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Taxes and Trend Equity

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On April 1, 2019

In Popular, Weekly Commentary

This post is available as a PDF download here.

Summary

  • Due to their highly active nature, trend following strategies are generally assumed to be tax inefficient.
  • Through the lens of a simple trend equity strategy, we explore this assertion to see what the actual profile of capital gains has looked like historically.
  • While a strategic allocation may only realize small capital gains at each rebalance, a trend equity strategy has a combination of large long-term capital gains interspersed with years that have either no gains or short-term capital losses.
  • Adding a little craftsmanship to the trend equity strategy can potentially improve the tax profile to make it less lumpy, thereby balancing the risk of having large unrealized gains with the risk of getting a large unwanted tax bill.
  • We believe that investors who expect to have higher tax rates in the future may benefit from strategies like trend equity that systematically lock in their gains more evenly through time.

Tax season for the year is quickly coming to a close, and while taxes are not a topic we cover frequently in these commentaries, it has a large impact on investor portfolios.

Source: xkcd

One of the primary reasons we do not cover it more is that it is investor-specific. Actionable insights are difficult to translate across investors without making broad assumptions about state and federal tax rates, security location (tax-exempt, tax deferred, or taxable), purchase time and holding period, losses or gains in other assets, health and family situation, etc.

Some sweeping generalizations can be made, such as that it is better to realize long-term capital gains than short-term ones, that having qualified dividends is better than having non-qualified ones, and that it is better to hold bonds in tax-deferred or tax-exempt accounts. But even these assertions are nuanced and depend on a variety of factors specific to an individual investor.

Trend equity strategies – and tactical strategies, in general – get a bad rap for being tax-inefficient. As assets are sold, capital gains are realized, often with no regard as to whether they are short-term or long-term. Wash sales are often ignored and holding periods may exclude dividends from qualifying status.

However, taxes represent yet another risk in a portfolio, and as you can likely guess if you are a frequent reader of these commentaries, reducing one risk is often done at the expense of increasing another.

The Risk in Taxes

Tax rates have been constant for long periods of time historically, especially in recent years, but they can change very rapidly depending on the overall economic environment.

Source: IRS, U.S. Census Bureau, and Tax Foundation. Calculations by Newfound Research. Series are limited by historical data availability.

The history shows a wide array of scenarios.

Prior to the 1980s, marginal tax rates spanned an extremely wide band, with the lowest tier near 0% and the top rate approaching 95%. However, this range has been much narrower for the past 30 years.

In the late 1980s when tax policy became much less progressive, investors could fall into only two tax brackets.

While the income quantile data history is limited, even prior to the narrowing of the marginal tax range, the bulk of individuals had marginal tax rates under 30%.

Turning to long-term capital gains rates, which apply to asset held for more than a year, we see similar changes over time.

Source: U.S. Department of the Treasury, Office of Tax Analysis and Tax Foundation.

For all earners, these rates are less than their marginal rates, which is currently the tax rate applied to short-term capital gains. While there were times in the 1970s when these long-term rates topped out at 40%, the maximum rate has dipped down as low as 15%. And since the Financial Crisis in 2008, taxpayers in the lower tax brackets pay 0% on long-term capital gains.

It is these large potential shifts in tax rates that introduce risk into the tax-aware investment planning process.

To see this more concretely, consider a hypothetical investment that earns 7% every year. Somehow – how is not relevant for this example – you have the choice of having the gains distributed annually as long-term capital gains or deferred until the sale of the asset.

Which option should you choose?

The natural choice is to have the taxes deferred until the sale of the asset. For a 10-year holding period where long-term capital gains are taxed at 20%, the pre-tax and after-tax values of a $1,000 investment are shown below.

The price return only version had a substantially higher pre-tax value as the full 7% was allowed to compound from year to year without the hinderance of an annual tax hit.

At the end of the 10-year period, the tax basis of the approach that distributed gains annually had increased up to the pre-tax amount, so it owed no additional taxes once the asset was sold. However, the approach that deferred taxes still ended up better after factoring in the tax on the embedded long-term capital gains that were realized upon the sale.

Now let’s consider the same assets but this time invested from 2004 to 2014 when the maximum long-term capital gains rate jumped to 25% in 2013 after being around 15% for the first 8 years.

The pre-tax picture is still the same: the deferred approach easily beat the asset that distributed capital gains annually.

But the after-tax values have changed order. Locking in more of the return when long-term capital gains tax rates were lower was advantageous.

The difference in this case may not be that significant. But consider a more extreme – yet still realistic – example where your tax rate on the gains jumps by more than ten percentage points (e.g. due to a change in employment or family situation or tax law changes), and the decision over which type of asset you prefer is not as clear cut.

Moving beyond this simple thought experiment, we now turn to the tax impacts on trend equity strategies.

Tax Impacts in Trend Equity

We will begin with a simple trend equity strategy that buys the U.S. stock market (the ETF VTI) when it has a positive 9-month return and buys short-term U.S. Treasuries (the ETF SHV) otherwise. Prior to ETF inception, we will rely on data from the Kenneth French Data Library to extend the analysis back to the 1920s. We will evaluate the strategy monthly and, for simplicity, will treat dividends as price returns.

