*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.

*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.*

*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.*

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.

## Time Dilation

By Corey Hoffstein

On March 25, 2019

In Portfolio Construction, Weekly Commentary

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

In the 2014 film

Interstellar, Earth has been plagued by crop blights and dust storms that threaten the survival of mankind. Unknown, interstellar beings have opened a wormhole near Saturn, creating a path to a distant galaxy and the potential of a new home for humanity.Twelve volunteers travel into the wormhole to explore twelve potentially hospitable planets, all located near a massive black hole named Gargantua. Of the twelve, only three reported back positive results.

With confirmation in hand, the crew of the spaceship Endurance sets out from Earth with 5,000 frozen human embryos, intent on colonizing the new planets.

After traversing the wormhole, the crew sets down upon the first planet – an ocean world – and quickly discovers that it is actually inhospitable. A gigantic tidal wave kills one member of the crew and severely delays the lander’s departure.

The close proximity of the planet to the gravitational forces of the supermassive black hole invites exponential time dilation effects. The positive beacon that had been tracked had perhaps been triggered just minutes prior on the planet. For the crew, the three hours spent on the planet amounted to over

23 yearson Earth. The crew can only watch, devastated, as their loved ones age before their eyes in the video messages received – and never responded to – in their multi-decade absence.Our lives revolve around the clock, though we do not often stop to reflect upon the nature of time.

Some aspects of time tie to corresponding natural events. A day is simply reckoned from one midnight to the next, reflecting the Earth’s full rotation about its axis. A year, which reflects the length of time it takes for the Earth to make a full revolution around the Sun, will also correspond to a full set of a seasons.

Others, however, are seemingly more arbitrary. The twenty-four-hour day is derived from ancient Egyptians, who divided day-time into 10 hours, bookended by twilight hours. The division of an hour into sixty minutes comes from the Babylonians, who used a sexagesimal counting system.

We impose the governance of the clock upon our financial system as well. Public companies prepare quarterly and annual reports. Economic data is released at a scheduled monthly or quarterly pace. Trading days for U.S. equity markets are defined as between the hours of 9:30am and 4:00pm ET.

In many ways, our imposition of the clock upon markets creates a natural cadence for the flow of information.

Yet, despite our best efforts to impose order, information most certainly does not flow into the market in a constant or steady manner.

New innovations, geopolitical frictions, and errant tweets all represent idiosyncratic events that can reshape our views in an instant. A single event can be of greater import than all the cumulative economic news that came before it; just consider the collapse of Lehman Brothers.

And much like the time dilation experienced by the crew of Endurance, a few, harrowing days of 2008 may have felt longer than the entirety of a tranquil year like 2017.

One way of trying to visualize this concept is by looking at the cumulative variance of returns. Given the clustered nature of volatility, we would expect to see periods where the variance accumulates slowly (“calm markets”) and periods where the variance accumulates rapidly (“chaotic markets”).

When we perform this exercise – by simply summing squared daily returns for the S&P 500 over time – we see precisely this. During market environments that exhibit stable economic growth and little market uncertainty, we see very slow and steady accumulation of variance. During periods when markets are seeking to rapidly reprice risk (e.g. 2008), we see rapid jumps.

Source: CSI Data. Calculations by Newfound Research.If we believe that information flow is not static and constant, then sampling data on a constant, fixed interval will mean that during calm markets we might be

over-samplingour data and during chaotic markets we might beunder-sampling.Let’s make this a bit more concrete.

Below we plot the –adjusted closing price of the S&P 500– and its –200-day simple moving average–. Here, the simple moving average aims to estimate the trend component of price. We can see that during the 2005-2007 period, it estimates the underlying trend well, while in 2008 it dramatically lags price decline.

Source: CSI Data. Calculations by Newfound Research.The question we might want to ask ourselves is,

why are looking at the prior 200 days?Or, more specifically, why is a day a meaningful unit of measure? We already demonstrated above that it very well may not be: one day might be packed with economically-relevant information and another entirely devoid.Perhaps there are other ways in which we might think about sampling data. We could, for example, sample data based upon cumulative volume intervals. Another might be on a fixed number of cumulative ticks or trades. Yet another might be on a fixed cumulative volatility or variance.

