^th. If you take a probabilistic view, then it is possible to be correctly positioned for the higher probability event and still be wrong. The odds were tilted strongly towards continued negative market pressure and a defensive stance was warranted at the time.

We would argue that there is a third model as well: sustainability (or, more morbidly, survivability). It does not matter if you have a 99% chance of success while playing Russian Roulette: play long enough and you’re eventually going to lose. Permanently. Sustainability argues that the low-probability bet may be the one worth taking if the payoff is sufficient enough or it protects us from ruin.

Thus, for investors for whom failing fast is a priority risk, a partially defensive allocation in January and February may be well warranted, even if the intrinsic probabilities have reversed course (which, based on trends, they largely had not).

But sustainability also needs to be a discussion about being able to stick with a strategy. It does not matter if the strategy survives over the long run if the investor does not participate.

That is why we believe transparency and continued education are so critical. If we do not know what we are invested in, we cannot set correct expectations. Without correct expectations, everything feels unexpected. And when everything feels unexpected, we have no way to determine if a strategy is behaving correctly or not.

Which brings us back to trend equity strategies in Q4 2018 and January 2019. Did trend equity behave as expected?

Trend following has empirically exhibited three attractive characteristics:

Positive Skew: The return distribution is asymmetric, with a larger right tail than left tail (i.e. greater frequency of larger, positive returns than large, negative returns).
Convex Payoff Profile: As a function of the underlying asset the trend following strategy is applied on, upside potential tends to be greater than downside risk.
Positive Premium: The strategy has a positive expected excess return.

While the first two features can be achieved by other means (e.g. option strategies), the third feature is downright anomalous, as we discussed in our recent commentary Trend: Convexity & Premium. Positive skew and convexity create and insurance-like payoff profile and therefore together tend to imply a negative premium.

The first two characteristics make trend following a potentially interesting portfolio diversifier. The last element, if it persists, makes it very interesting.

Yet while we may talk about these features as historically intrinsic properties of trend following, the nature of the trend-following strategy will significantly impact the horizon over which these features are observed. What is most important to acknowledge here is that skew and convexity are more akin to beta than they are alpha; they are byproducts of the trading strategy itself. While it can be hard to say things about alpha, we often can say quite a bit more about beta.

For example, a fast trend following system (typically characterized by a short lookback horizon) would be expected to rapidly adapt to changing market dynamics. This allows the system to quickly position itself for emerging trends, but also potentially makes the strategy more susceptible to losses from short-term reversals.

A slow trend following system (characterized by a long lookback period), on the other hand, would be less likely to change positioning due to short-term market noise, but is also therefore likely to adapt to changing trend dynamics more slowly.

Thus, we might suspect that a fast-paced trend system might be able to exhibit convexity over a shorter measurement period, whereas a slow-paced system will not be able to adapt rapidly. On the other hand, a fast trend following system may have less average exposure to the underlying asset over time and may compound trading losses due to whipsaw more frequently.

To get a better sense of these tradeoffs, we will construct prototype trend equity strategies which will invest either in broad U.S. equities or risk-free bonds. The strategies will be re-evaluated on a daily basis and are assumed to be traded at the close of the day following a signal change. Trend signals will be based upon prior total returns; e.g. a 252-day system will have a positive (negative) signal if prior 252-day total returns in U.S. equity markets are positive (negative).

Below we plot the monthly returns of a -short-term trend equity system (21 day)- and a -long-term trend equity system (252 day)- versus U.S. equity returns.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, neither the Short-Term nor Long-Term Trend Equity strategy reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.

We can see that the fast-paced system exhibits convexity over the monthly measurement horizon, while the slower system exhibits a more linear return profile.

As mentioned above, however, the more rapid adaptation in the short-term system might cause more frequent realization of whipsaw due to price reversals and therefore an erosion in long-term convexity. Furthermore, more frequent changes might also reduce long-term participation.

We now plot annual returns versus U.S. equities below.

We can see that while the convexity of the short-term system remains intact, the long-term system exhibits greater upside participation.

To get a better sense of these trade-offs, we will follow Sepp (2018)¹ and use the following model to deconstruct our prototype long/flat trend equity strategies:

By comparing daily, weekly, monthly, quarterly, and annual returns, we can extract the linear and convexity exposure fast- and slow-paced systems have historically exhibited over a given horizon.

