Flirting with Models

The Research Library of Newfound Research

Author: Nathan Faber Page 3 of 5

Nathan is a Portfolio Manager at Newfound Research. At Newfound, Nathan is responsible for investment research, strategy development, and supporting the portfolio management team.

Prior to joining Newfound, he was a chemical engineer at URS, a global engineering firm in the oil, natural gas, and biofuels industry where he was responsible for process simulation development, project economic analysis, and the creation of in-house software.

Nathan holds a Master of Science in Computational Finance from Carnegie Mellon University and graduated summa cum laude from Case Western Reserve University with a Bachelor of Science in Chemical Engineering and a minor in Mathematics.

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.

How Much Accuracy Is Enough?

By

On March 4, 2019

In Craftsmanship, Portfolio Construction, Trend, Weekly Commentary

Available as a PDF download here.

Summary­

  • It can be difficult to disentangle the difference between luck and skill by examining performance on its own.
  • We simulate the returns of investors with different prediction accuracy levels and find that an investor with the skill of a fair coin (i.e. 50%) would likely under-perform a simple buy-and-hold investor, even before costs are considered.
  • It is not until an investor exhibits accuracy in excess of 60% that a buy-and-hold investor is meaningfully “beaten” over rolling 5-year evaluation periods.
  • In the short-term, however, a strategy with a known accuracy rate can still masquerade as one far more accurate or far less accurate due to luck.
  • Further confounding the analysis is the role of skewness of the return distribution. Positively skewed strategies, like trend following, can actually exhibit accuracy rates lower than 50% and still be successful over the long run.
  • Relying on perceptions of accuracy alone may lead to highly misguided conclusions.

The only thing sure about luck is that it will change. — Bret Harte1

The distinction between luck and skill in investing can be extremely difficult to measure. Seemingly good or bad strategies can be attributable to either luck or skill, and the truth has important implications for the future prospects of the strategy.Source: Grinold and Kahn, Active Portfolio Management. (New York: McGraw-Hill, 1999).

Time is one of the surest ways to weed out lucky strategies, but the amount of time needed to make this decision with a high degree of confidence can be longer than we are willing to wait.  Or, sometimes, even longer than the data we have.

For example, in order to be 95% confident that a strategy with a 7% historical return and a volatility of 15% has a true expected return that is greater than a 2% risk-free rate, we would need 27 years of data. While this is possible for equity and bond strategies, we would have a long time to wait in order to be confident in a Bitcoin strategy with these specifications.

Even after passing that test, however, that same strategy could easily return less than the risk-free rate over the next 5 years (the probability is 25%).

Regardless of the skill, would you continue to hold a strategy that underperformed for that long?

In this commentary, we will use a sample U.S. sector strategy that isolates luck and skill to explore the impacts of varying accuracy and how even increased accuracy may only be an idealized goal.

The (In)Accurate Investor

To investigate the historical impact of luck and skill in the arena of U.S. equity investing, we will consider a strategy that invests in the 30 industries from the Kenneth French Data Library.

Each month, the strategy independently evaluates each sector and either holds it or invests the capital at the risk-free rate. The term “evaluates” is used loosely here; the evaluation can be as simple as flipping a (potentially biased) coin.

The allocation allotted to each sector is 1/30th of the portfolio (3.33%). We are purposely not reallocating capital among the sectors chosen so that the sector calls based on the accuracy straightforwardly determine the performance.

To get an idea for the bounds of how well – or poorly – this strategy would have performed over time, we can consider three investors:

  1. The Plain Investor – This investor simply holds all 30 sectors, equally weighted, all the time.
  2. The Perfect Investor – This investor allocates with 100% accuracy. Using a crystal ball to look into the future, if a sector will go up in the subsequent month, this investor will allocate to it. If the sector will go down, this investor will invest the capital in cash.
  3. The Anti-Perfect Investor – This investor not merely imperfect, they are the complete opposite of the Perfect Investor. They make the wrong calls to invest or not without fail. Their accuracy is 0%. They are so reliably bad that if you could short their strategy, you would be the Perfect Investor.