With taxes now in the mix, we must track the individual tax lots as the strategy trades over time based on the tactical model. For deciding which tax lots to sell, we will select the ones with the lowest tax cost, making the assumption that short-term capital gains are taxed 50% higher than long-term capital gains (approximately true for investors with tax rates of 22% and 15%, respectively, in the current tax code).

We must address the question of when an investor purchases the trend equity strategy as a long bull market with a consistent positive trend would have very different tax costs for an investor holding all the way through versus one who bought at end.

To keep the analysis as simple as possible given the already difficult specification, we will look at an investment that is made at the very beginning, assume that taxes are paid at the end of each year, and compare the average annualized pre-tax and after-tax returns. Fortunately, for this type of trend strategy that can move entirely in and out of assets, the tax memory will occasionally reset.

To set some context, first, we need a benchmark.

Obviously, if you purchased VTI and held it for the entire time, you would be sitting on some large embedded capital gains.1

Instead, we will use a more appropriate benchmark for trend equity: a 50%/50% blend of VTI and SHV. We will rebalance this blend annually, which will lead to some capital gains.

The following chart shows the capital gains aggregated by year as a percentage of the end of the year account value.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

As expected with the annual rebalancing, all of the capital gains are long-term. Any short-term gains are an artifact of the rigidity of the rebalancing system where the first business day of subsequent years might be fewer than 365 days apart. In reality, you would likely incorporate some flexibility in the rebalances to ensure all long-term capital gains.

While this strategy incurs some capital gains, they are modest, with none surpassing 10%. Paying taxes on these gains is a small price to pay for maintaining a target allocation, supposing that is the primary goal.

Assuming tax rates of 15% for long-term gains and 25% for short-term gains, the annualized returns of the strategic allocation pre-tax and after-tax are shown below. The difference is minor.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

Now on to the trend equity strategy.

The historical capital gains look very different than those of the strategic portfolio.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

In certain years, the strategy locks in long-term capital gains greater than 50%. The time between these years is interspersed with larger short-term capital losses from whipsaws or year with essentially no realized gains or losses, either short- or long-term.

In fact, 31 of the 91 years had absolute realized gains/losses of less than 1% for both short- and long-term.

Now the difference between pre-tax and after-tax returns is 100 bps per year using the assumed tax rates (15% and 25%). This is significantly higher than with the strategic allocation.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

It would appear that trend equity is far less tax efficient than the strategic benchmark. As with all things taxes, however, there are nuances. As we mentioned in the first section of this commentary, tax rates can change at any time, either from a federal mandate or a change in an individual’s situation. If you are stuck with a considerable unrealized capital gain, it may be too late to adjust the course.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

The median unrealized capital gain for the trend equity strategy is 10%. This, of course, means that you must realize the gains periodically and therefore pay taxes.

But if you are sitting with a 400% unrealized gain in a different strategy, behaviorally, it may be difficult to make a prudent investment decision knowing that a large tax bill will soon follow a sale. And a 10 percentage point increase in the capital gains tax rate can have a much larger impact in dollar terms on the large unrealized gain than missing out on some compounding when rates were lower.

Even so, the thought of paying taxes intermediately and missing out on compound growth can still be irksome. Some small improvement to the trend equity strategy design can prove beneficial.

Improving the Tax Profile Within Trend Equity

This commentary would be incomplete without a further exploration down some of the axes of diversification.

We can take the simple 9-month trend following strategy and diversify it along the “how” axis using a multi-model approach with multiple lookback periods.

Specifically, we will use price versus moving average and moving average cross-overs in addition to the trailing return signal and look at windows of data ranging from 6 to 12 months.2

We can also diversify along the “when” axis by tranching the monthly strategy over 20 days. This has the effect of removing the luck – either good or bad – of rebalancing on a certain day of the month.

Below, we plot the characteristics of the long-term capital gains for the strategies in years in which a long-term gain was realized.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

The single monthly model had about a third of the years with long-term gains. Tranching it took that fraction to over a half. Moving to a multi-model approach brought the fraction to 60%, and tranching that upped it to 2 out of every 3 years.

Source: CSI Data and Kenneth French Data Library. Calculations by Newfound.

From an annualized return perspective, all of these trend equity strategies exhibited similar return differentials between pre-tax and after-tax.

In previous commentaries, we have illustrated how tranching to remove timing luck and utilizing multiple trend following models can remove the potential dispersion in realized terminal wealth. However, in the case of taxes, these embellishments did not yield a reduction in the tax gap.

While these improvements to trend equity strategies reduce specification-based whipsaw, they often result in similar allocations for large periods of time, especially since these strategies only utilize a single asset.

But to assume that simplicity trumps complexity just because the return differentials are not improved misses the point.3

With similar returns among within the trend-following strategies, using an approach that realizes more long-term capital gains could still be beneficial from a tax perspective.

In essence, this can be thought of as akin to dollar-cost averaging.

Dollar-cost averaging to invest a lump sum of capital is often not optimal if the sole goal is to generate the highest return.4 However, it is often beneficial in that it reduces the risk of bad outcomes (i.e. tail events).

