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Taxes and Trend Equity

On April 1, 2019

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

By Nathan Faber

On March 18, 2019

This post is available as a PDF download here.

Summary

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

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

Source: Investment Company Institute (ICI).

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

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

Source: Kravitz. 2018 National Cash Balance Research Report.

What is a cash balance plan?

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

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

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

What’s the appeal?

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

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

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

Source: Kravitz. 2018 National Cash Balance Research Report.

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

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

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

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

Source: Kravitz.

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

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

The Return Guarantee

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

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

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

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

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

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

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

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

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

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

Investing a Cash Balance Plan

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

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

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

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

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

The failure rate for the portfolios are shown below.³

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

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

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

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

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

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

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

Using Trend Following in a Cash Balance Plan

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

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

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

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

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

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

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

So which risks should a cash balance plan bear?

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

No Pain, No Premium

By Corey Hoffstein

On February 4, 2019

Summary

In this commentary, we discuss what we mean by the phrase, “no pain, no premium.”
We re-frame the discussion of portfolio construction from one about returns to one about risk and argue that without risk, there should be no expectation of return.
With a risk-based framework, we argue that investors inherently act as insurance companies, earning a premium for bearing risk. This risk often manifests as significant negative skew and kurtosis in the distribution of asset returns.
We introduce the philosophical limits of diversification, arguing that we should not be able to eliminate risk from the portfolio without eliminating return as well.
Therefore, we should seek to eliminate uncompensated risks while diversifying across compensated ones.
We explore the three axes of diversification – what, how, and when – and demonstrate how thinking in a correlation-driven, payoff-driven, and opportunity-driven framework may help investors find better diversification.

1. Is it About Risk or Return?

For graduate school, I pursued my Masters of Science in Computational Finance at Carnegie Mellon University. One of the first degrees of its kind in the late 1990s, this financial engineering program is a cross-disciplinary collaboration between the finance, mathematics, statistics, and computer-science departments.

In practice, it was an intensive year-and-a-half study on the theoretical and practical considerations of pricing financial derivatives.

I do not recall quite when it struck me, but at some point I recognized a broader pattern at play in every assignment. The instruments we were pricing were always about the transference of risk in some capacity. Our goal was to identify that risk, figure out how to isolate and extract it, package it into the appropriate product type, and then price it for sale.

Risk was driving the entire equation. Pricing was all about understanding distribution of the potential payoffs and trying to identify “fair compensation” for the variety of risks and assumptions we were making.

For every buyer, there is a seller and vice versa and, at the end of the day, sellers who did not want risk and would have to compensate buyers to bear it.

1.1 Stocks for the Long Run

The idea that reward is compensation for risk is certainly not a new one. It is, more or less, the entire foundation of modern finance.

But sometimes, it seems, we forget it.

We are often presented with a return-based lens through which to evaluate the world of finance. Commonly reprinted are graphs like the one below, demonstrating century-long returns for stocks, bonds, and cash and accompanied by broad, sweeping generalizations like, “stocks for the long run.”

The truth is, if you plot anything on a log-axis over a long enough time horizon and draw it with a thick enough crayon, the line will eventually look pretty straight.

But if we zoom in to a horizon far more relevant to the lifecycle of most individual investors, we see a very different picture.

What we see is the realization of risk. We have to remember that the excess returns we expect to earn over the long run are compensation for bearing risk. And that risk needs to manifest, from time-to-time. Otherwise, if the probability of the risk being realized goes down, then so should the excess premium we expect to earn.

From a quantitative perspective, risk is often measured as volatility. In our opinion, that’s not quite right. We believe, given a long enough return history with enough realized risk events, risk can be better measured in a return’s distribution symmetry and fat-tailed-ness (i.e. “skew” and “kurtosis” respectively).

Below we plot the annualized excess real return distribution for U.S. equities over the last 100 years. We can see that the distribution is “leaning” to the right, indicating that large losses are more frequent than large gains.

We would argue that when we buy equities, what we are really buying is a risk. In particular, we are buying an uncertain stream of cash flows.

Now, this might seem a little weird. Why would we ever pay someone to bear their risk?

The answer is because, in many ways, we can think of equities as a swap of cashflows: one up-front bullet payment for the rights to an uncertain stream of future cash flows generated by the underlying business.

In theory, the price we pay today should be less than the net present value of all those future cash flows, with the difference representing the premium we expect to earn over time.

Uncertainty is the wedge between the values. Without uncertainty, no rational seller would give up their future cash flows for less than they are worth (or, if we do have an irrational seller, we would expect buyers to compete over those cashflows to the point they are fairly valued).

Thus, the premium will be driven both by certainty about the future cash flows (growth rate and duration) as well as the market’s appetite for bearing risk.

The more certain we are of those future cash flows or the higher the market’s appetite to bear risk, the smaller the expected premium should be.

1.2 “Funding Secured”

To get a better sense of the play between certainty and premium in the market, we can explore an example where we effectively collapse price into a binary “yes or no” event.

On August 7th, 2018, Elon Musk sent out the following tweets:

At the time he sent the tweet, Tesla shares were trading around approximately $365. The stock had opened around $340 that day and had jumped on news reporting that the Saudi sovereign fund had built a $2b stake in Tesla and some speculation about a potential buy-out.

Now let’s assume, for a moment, that Elon’s tweet said, “Deal struck to take Tesla private at $420, effectively immediately” What should the price of Tesla’s stock jump to? $420, of course.