The Perfect and Anti-Perfect investors set the bounds for what performance is possible within this framework, and the Plain Investor denotes the performance of not making any decisions.

The growth of each boundary strategy over the entire time period is a little outrageous.

Annualized ReturnAnnualized VolatilityMaximum Drawdown
Plain Investor10.5%19.3%83.9%
Perfect Investor42.6%11.0%0.0%
Anti-Perfect Investor-20.0%12.1%100.0%

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

A more informative illustration is the rolling annualized 5-year return for each strategy.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

While the spread between the Perfect and Anti-Perfect investors ebbs and flows, its median value Is 59,000 basis points (“bps”). Between the Perfect and Plain investors, there is still 29,000 bps of annualized outperformance to be had. A natural wish is to make calls that harvest some of this spread.

Accounting for Accuracy

Now we will look at a set of investors who are able to evaluate each sector with some known degree of accuracy.

For each accuracy level between 0% and 100% (i.e. our Anti-Perfect and Perfect investors, respectively), we simulate 1,000 trials and look at how the historical results have played out.

A natural starting point is the investor who merely flips a fair coin for each sector. Their accuracy is 50%.

The chart below shows the rolling 5-year performance range of the simulated trials for the 50% Accurate Investor.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

In 59% of the rolling periods, the buy-and-hold Plain Investor beat even the best 50% Accurate Investor. The Plain Investor was only worse than the worst performing coin flip strategy in 6% of rolling periods.

Beating buy-and-hold is hard to do reliably if you rely only on luck.

In this case, having a neutral hit rate with the negative skew of the sector equity returns leads to negative information coefficients. Taking more bets over time and across sectors did not help offset this distributional disadvantage.

So, let’s improve the accuracy slightly to see if the rolling results improve. Even with negative skew (-0.42 median value for the 30 sectors), an improvement in the accuracy to 60% is enough to bring the theoretical information coefficient back into the positive realm.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

The worst of these more skilled investors is now beating the Plain Investor in 41% of the rolling periods, and the best is losing to the buy-and-hold investor in 13% of the periods.

Going the other way, to a 40% accurate investor, we find that the best one was beaten by the Plain investor 93% of the time, and the worst one never beats the buy-and-hold investor.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

If we only require a modest increase in our accuracy to beat buy-and-hold strategies over shorter time horizons, why isn’t diligently focusing on increasing our accuracy an easy approach to success?

In order to increase our accuracy, we must first find a reliable way to do so: a task easier said than done due to the inherent nature of probability. Something having a 60% probability of being right does not preclude it from being wrong for a long time. The Law of Large Numbers can require larger numbers than our portfolios can stand.

Thus, even if we have found a way that will reliably lead to a 60% accuracy, we may not be able to establish confidence in that accuracy rate. This uncertainty in the accuracy can be unnerving. And it can cut both ways.

A strategy with a hit rate of less than 50% can masquerade as a more accurate strategy simply for lack of sufficient data to sniff out the true probability.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

You may think you have an edge when you do not. And if you do not have an edge, repeatedly applying it will lead to worse and worse outcomes.2

Accuracy Schmaccuracy

Our preference is to rely on systematic bets, which generally fall under the umbrella of factor investing. Even slight improvements to the accuracy can lead to better results when applied over a sufficient breadth of investments. Some of these factors also alter the distribution of returns (i.e. the skew) so that accuracy improvements have a larger impact.

Consider two popular measures of trend, used as the signals to determine the allocations in our 30 sector US equity strategy from the previous sections:

  • 12-1 Momentum: We calculate the return over an 11-month period, starting one month ago to account for mean reversionary effects. If this number is positive, we hold the sector; if it is negative, we invest that capital at the risk-free rate.
  • 10-month Simple Moving Average (SMA): We average the prices over the prior 10 months and compare that value to the current price. If the current price is greater than or equal to the average, we hold the sector; if it is less than, we invest that capital at the risk-free rate.

These strategies have volatilities in line with the Perfect and Anti-Perfect Investors and returns similar to the Plain Investor.

Using our measure of accuracy as correctly calling the direction of the sector returns over the subsequent month, it might come as a surprise that the accuracies for the 12-1 Momentum and 10-month SMA signals are only 42% and 41%, respectively.