Having a strategy – like trend equity – that has the potential to generate strong returns while taking some of those returns as long-term capital gains can be a good hedge against rising tax rates. And having a diversified trend equity strategy that can realize these capital gains in a smoother fashion is icing on the cake.

Conclusion

Taxes are a tricky subject, especially from the asset manager’s perspective. How do you design a strategy that suits all tax needs of its investors?

Rather than trying to develop a one-size-fits-all strategy, we believe that a better approach to the tax question is education. By more thoroughly understanding the tax profile of a strategy, investors can more comfortably deploy it appropriately in their portfolios.

As highly active strategies, trend equity mandates are generally assumed to be highly tax-inefficient. We believe it is more meaningful to represent the tax characteristics an exchange of risks: capital gains are locked in at the current tax rates (most often long-term) while unrealized capital gains are kept below a reasonable level. These strategies have also historically exhibited occasional periods with short-term capital losses.

These strategies can benefit investors who expect to have higher tax rates in the future without the option of having a way to mitigate this risk otherwise (e.g. a large tax-deferred account like a cash balance plan, donations to charity, a step-up in cost basis, etc.).

Of course, the question about the interplay between tax rates and asset returns, which was ignored in this analysis, remains. But in an uncertain future, the best course of investment action is often the one that diversifies away as much uncompensated risk as possible and includes a comprehensive plan for risk management.

Trend Following in Cash Balance Plans

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On March 18, 2019

In Popular, Risk Management, Weekly Commentary

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:

  1. A fixed rate of return per year, between 2% and 6%.
  2. The 30-year U.S. Treasury rate.
  3. The 30-year U.S. Treasury rate with a floor of between 3% and 5%.
  4. 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.

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.

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.

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.

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.

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.

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.

Measuring the Benefit of Diversification

By

On November 5, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • The benefits of diversification are often touted, but many investors feel disappointed in diversified portfolios because of the dispersion in performance of the individual holdings.
  • In the context of three different unconstrained sleeves, we look at a way to measure and visualize the benefit (or detriment) of diversification based on achieving different objectives.
  • Through this lens, we get a picture of how good or bad the results might have been, which can lead to confidence either in the robustness of the allocation or in the need to take a different approach.
  • Since we only experience one path of history, it is difficult to assess the benefit of diversification unless we consider what could have happened.
  • We believe that taking a systematic approach does not fully remove the art of the analysis but can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

Introduction

Diversification is a standard risk management tool in any portfolio. Reducing the impact of idiosyncratic risks in individual investments by holding a suite of stocks, asset classes, strategies, etc. produces a smoother investment ride most of the time and reduces the risk of negative surprises.

But in a world where we only experience one outcome out of the multitude of possibilities, gauging the benefit of diversification is difficult. It is even hard to do in hindsight, not so much because we can’t but more often that we won’t. The results already happened.

Over a single time period with no rebalancing, a diversified portfolio will underperform the best asset that it holds. This is a mathematical fact when there is any dispersion in the returns of the assets and it is why we have said that diversification will always disappoint. Our natural behavioral tendencies can often get the better of us, despite the fact that diversification might be doing a great job, especially when examined through the appropriate lens and measured in the context of what could have happened.

Last summer, we published a presentation entitled Building an Unconstrained Sleeve. In it, we looked at ways to combine traditional and non-traditional assets and strategies to target specific objectives: equity hedging, absolute return, and equity-like with downside management.

Now that we have 15 months of subsequent data for all the underlying strategies, we want to revisit that piece and  explore the benefit of diversification in the context of hindsight.

A Recap of the Process

As a quick refresher, we included seven strategies and asset classes in the construction of our unconstrained sleeves:

  • Long/flat trend-following equities
  • Minimum volatility equities
  • Macro trend-following (managed futures)
  • Macro risk parity
  • Macro value
  • Macro income
  • Intermediate U.S. Treasuries

While these strategies are surely not exhaustive, they cover a range of factors (value, momentum, low volatility, etc.) and a global set of asset classes (equities, bonds, commodities, and currencies) commonly included in unconstrained sleeves. They were also selected because many of these strategies are conveniently packaged as ETFs or mutual funds, making the resulting sleeves more easily implementable.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

Over the 15 months, world equity was by far the best performer and the spread between best-performing and worst-performing positions exceeded 20 percentage points.  If you wanted high returns – and going back to our statement about how diversification will always disappoint – you could have just held world equities and been quite content.

But putting ourselves back in June 2017, we did not know a priori that simply holding equities would have generated the highest returns. Looking at this type of chart in November 2008 would have led to a very different emotional conclusion.

The aim of our original study was to develop unconstrained sleeves that would meet their objectives regardless of how the future played out. Therefore, we employed a simulation-based method that aimed to preserve some of the unique correlation structure between the strategies across different market environments and reduce the risk of overfitting to a single realization of history. With this approach, we constructed portfolios that targeted three different objectives that investors might be interested in:

  1. Equity hedge – designed to offset significant equity losses.
  2. Absolute return – designed to create a stable and consistent return stream in all environments.
  3. Equity-like – designed to capture significant equity upside with reduced downside.

(Note: Greater detail about portfolio construction process, strategy descriptions, and performance attributes of each strategy can be found in our original presentation.)