As a firm which makes heavy use of trend-following techniques, we are particularly partial to the latter approach, as the volatility of an asset’s trend versus its price should inform the trend lookback horizon. If we think of trend following as being the trading strategy that replicates the payoff profile of a straddle, increased volatility levels will decrease the delta of the option positions, and therefore decrease our position size. An interpretation of this effect is that the increased volatility decreases our certainty of where price will fall at expiration, and therefore we need to decrease our sensitivity to price movements.

If that all sounds like Greek, consider this simple example. Assume that price follows a highly simplified model as a function of time:

There are two components of this model: the linear trend and the noise.

Now let’s assume we are attempting to identify whether the linear trend is positive or negative by using a simple moving average (“SMA”) of price:

To determine if there is a positive or a negative trend, we simply ask if our current SMA value is greater or less than the prior SMA value. For a positive trend, we require:

Substituting our above definition of the simple moving average:

When we recognize that most of the terms on the left also appear on the right, we can re-write the whole comparison as the new price in the SMA being greater than the old price dropping out of the SMA:

Which, through substitution of our original definition, leaves us with:

Re-arranging a bit, we get:

Here we use the fact that sin(x) is bounded between -1 and 1, meaning that:

Assuming a positive trend (m > 0), we can replace with our worst-case scenario,

To quickly test this result, we can construct a simple time series where we assume a=3 and m=0.5, which implies that our SMA length should be greater than 11. We plot the –time series– and –SMA– below. Note that the –SMA– is always increasing.

Despite being a highly simplified model, it illuminates that our lookback length should be a function of noise versus trend strength. The higher the ratio of noise to trend, the longer the lookback required to smooth out the noise. On the other hand, when the trend is very strong and the noise is weak, the lookback can be quite short.

^{1}Thus, if trend and noise change over time (which we would expect them to), the optimal lookback will be a dynamic function. When trend is much weaker than noise, we our lookback period will be extended; when trend is much stronger than noise, the lookback period shrinks.

But what if we transform the sampling domain? Rather than sampling price every time step, what if we sample price as a function of cumulative noise? For example, using our simple model, we could sample when cumulative noise sums back to zero (which, in this example, will be the equivalent of sampling every 2π time-steps).

^{2}Sampling at that frequency, how many of data points would we need to estimate our trend? We need not even work out the math as before; a bit of analytical logic will suffice. In this case, because we know the cumulative noise equals zero, we know that a point-to-point comparison will be affected

onlyby the trend component. Thus, we only need n=1 in this new domain.And this is true regardless of the parameterization of trend or noise.

Goodbye!dynamic lookback function.Of course, this is a purely hypothetical – and dramatically over-simplified – model. Nevertheless, it may illuminate why time-based sampling may not be the most efficient practice if we do not believe that information flow is constant.

Below, we again plot the –S&P 500– as well as a standard –200-day simple moving average–.

We also sample prices of the S&P 500 based upon cumulative magnitude of log differences, approximating a cumulative 2.5% volatility move. When the market exhibits low volatility levels, the process samples price less frequently. When the market exhibits high volatility, it samples more frequently. Finally, we plot a –200 period moving average– based upon these samples.

We can see that sampling in a different domain – in this case, the log difference space – we can generate a process that reacts dynamically in the time domain. During the calm markets of 2006 and early 2007, the –200 period moving average– behaves like the –200-day simple moving average–, whereas during the 2008 crisis it adapts to the changing price level far more quickly.

By changing the domain in which we sample, we may be able to create a model that is dynamic in the time domain, avoiding the time-dilation effects of information flow.

## Conclusion

Each morning the sun rises and each evening it sets. Every year the Earth travels in orbit around the sun. What occurs during those time spans, however, varies dramatically day-by-day and year-by-year. Yet in finance – and especially quantitative finance – we often find ourselves using time as a measuring stick.

We find the notion of time almost everywhere in portfolio construction. Factors, for example, are often defined by measurements over a certain lookback horizon and reformed based upon the decay speed of the signal.

Even strategic portfolios are often rebalanced based upon the calendar. As we demonstrated in our paper

Rebalance Timing Luck: The Difference Between Hired and Fired, fixed-schedule rebalancing can invite tremendous random impact in our portfolios.Information does not flow into the market at a constant rate. While time may be a convenient measure, it may actually cause us to sample too frequently in some market environments and not frequently enough in others.

One answer may be to transform our measurements into a different domain. Rather than sampling price based upon the market close of each day, we might sample price based upon a fixed amount of cumulative volume, trades, or even variance. In doing so, we might find that our measures now represent a more consistent amount of information flow, despite representing a dynamic amount of data in the time domain.