Even with this low accuracy, the following chart shows that over the entire time period, the returns of these strategies more closely resemble those of the 55% Accurate Investor and have even looked like those of the 70% Accurate Investor over some time periods. What gives? 

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not a guarantee of future results.  All returns are hypothetical and backtested. Returns are gross of all fees. 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.

This is an example of how addressing the negative skew in the underlying asset returns can offset a sacrifice in accuracy. These trend following strategies may have overall accuracy of less than 50%, but they have been historically right when it counts.

Consistently removing large negative returns – at the expense of giving up some large positive returns – is enough to generate a return profile that looks much like a strategy that picks sectors with above average accuracy.

Whether investors can stick with a strategy that exhibits below 50% accuracy, however, is another question entirely.

Conclusion

While most investors expect the proof to be in the eating of the pudding, in this commentary we demonstrate how luck can have a meaningful impact in the determination of whether skill exists. While skill should eventually differentiate itself from luck, the horizon over which it will do so may be far, far longer than most investors suspect.

To explore this idea, we construct portfolios comprised of all thirty industry groups. We then simulate the results of investors with known accuracy rates, comparing their outcomes to 100% Accuracy, 100% Inaccurate, and Buy-and-Hold benchmarks.

Perhaps somewhat counter-intuitively, we find that an investor exhibiting 50% accuracy would have fairly reliably underperformed a Buy-and-Hold Investor. This seems somewhat counter-intuitive until we acknowledge that equity returns have historically exhibit negative skew, with the left tail of their return distribution (“losses”) being longer and fatter than the right (“gains”). Combining a neutral hit rate with negative skew creates negative information coefficients.

To offset this negative skew, we require increased accuracy. Unfortunately, even in the case where an investor exhibits 60% accuracy, there are a significant number of 5-year periods where it might masquerade as a strategy with a much higher or lower hit-rate, inviting false conclusions.

This is all made somewhat more confusing when we consider that a strategy can have an accuracy rate below 50% and still be successful. Trend following strategies are a perfect example of this phenomenon. The positive skew that has been historically exhibited by these strategies means that frequently inaccurate trades of small magnitude are offset by infrequent, by very large accurate trades.

Yet if we measure success by short-term accuracy rates, we will almost certainly dismiss this type of strategy as one with no skill.

When taken together, this evidence suggests that not only might it be difficult for investors to meaningfully determine the difference between skill and luck over seemingly meaningful time horizons (e.g. 5 years), but also that short-term perceptions of accuracy can be woefully misleading for long-term success. Highly accurate strategies can still lead to catastrophe if there is significant negative skew lurking in the shadows (e.g. an ETF like XIV), while inaccurate strategies can be successful with enough positive skew (e.g. trend following).

Tightening the Uncertain Payout of Trend-Following

By

On January 28, 2019

In Craftsmanship, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Long/flat trend-following strategies have historically delivered payout profiles similar to those of call options, with positive payouts for larger positive underlying asset returns and slightly negative payouts for near-zero or negative underlying returns.
  • However, this functional relationship contains a fair amount of uncertainty for any given trend-following model and lookback period.
  • In portfolio construction, we tend to favor assets that have a combination of high expected returns or diversifying return profiles.
  • Since broad investor behavior provides a basis for systematic trend-following models to have positive expected returns, taking a multi-model approach to trend-following can be used to reduce the variance around the expected payout profile.

Introduction

Over the past few months, we have written much about model diversification as a tactic for managing specification risk, even with specific case studies. When we consider the three axes of diversification, model diversification pertains to the “how” axis, which focuses on strategies that have the same overarching objective but go about achieving it in different ways.

Long/flat trend-following, especially with equity investments, aims to protect capital on the downside while maintaining participation in positive markets. This leads to a payout profile that looks similar to that of a call option.1

However, while a call option offers a defined payout based on the price of an underlying asset and a specific maturity date, a trend-following strategy does not provide such a guarantee. There is a degree of uncertainty.

The good news is that uncertainty can potentially be diversified given the right combinations of assets or strategies.