But were our constructed portfolios successful in achieving their objectives out-of-sample? To analyze this question, as well as explore the benefits/detractors of diversification for each objective, we will calculate the distribution of what could have happened. The hope is that, each strategy would perform well relative to all other possible portfolios that could have been chosen for the sleeve.

Saying exactly what portfolios we could have chosen is where a little art comes into play. For example, in the equity-like strategies, it is difficult to say that a 100% bond portfolio would have ever been a viable option and therefore may not be an apt out-of-sample comparison.

However, since our original process did not have any specific override for these intuitive constraints, and since we do not wish to assert after-the-fact which portfolios would have been rejected, we will allow the entire potential allocation space to be fair game in our comparison.

There are a number of ways to sample the set of allocations over the 7 asset classes that could have formed the portfolios for each sleeve. Perhaps the most obvious choice would be to sample uniformly over the possible allocations. The issue to balance in this case is coverage of the space (a 6-dimensional simplex) with the number of samples. To be 95% confident that we sampled an allocation above 95% for only a single asset class would require nearly 200 million samples.  We have used modified Sobol sequences in the past to ensure coverage of more of the space with fewer points. However, in the current case, to mimic the rounding that is often found in portfolio allocations, we will use a lattice of points spaced 2.5% apart covering the entire space. This requires just under 10 million points in the simulations.

Equity Hedge

This sleeve was designed to offset significant equity losses by limiting downside capture.  The resulting optimized portfolio was relatively concentrated in two main positions that historically have exhibited low-to-negative correlations to equities and exhibited potential crisis alpha during significant and prolonged drawdowns.Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

The down capture this portfolio during the out-of-sample period was 0.44.  This result falls in the 70th percentile (that is, better than 70% of the other sample portfolios and where lower down-capture is better) when compared to the 10 million possible other portfolios we could have originally selected. Not surprisingly, the 100% intermediate-term Treasury portfolio had the best down capture (-0.05) over the out-of-sample. Of the portfolios with better down capture, Intermediate Treasuries and Macro – Income were generally the highest allocations.

This does not come as much of a surprise to anyone who has followed the managed futures space for the last 15 months.  The category largely remains in a multi-year drawdown (peaking in early 2014), but it has also done little to offset the rapid sell-offs seen in equities in 2018.  Therefore, with the full benefit of hindsight, any allocation to Macro – Trend in the original portfolio would be a detriment realizing our out-of-sample objective.

Yet even with this lackluster performance, an out-of-sample realized 70th percentile result over a short, 15-month horizon is a result to be pleased with.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

Absolute Return

This sleeve was designed to seek a stable and consistent return stream in all market environments. We aimed to accomplish this by utilizing a risk parity approach. As expected, this sleeve holds all asset classes and is very well diversified across them.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

To measure the success of the risk parity over the live period, we will look at the Gini coefficient for each of the ten million potential portfolios we could have initially selected. The Gini coefficient quantifies the equality of the distribution, with a value of 1 representing 100% concentration and 0 representing perfect equality.

The Gini coefficient of the actual portfolio was 0.25 which was in the 99.8th percentile of possible outcomes (i.e. highly diversified on a relative basis). Here, the percentile estimate is padded by the fact that many of the simulated portfolios (e.g. the 100% ones) would clearly not be close to equal risk contribution.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

Did our original portfolio achieve its out-of-sample goal?  Here, we can evaluate success as to whether the realized contribution to risk of each exposure was close to equivalent; i.e. did we actually achieve risk parity as desired?  We can see below that indeed we did, with the main exception of Macro – Trend, which was the most volatile asset class over the period.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Over the sample space of potential portfolios, the portfolio with the minimum out-of-sample Gini coefficient (0.08) was tilted toward the less volatile and more diversifying asset classes (Intermediate Treasuries and Macro – Income). Even so, due to the limited granularity of the sampled portfolios, the risk contribution of Macro – Income was still half of that for each of the other strategies.

It is also worth noting how similar this solution is – generated with the complete benefit of hindsight – to our originally constructed portfolio.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

Equity-like with Downside Management

This sleeve was designed in an effort to capture equity market growth while managing the risk of severe and prolonged drawdowns. It was tilted toward the equity-like exposures with a split among risk management styles (trend, minimum volatility, macro strategies, etc.). The allocation to U.S. Treasuries is very small.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research.

For this portfolio, we have two variables to analyze: the up capture relative to global equities and the Ulcer index, a measure of the severity and duration of drawdowns. In the construction of the sleeve, the target was to keep the Ulcer index less than 25% of the value for global equities. The joint distribution of these quantities over the live period is shown below with the actual values over the live period for the sleeve indicated.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

The realized Ulcer level was 68% of that of world equity – a far cry from the 25% that the portfolio was optimized for – and was in the 42nd percentile while the up capture of 0.60 was in the 93rd percentile.

With the explicit goal of achieving a relative Ulcer level, a comparison against the entire potential allocation space of 10 million portfolios is not appropriate.  Therefore, we reduce the set of 10 million comparative portfolios to only those that would have given a relative Ulcer index less than 25% compared to world equities, eliminating approximately 40% of possible portfolios.