Below we plot the regression coefficients (“betas”) for a fast-paced system.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, the Short-Term Trend Equity strategy does not reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.

We can see that the linear exposure remains fairly constant (and in line with decompositions we’ve performed in the past which demonstrate that long/flat trend equity can be thought of as a 50/50 stock/cash strategic portfolio plus a long/short overlay²). The convexity profile, however, is most significant when measured over weekly or monthly horizons.

Long-term trend following systems, on the other hand, exhibit negative or insignificant convexity profiles over these horizons. Even over a quarterly horizon we see insignificant convexity. It is not until we evaluate returns on an annual horizon that a meaningful convexity profile is established.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results. All returns are hypothetical and backtested. Returns are gross of all fees. For the avoidance of doubt, the Long-Term Trend Equity strategy does not reflect any investment strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index.

These results have very important implications for investors in trend following strategies.

We can see that long-term trend following, for example, is unlikely to be successful as a tail risk hedge for short-term events. Short-term trend following may have a higher probability of success in such a scenario, but only so long as the crisis occurs over a weekly or monthly horizon.³

Short-term trend following, however, appears to exhibit less convexity with annual returns and has lower linear exposure. This implies less upside capture to the underlying asset.

Neither approach is likely to be particularly successful at hedging against daily crises (e.g. a 1987-type event), as the period is meaningfully shorter than the adaptation speed of either of the strategies.

These results are neither feature nor glitch. They are simply the characteristics we select when we choose either a fast or slow trend-following strategy. While trend-following strategies are often pitched as crisis alpha, we believe that skew and convexity components are more akin to crisis beta. And this is a good thing. While alpha is often ephemeral and unpredictable, we can more consistently plan around beta.

Thus, when we look back on Q4 2018 and January 2019, we need to acknowledge that we are evaluating results over a monthly / quarterly horizon. This is fine if we are evaluating the results of fast-paced trend-following strategies, but we certainly should not expect any convexity benefits from slower trend models. Quite simply, it all happened too fast.

Conclusion

When markets rapidly reverse course, trend following can be a frustrating style to allocate to. With trend equity styles exhibiting whipsaws in 2010, 2011, 2015-2016, and early 2018, the most recent bout of volatility may have investors rolling their eyes and thinking, “again?”

“Where’s the crisis alpha?” investors cry. “Where’s the crisis?” managers respond back.

Yet as we demonstrated in our last commentary, two of the three salient features of trend following – namely positive skew and positive convexity – may be byproducts of the trading strategy and not an anomaly. Rather, the historically positive premium that trend following has generated has been the anomaly.

While the potential to harvest alpha is all well and good, we should probably think more in the context of crisis beta than crisis alpha when setting expectations. And that beta will be largely defined by the speed of the trend following strategy.

But it will also be defined by the period we are measuring the crisis over.

For example, we found that fast-paced trend equity strategies exhibit positive convexity when measured over weekly and monthly time horizons, but that the convexity decays when measured over annual horizons.

Strategies that employ longer-term trend models, on the other hand, fail to exhibit positive convexity over shorter time horizons, but exhibit meaningful convexity over longer-horizons. The failure of long-term trend strategies to meaningfully de-allocate in Q4 2018 or rapidly re-allocate in Q1 2019 is not a glitch: it is encoded into the DNA of the strategy.

Put more simply: if we expect long-term trend models to protect against short-term sell-offs, we should prepare to be disappointed. On the other hand, the rapid adaptation of short-term models comes at a cost, which can materialize as lower up-capture over longer horizons.

Thus, when it comes to these types of models, we have to ask ourselves about the risks we are trying to manage and the trade-offs we are willing to make. After all, “risk cannot be destroyed, only transformed.”

Category: Risk Management Page 4 of 11

Dynamic Spending in Retirement Monte Carlo

Summary­

The Initial Plan

Aligning the Plan with Reality

Dynamic Spending Rules

Conclusion

The Path-Dependent Nature of Perfect Withdrawal Rates

Summary

Perfect Withdrawal Rates

The Risk in Withdrawal Rates

Conclusion

Trend Following in Cash Balance Plans

Summary

The Return Guarantee

Investing a Cash Balance Plan

Using Trend Following in a Cash Balance Plan

Conclusion

The Monsters of Investing: Fast and Slow Failure

Summary

Conclusion

G̷̖̱̓́̀litch

Summary­

Conclusion

Summary

Summary