In this commentary, we will dive into a number of trend-following strategies to see what has historically led to this benefit and the extent that diversification would reduce the uncertainty around the expected payoff.

Diversification in Trend-Following

The justification for a multi-model approach boils down to a simple diversification argument.

Say you would like to include trend-following in a portfolio as a way to manage risk (e.g. sequence risk for a retiree). There is academic and empirical evidence that trend-following works over a variety of time horizons, generally ranging from 3 to 12 months. And there are many ways to measure trends, such as moving average crossovers, trailing returns, deviations from moving averages, risk adjusted returns, etc.

The basis for deciding ex-ante which variant will be the best over our own investment horizon is tenuous at best. Backtests can show one iteration outperforming over a given time horizon, but most of the differences between strategies are either noise from a statistical point of view or realized over a longer time period than any investor has the lifespan (or mettle) to endure.

However, we expect each one to generate positive returns over a sufficiently long time horizon. Whether this is one year, three years, five years, 10 years, 50 years… we don’t know. What we do know is that out of the multitude the variations of trend-following, we are very likely to pick one that is not the best or even in the top segment of the pack in the short-term.

From a volatility standpoint, when the strategies are fully invested, they will have volatility equal to the underlying asset. Determining exactly when the diversification benefits will come in to play – that is, when some strategies are invested and others are not – is a fool’s errand.

Modern portfolio theory has done a disservice in making correlation seem like an inherent trait of an investment. It is not.

Looking at multiple trend-following strategies that can coincide precisely for stretches of time before behaving completely differently from each other, makes many portfolio construction techniques useless.  We do not expect correlation benefits to always be present.  These are nonlinear strategies, and fitting them into a linear world does not make sense.

If you have pinned up ReSolve Asset Management’s flow chart of portfolio choice above your desk (from Portfolio Optimization: A General Framework for Portfolio Choice), then the decision on this is easy.

Source: ReSolve Asset Management.  Reprinted with permission

From this simple framework, we can break the different performance regimes down as follows:

The Math Behind the Diversification

The expected value of a trend-following strategy can be thought of as a function of the underlying security return:

Where the subscript i is used to indicate that the function is dependent on the specific trend-following strategy.

If we combine multiple trend-following strategies into a portfolio, then the expectation is the average of these functions (assuming an equal weight portfolio per the ReSolve chart above):

What’s left to determine is the functional form of f.

Continuing in the vein of the call option payoff profile, we can use the Black-Scholes equation as the functional form (with the risk-free rate set to 0). This leaves three parameters with which to fit the formula to the data: the volatility (with the time to expiration term lumped in, i.e. sigma * sqrt(T-t)), the strike, and the initial cost of the option.

where d1 and d2 are defined in the standard fashion and N is the cumulative normal distribution function.

rK is the strike price in the option formula expressed as a percent relative to the current value of the underlying security.

In the following example, we will attempt to provide some meaning to the fitted parameters. However, keep in mind that any mapping is not necessarily one-to-one with the option parameters. The functional form may apply, but the parameters are not ones that were set in stone ex-ante.2

An Example: Trend-Following on the S&P 500

As an example, we will consider a trend-following model on the S&P 500 using monthly time-series momentum with lookback windows ranging from 4 to 16 months. The risk-free rate was used when the trends were negative.

The graph below shows an example of the option price fit to the data using a least-squares regression for the 15-month time series momentum strategy using rolling 3-year returns from 1927 to 2018.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The volatility parameter was 9.5%, the strike was 2.3%, and the cost was 1.7%.

What do these parameters mean?

As we said before this can be a bit tricky. Painting in broad strokes:

  • The volatility parameter describes how “elbowed” payoff profile is. Small values are akin to an option close to expiry where the payoff profile changes abruptly around the strike price. Larger values yield a more gentle change in slope.
  • The strike represents the point at which the payoff profile changes from participation to protection using trend-following lingo. In the example where the strike is 2.3%, this means that the strategy would be expected to start protecting capital when the S&P 500 return is less than 2.3%. There is some cost associated with this value being high.
  • The cost is the vertical shift of the payoff profile, but it is not good to think of it as the insurance premium of the trend-following strategy. It is only one piece. To see why this is the case, consider that the fitted volatility may be large and that the option price curve may be significantly above the final payout curve (i.e. if the time-scaled volatility went to zero).