The distributions of allocations to each of the strategies in the acceptable subset are shown below. We can see that the more diversifying strategies take on a larger range of allocations.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

Interestingly, looking only over this subset of the original 10 million portfolios improves the out-of-sample up capture of our originally constructed portfolio to the 99th percentile but does not change the percentile of the Ulcer index over the live period. Why is this?

The correlation of the relative Ulcer index over the live period with that over the historical period is only 0.1, indicating that the out of sample data did not line up with our expectations at first glance. However, this makes sense when we recall that the optimization was carried out using data from much more extreme market environments (think 2001 and 2008).  It is a good reminder that, just because you optimize for a certain parameter value does not mean you will get it over the live data.

Higher up-capture typically goes hand-in-hand with a higher Ulcer index, as higher return often requires bearing more risk.  Therefore, one way to standardize our measures across the potential set of portfolios is to calculate the ratio of up-capture to the Ulcer index. With this transformation, the risk-adjusted up capture falls in the 87th percentile over the set of sample allocations, indicating a very high realized risk-adjusted return.

Source: St. Louis Federal Reserve, MSCI, Salient, HFRI, CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index.  Past performance does not guarantee future results.  Index returns are total returns and are gross of all fees.

Conclusion

We only experience one path of the world and do not know the infinite alternate course history could have taken. But it is exactly this infinitude of alternate states that diversification is meant to address.

Diversification generally has no apparent benefit unless we envision what could have happened. Unfortunately our innate natures make this difficult. We do not often value our realized path in this context. After all, none of these alternate states actually happened, so it is difficult to picture what we did not experience.

A quantitative approach can yield a systematic way to evaluate the benefit (or detriment) of diversification. This way, we are not relying as much on intuition – how did our performance feel? – and are looking through a more objective lens at our initial decisions.

In the examples using the Unconstrained Sleeves, diversification focused on more than just returns. The objectives that initially went in to the portfolio construction were the parameters of interest.

Taking a systematic approach does not fully remove the art of the analysis, as was evident in the construction of the potential sample of portfolios used in the comparisons, but having a process can remove some of the behavioral biases that make sticking with a portfolio difficult in the first place.

The State of Risk Management

By

On August 20, 2018

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as PDF download here. 

Summary

  • We compare and contrast different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies; over the last 20 years.
  • We find that all eight strategies studied successfully reduce risk, while six of the eight strategies improve risk-adjusted returns. The lone exceptions are two options-based strategies that involve being long volatility and therefore are on the wrong side of the volatility risk premium.
  • Over time, performance of the risk management strategies varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
  • Diversifying your diversifiers by blending a number of complementary risk-managed strategies together can be a powerful method of improving long-term outcomes. The diversified approach to risk management shows promise in terms of reducing sequence risk for those investors nearing or in retirement.

I was perusing Twitter the other day and came across this tweet from Jim O’Shaughnessy, legendary investor and author of What Works on Wall Street.

As always. Jim’s wisdom is invaluable.  But what does this idea mean for Newfound as a firm?  Our first focus is on managing risk.  As a result, one of the questions that we MUST know the answer to is how to get more investors comfortable with sticking to a risk management plan through a full market cycle.

Unfortunately, performance chasing seems to us to be just as prevalent in risk management as it is in investing as a whole.  The benefits of giving up some upside participation in exchange for downside protection seemed like a no brainer in March of 2009.  After 8+ years of strong equity market returns (although it hasn’t always been as smooth of a ride as the market commentators may make you think), the juice may not quite seem worth the squeeze.

While we certainly don’t profess to know the answer to our burning question from above, we do think the first step towards finding one is a thorough understanding on the risk management landscape.  In that vein, this week we will update our State of Risk Management presentation from early 2016.

We examine eight strategies that roughly fit into four categories:

  • Diversification Strategies: strategic 60/40 stock/bond mix1 and risk parity2
  • Options Strategies: equity collar3, protective put4, and put-write5
  • Equity Strategies: long-only defensive equity that blends a minimum volatility strategy6, a quality strategy7, and a dividend growth strategy8 in equal weights
  • Trend-Following Strategies: managed futures9 and tactical equity10

The Historical Record

We find that over the period studied (December 1997 to July 2018) six of the eight strategies outperform the S&P 500 on a risk-adjusted basis both when we define risk as volatility and when we define risk as maximum drawdown.  The two exceptions are the equity collar strategy and the protective put strategy.  Both of these strategies are net long options and therefore are forced to pay the volatility risk premium.  This return drag more than offsets the reduction of losses on the downside.

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. Volatility is a statistical measure of the amount of variation around the average returns for a security or strategy. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. Drawdown is a statistical measure of the losses experienced by a security or strategy relative to its historical maximum. The maximum drawdown is the largest drawdown over the security or strategy’s history. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Not Always a Smooth Ride

While it would be nice if this outperformance accrued steadily over time, reality is quite a bit messier.  All eight strategies exhibit significant variation in their rolling one-year returns vs. the S&P 500.  Interestingly, the two strategies with the widest ranges of historical one-year performance vs. the S&P 500 are also the two strategies that have delivered the most downside protection (as measured by maximum drawdown).  Yet another reminder that there is no free lunch in investing.  The more aggressively you wish to reduce downside capture, the more short-term tracking error you must endure.

Relative 1-Year Performance vs. S&P 500 (December 1997 to July 2018)

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Thinking of Risk Management as (Uncertain) Portfolio Insurance

When we examine this performance dispersion across different market environments, we find a totally intuitive result: risk management strategies generally underperform the S&P 500 when stocks advance and outperform the S&P 500 when stocks decline.  The hit rate for the risk management strategies relative to the S&P 500 is 81.2% in the four years that the S&P 500 was down (2000, 2001, 2002, and 2008) and 19.8% in the seventeen years that the S&P was up.

In this way, risk management strategies are akin to insurance.  A premium, in the form of upside capture ratios less than 100%, is paid in exchange for a (hopeful) reduction in downside capture.

With this perspective, it’s totally unsurprising that these strategies have underperformed since the market bottomed during the global market crisis.   Seven of the eight strategies (with the long-only defensive equity strategy being the lone exception) underperformed the S&P 500 on an absolute return basis and six of the eight strategies (with defensive equity and the 60/40 stock/bond blend) underperformed on a risk-adjusted basis.

Annual Out/Underperformance Relative to S&P 500 (December 1997 to July 2018)

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Diversifying Your Diversifiers

The good news is that there is significant year-to-year variation in the performance across strategies, as evidenced by the periodic table of returns above, suggesting there are diversification benefits to be harvested by allocating to multiple risk management strategies.  The average annual performance differential between the best performing strategy and the worst performing strategy is 20.0%.  This spread was less than 10% in only 3 of the 21 years studied.

We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies.  Both blends have higher Sharpe Ratios than 7 of the 8 individual strategies and higher excess return to drawdown ratios than 6 of the eight individual strategies.

This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.

Data Source: Bloomberg, CSI. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. The Tactical Equity strategy was constructed by Newfound in August 2018 for purposes of this analysis and is therefore entirely backtested and not an investment strategy that is currently managed and offered by Newfound.

 

Why Bother with Risk Management in the First Place?

As we’ve written about previously, we believe that for most investors investing “failure” means not meeting one’s financial objectives.  In the portfolio management context, failure comes in two flavors.  “Slow” failure results from taking too little risk, while “fast” failure results from taking too much risk.

In this book, Red Blooded Risk, Aaron Brown summed up this idea nicely: “Taking less risk than is optimal is not safer; it just locks in a worse outcome.  Taking more risk than is optimal also results in a worst outcome, and often leads to complete disaster.”

Risk management is not synonymous with risk reduction.  It is about taking the right amount of risk, not too much or too little.

Having a pre-defined risk management plan in place before a crisis can help investors avoid panicked decisions that can turn a bad, but survivable event into catastrophe (e.g. the retiree that sells all of his equity exposure in early 2009 and then stays out of the market for the next five years).

It’s also important to remember that individuals are not institutions.  They have a finite investment horizon.  Those that are at or near retirement are exposed to sequence risk, the risk of experiencing a bad investment outcome at the wrong time.

We can explore sequence risk using Monte Carlo simulation.  We start by assessing the S&P 500 with no risk management overlay and assume a 30-year retirement horizon.  The simulation process works as follows:

  1. Randomly choose a sequence of 30 annual returns from the set of actual annual returns over the period we studied (December 1998 to July 2018).
  2. Adjust returns for inflation.
  3. For the sequence of returns chosen, calculate the perfect withdrawal rate (PWR). Clare et al, 2016 defines the PWR as “the withdrawal rate that effectively exhausts wealth at death (or at the end of a fixed period, known period) if one had perfect foresight of all returns over the period.11
  4. Return to #1, repeating 1000 times in total.

We plot the distribution of PWRs for the S&P 500 below.  While the average PWR is a respectable 5.7%, the range of outcomes is very wide (0.6% to 14.7%).  The 95 percent confidence interval around the mean is 2.0% to 10.3%.  This is sequence risk.  Unfortunately, investors do not have the luxury of experiencing the average, they only see one draw.  Get lucky and you may get to fund a better lifestyle than you could have imagined with little to no financial stress.  Get unlucky and you may have trouble paying the bills and will be sweating every market move.

Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends.

 

Next, we repeat the simulation, replacing the pure S&P 500 exposure with the equal-weight blend of risk management strategies excluding the equity collar and the protective put.  We see quite a different result.  The average PWR is similar (6.2% to 5.7%), but the range of outcomes is much smaller (95% confidence interval from 4.4% to 8.1%).  At its very core, this is what implementing a risk management plan is all about.  Reducing the role of investment luck in financial planning.  We give up some of the best outcomes (in the right tail of the S&P 500 distribution) in exchange for reducing the probability of the very worst outcomes (in the left tail).

Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends.

Conclusion

There is no holy grail when it comes to risk management.  While a number of approaches have historically delivered strong results, each comes with its own pros and cons.

In an uncertain world where we cannot predict exactly what the next crisis will look like, diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action. We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.

Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).