So what is the actual “cost” of the strategy?

With trend-following, since whipsaw is generally the largest potential detractor, we will look at the expected return on the strategy when the S&P 500 is flat, that is, an absence of an average trend. It is possible for the cost to be negative, indicating a positive expected trend-following return when the market was flat.

Looking at the actual fit of the data from a statistical perspective, the largest deviations from the expected value (the residuals from the regression) are seen during large positive returns for the S&P 500, mainly coming out of the Great Depression. This characteristic of individual trend-following models is generally attributable to the delay in getting back into the market after a prolonged, severe drawdown due to the time it takes for a new positive trend to be established.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Part of the seemingly large number of outliers is simply due to the fact that these returns exhibit autocorrelation since the periods are rolling, which means that the data points have some overlap. If we filtered the data down into non-overlapping periods, some of these outliers would be removed.

The outliers that remain are a fact of trend-following strategies. While this fact of trend-following cannot be totally removed, some of the outliers may be managed using multiple lookback periods.

The following chart illustrates the expected values for the trend-following strategies over all the lookback periods.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The shorter-term lookback windows have the expected value curves that are less horizontal on the left side of the chart (higher volatility parameter).

As we said before the cost of the trend-following strategy can be represented by the strategy’s expected return when the S&P 500 is flat. This can be thought of as the premium for the insurance policy of the trend-following strategies.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions.  Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

The blend does not have the lowest cost, but this cost is only one part of the picture. The parameters for the expected value functions do nothing to capture the distribution of the data around – either above or below – these curves.

The diversification benefits are best seen in the distribution of the rolling returns around the expected value functions.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Now with a more comprehensive picture of the potential outcomes, a cost difference of even 3% is less than one standard deviation, making the blended strategy much more robust to whipsaw for the potential range of S&P 500 returns.

As a side note, the cost of the short window (4 and 5 month) strategies is relatively high. However, since there are many rolling periods when these models are the best performing of the group, there can still be a benefit to including them. With them in the blend, we still see a reduction in the dispersion around the expected value function.

Expanding the Multitude of Models

To take the example even further down the multi-model path, we can look at the same analysis for varying lookback windows for a price-minus-moving-average model and an exponentially weighted moving average model.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

And finally, we can combine all three trend-following measurement style blends into a final composite blend.

Source: Global Financial Data and Kenneth French Data Library. Calculation by Newfound. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.

As with nearly every study on diversification, the overall blend is not the best by all metrics. In this case, its cost is higher than the EWMA blended model and its dispersion is higher than the TS blended model. But it exhibits the type of middle-of-the-road characteristics that lead to results that are robust to an uncertain future.

Conclusion

Long/flat trend-following strategies have payoff profiles similar to call options, with larger upsides and limited downsides. Unlike call options (and all derivative securities) that pay a deterministic amount based on the underlying securities prices, the payoff of a trend-following strategy is uncertain,

Using historical data, we can calculate the expected payoff profile and the dispersion around it. We find that by blending a variety of trend-following models, both in how they measure trend and the length of the lookback window, we can often reduce the implied cost of the call option and the dispersion of outcomes.

A backtest of an individual trend-following model can look the best over a given time period, but there are many factors that play into whether that performance will be valid going forward. The assets have to behave similarly, potentially both on an absolute and relative basis, and an investor has to hold the investment for a long enough time to weather short-term underperformance.

A multi-model approach can address both of these.

It will reduce the model specification risk that is present ex-ante. It will not pick the best model, but then again, it will not pick the worst.

From an investor perspective, this diversification reduces the spread of outcomes which can lead to an easier product to hold as a long-term investment. Diversification among the models may not always be present (i.e. when style risk dominates and all trend-following strategies do poorly), but when it is, it reduces the chance of taking on uncompensated risks.

Taking on compensated risks is a necessary part of investing, and in the case of trend-following, the style risk is something we desire. Removing as many uncompensated risks as possible leads to more pure forms of this style risk and strategies that are robust to unfavorable specifications.

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.

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