That being said, having the discipline to stick with a risk management plan also requires being realistic.  While it would be great to build a strategy with 100% upside and 0% downside, such an outcome is unrealistic.  Risk-managed strategies tend to behave a lot like uncertain insurance for the portfolio.  A premium, in the form of upside capture ratios less than 100%, is paid in exchange for a (hopeful) reduction in downside capture.  This upside underperformance is a feature, not a bug.  Trying too hard to correct it may lead to overfit strategies fail to deliver adequate protection on the downside.

How to Benchmark Trend-Following

By

On May 14, 2018

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

This post is available as a PDF download here.

Summary­

  • Benchmarking a trend-following strategy can be a difficult exercise in managing behavioral biases.
  • While the natural tendency is often to benchmark equity trend-following to all-equities (e.g. the S&P 500), this does not accurately give the strategy credit for choosing to be invested when the market is going up.
  • A 50/50 portfolio of equities and cash is generally an appropriate benchmark for long/flat trend-following strategies, both for setting expectations and for gauging current relative performance.
  • If we acknowledge that for a strategy to outperform over the long-run, it must undergo shorter periods of underperformance, using this symmetric benchmark can isolate market environments that underperformance should be expected.
  • Diversifying risk-management approaches (e.g. pairing strategic allocation with tactical trend-following) can manage events that are unfavorable to one strategy, and benchmarking is a tool to set expectations around the level of risk management necessary in different market environments.

Any strategy that deviates from the most basic is compared to a benchmark. But how do you choose an appropriate benchmark?

The complicated nature of benchmarking can be easily seen by considering something as simple as a value stock strategy.

You may pit your concentrated value manager you currently use up against the more diversified value manager you used previously. At that time, you may have compared that value manager to a systematic smart-beta ETF like the iShares S&P 500 Value ETF (ticker: IVE). And if you were invested in that ETF, you might compare its performance to the S&P 500.

What prevents you from benchmarking them all to the S&P 500? Or from benchmarking the concentrated value strategy to all of the other three?

Benchmark choices are not unique and are highly dependent on what aspect of performance you wish to measure.

Benchmarking is one of the most frequently abused facets of investing. It can be extremely useful when applied in the correct manner, but most of the time, it is simply a hurdle to sticking with an investment plan.

In an ideal world, the only benchmark for an investor would be whether or not they are on track for hitting their financial goals. However, in an industry obsessed with relative performance, choosing a benchmark is a necessary exercise.

This commentary will explore some of the important considerations when choosing a benchmark for trend-following strategies.

The Purpose of a Trend-Following Benchmark

As an investment manager, our goal with benchmarking is to check that a strategy’s performance is in line with our expectations. Performance versus a benchmark can answer questions such as:

  • Is the out- or underperformance appropriate for the given market environment?
  • Is the magnitude of out- or underperformance typical?
  • How is the strategy behaving in the context of other ways of managing risk?

With long/flat trend-following strategies, the appropriate benchmark should gauge when the manager is making correct or incorrect calls in either direction.

Unfortunately, we frequently see long/flat equity trend-following strategies benchmarked to an all-equity index like the S&P 500. This is similar to the coinflip game we outlined in our previous commentary about protecting and participating with trend-following.[1]

The behavioral implications of this kind of benchmarking are summarized in the table below.

The two cases with wrong calls – to move to cash when the market goes up or remain invested when the market goes down – are appropriately labeled, as is the correct call to move to cash when the market is going down. However, when the market is going up and the strategy is invested, it is merely keeping up with its benchmark even though it is behaving just as one would want it to.

To reward the strategy in either correct call case, the benchmark should consist of allocations to both equity and cash.

A benchmark like this can provide objective answers to the questions outlined above.

Deriving a Trend-Following Benchmark

Sticking with the trend-following strategy example we outlined in our previous commentary[2], we can look at some of the consequences of choosing different benchmarks in terms of how much the trend-following strategy deviates from them over time.

The chart below shows the annualized tracking error of the strategy to the range of strategic proportions of equity and cash.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The benchmark that minimizes the tracking error is a 47% allocation to equities and 53% to cash. This 0.47 is also the beta of the trend-following strategy, so we can think of this benchmark as accounting for the risk profile of the strategy over the entire 92-year period.

But what if we took a narrower view by constraining this analysis to recent performance?

The chart below shows the equity allocation of the benchmark that minimizes the tracking error to the trend-following strategy over rolling 1-year periods.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

A couple of features stand out here.

First, if we constrain our lookback period to one year, a time-period over which many investors exhibit anchoring bias, then the “benchmark” that we may think we will closely track – the one we are mentally tied to – might be the one that we deviate the most from over the next year.

And secondly, the approximately 50/50 benchmark calculated using the entire history of the strategy is rarely the one that minimizes tracking error over the short term.

The median equity allocation in these benchmarks is 80%, the average is 67%, and the data is highly clustered at the extremes of 100% equity and 100% cash.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions. This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The Intuitive Trend-Following Benchmark

Is there a problem in determining a benchmark using the tracking error over the entire period?

One issue is that it is being calculated with the benefit of hindsight. If you had started a trend-following strategy back in the 1930s, you would have arrived at a different equity allocation for the benchmark based on this analysis given the available data (e.g. using data up until the end of 1935 yields an equity allocation of 37%).

To remove this reliance on having a sufficiently long backtest, our preference is to rely more on the strategy’s rules and how we would use it in a portfolio to determine our trend-following benchmarks.

For a trend following strategy that pivots between stocks and cash, a 50/50 benchmark is a natural choice.

It is broad enough to include the assets in the trend-following strategy’s investment universe while being neutral to the calls to be long or flat.

Seeing the 50/50 portfolio be the answer to the tracking error minimization problem over the entire data simply provides empirical evidence for its use.

One argument against using a 50/50 blend could focus on the fact that the market is generally up more frequently than it is down, at least historically. While this is true, the magnitude of down moves has often been larger than the magnitude of up moves. Since this strategy is explicitly meant as a risk management tool, accounting for both the magnitude and the frequency is prudent.

Another argument against its use could be the belief that we are entering a different market environment where history will not be an accurate guide going forward. However, given the random nature of market moves coupled with the behavioral tendencies of investors to overreact, herd, and anchor, a benchmark close to a 50/50 is likely still a fitting choice.

Setting Expectations with a Trend-Following Benchmark

Now that we have a benchmark to use, how do we use it to set our expectations?

Neglecting the historical data for the moment, from the ex-ante perspective, it is helpful to decompose a typical market cycle into four different segments and assess how we expect trend-following to behave:

  • Initial decline – Equity markets begin to sell off, and the fully invested trend-following strategy underperforms the 50/50 benchmark.
  • Prolonged drawdown – The trend-following strategy adapts to the decline and moves to cash. The trend-following strategy outperforms.
  • Initial recovery – The trend-following strategy is still in cash and lags the benchmark as prices rebound off the bottom.
  • Sustained recovery – The trend-following strategy reinvests and captures more of the upside than the benchmark.

Of course, this is a somewhat ideal scenario that rarely plays out perfectly. Whipsaw events occur as prices recover (decline) before declining (recovering) again.

But it is important to note how the level of risk relative to this 50/50 benchmark varies over time.

Contrast this with something like an all equity strategy benchmarked to the S&P 500 where the risk is likely to be similar during most market environments.

Now, if we look at the historical data, we can see this borne out in the graph of the drawdowns for trend-following and the 50/50 benchmark.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

In most prolonged and major (>20%) drawdowns, trend-following first underperforms the benchmark, then outperforms, then lags as equities improve, and then outperform again.

Using the most recent example of the Financial Crisis, we can see the capture ratios verses the benchmark in each regime.

Source: Kenneth French Data Library. Data from October 2007 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

The underperformance of the trend-following strategy verses the benchmark is in line with expectations based on how the strategy is desired to work.

Another way to use the benchmark to set expectations is to look at rolling returns historically. This gives context for the current out- or underperformance relative to the benchmark.

From this we can see which percentile the current return falls into or check to see how many standard deviations it is away from the average level of relative performance.

Source: Kenneth French Data Library. Data from July 1926 – February 2018. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees.  Returns assume the reinvestment of all distributions.  This document does not reflect the actual performance results of any Newfound investment strategy or index.  All returns are backtested and hypothetical.  Past performance is not a guarantee of future results.

In all this, there are a few important points to keep in mind:

  • Price moves that occur faster than the scope of the trend-following measurement can be one source of the largest underperformance events.
  • Along a similar vein, whipsaw is a key risk of trend-following. Highly oscillatory markets will not be favorable to trend-following. In these scenarios, trend following can underperform even fully invested equities.
  • With percentile analysis, there is always a first time for anything. Having a rich data history covering a variety of market scenarios mitigates this, but setting new percentiles, either on the low end or high end, is always possible.
  • Sometimes a strategy is expected to lag its benchmark in a given market environment. A primary goal with benchmarking is it accurately set these expectations for the potential magnitude of relative performance and design the portfolio accordingly.

Conclusion

Benchmarking a trend-following strategy can be a difficult exercise in managing behavioral biases. With the tendency to benchmark all equity-based strategies to an all-equity index, investors often set themselves up for a let-down in a bull market with trend-following.

With benchmarking, the focus is often on lagging the benchmark by “too much.” This is what an all-equity benchmark can do to trend-following. However, the issue is symmetric: beating the benchmark by “too much” can also signal either an issue with the strategy or with the benchmark choice. This is why we would not benchmark a long/flat trend-following strategy to cash.

A 50/50 portfolio of equities and cash is generally an appropriate benchmark for long/flat trend-following strategies. This benchmark allows us to measure the strategy’s ability to correctly allocate when equities are both increasing or decreasing.

Too often, investors use benchmarking solely to see which strategy is beating the benchmark by the most. While this can be a use for very similar strategies (e.g. a set of different value managers), we must always be careful not to compare apples to oranges.

A benchmark should not conjure up an image of a dog race where the set of investment strategies are the dogs and the benchmark is the bunny out ahead, always leading the way.

We must always acknowledge that for a strategy to outperform over the long-run, it must undergo shorter periods of underperformance. Diversifying approaches can manage events that are unfavorable to one strategy, and benchmarking is a tool to set expectations around the level of risk management necessary in different market environments.

 

[1] https://blog.thinknewfound.com/2018/05/leverage-and-trend-following/

[2] https://blog.thinknewfound.com/2018/03/protect-participate-managing-drawdowns-with-trend-following/

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