Now Elon’s tweet merely said he was considering it. He also did not specify a timeline. But let’s consider two cases:

The market believes a deal will be struck to take Tesla at $420 in the near future.
The market does not believe Tesla will be taken private.

In the former case, the right price is approximately $420. In the latter case, the appropriate price is whatever the shares were trading at before the announcement.¹

Thus, where price trades between the two points can be interpreted as to the market’s confidence in the deal being done.

Hence, I tweeted the following:

(Note that when I sent out the first tweet, I hadn’t realized trading had been halted in Tesla.)

Assuming the entire day’s move was attributed to the buyout news, a price change from $340 to $380 only represents a 50% move towards the buy-out price of $420. The market was basically saying, “we give this coin-flip odds.”

1.2 Well ‘Skews Me

While modern portfolio theory uses volatility as the measure of risk, the connection between excess realized premia and volatility is tenuous at best. It certainty falls apart in highly skewed, fat-tailed return distributions.

Rather, skewness appears to be a much better measure of risk for most financial assets. And when we look at equity markets around the globe, we see the same fact pattern emerge: return distributions with negative skew indicating that losses tend to be (much) bigger than gains.

2. You’re An Insurance Company

What this type of risk-based thinking all boils down to is that you – and your portfolio – are really acting as an insurance company of sorts.

When we purchase insurance, we are really transferring our associated risk to the insurance company. To incentivize them to bear the risk, we have to pay an annual premium.

Similarly, when we buy stocks, we are really trading a certain cashflow today (the price) for a stream of uncertain cash flows in the future. The discount between the price we pay and the net present value of future cash flows is the premium we expect to earn. And when we sell stocks, we are effectively paying that premium.

So in building our portfolios, we should think like an insurance company.

Like an insurance company, we want to diversify the premiums we earn. Not only do we want to diversify within a given type of insurance, but we probably also want to diversify the type of insurance we offer. And, in an ideal world, the type of insurance would be uncorrelated!

2.1 Diversifying with Bonds

Enter the most traditional portfolio diversifier: bonds. Typically considered to be a “safe” asset, if we look at them through the lens of real excess returns, we can see that bond returns also exhibit negative skew and fat tails.

This makes sense, as when we buy a bond we are still bearing all sorts of risks. Not only do we bear the risk of a default, but we also bear inflation risk and interest rate path-dependency risk.

With U.S. Treasuries, default risk is likely minimized (depending on your perspective), and the other two risks might be less correlated than the traditional risks (e.g. economic growth) we see with equities. So combining stocks and bonds should help us control skew, right?

Well, not quite. Below we plot the annualized excess real returns for a 60/40 portfolio.

We see that skew and kurtosis remain. What gives?

Well, one answer is that while a 60/40 portfolio might be close to balanced in the terms of notional dollar exposure to each asset, it is completely unbalanced from the perspective of residual volatility.

Below we plot the relative contribution to risk of stocks and bonds over time in a 60/40 portfolio.

Because the payout for bonds is far more certain than the payout for stocks, not only is the expected excess premium much lower, but volatility tends to be much lower as well. This means that the premium earned from holding bonds is not large enough to offset the losses realized in equities.

Savvy readers will recognize this as the driving thesis behind risk parity. To strike a balance, we need to allocate to stocks and bonds in such a manner that they provide equal contribution to portfolio risk.

Below, we plot the annual excess real return distribution for a stock/bond risk parity portfolio that is levered to a constant volatility target of 8%.

What do we see? Skew and fat tails remain. Perhaps the answer is simply that we need more diversification. While in practice this might mean buying different assets, in theory it means exposing ourselves to different types of risk sources that lead to uncertainty in the value of future cash flows. We enumerate a few below.

In traditional asset allocation, trying to isolate and add these different exposures is very difficult.

First, it is worth acknowledging that not every type of risk necessarily deserves to earn compensation. In theory, we should only be compensated for un-diversifiable risks.

Furthermore, many of these risks have time-varying correlations and magnitudes, and often collapse towards a single risk factor during crisis states of the world.

Yet we would argue that there is a deeper, philosophical limit we should consider.

3. The Philosophical Limits of Diversification

What we keep running up against is what we call the “philosophical limit of diversification.”

The simplest way to think about the limit is this: If we can diversify away all of our risk, we should not expect to earn any reward.

After all, if we found some magical combination of assets that eliminated downside risk in all future states of the world, we would have constructed an arbitrage. We could simply borrow at the risk-free rate, invest in the appropriate blend of assets, and reap our risk-free reward.

That is why years like 2018, when 90% of assets lose money, have to occur from time to time. Without the eventual realization of risk, there is no reason to expect return.

3.1 The Frustrating Law of Active Management

A corollary of this philosophical limit is what we like to call “The Frustrating Law of Active Management.”

We go further in depth into this idea in another commentary, but the basic idea follows: if an investment strategy is perceived both to have alpha and to be easy, investors will allocate to it and erode the associated premium.

How can a strategy be “hard”? Well, a manager might have a substantial informational or analytical edge. Or, the manager might have a structural moat, accessing trades others do not have the opportunity to pursue.

But for most well-known edges (e.g. most major style premia), “hard” is going to be behavioral. The strategy has to be hard enough to hold on to that it does not get arbitraged away. Which implies that,

For any disciplined investment approach to outperform over the long run, it must experience periods of underperformance in the short run.

This also implies that,

For any disciplined investment approach to underperform over the long run, it must experience periods of outperformance in the short run.

For active managers, the frustration is that not only does their investment approach have to under-perform from time-to-time, but bad strategies will have to out-perform. The latter may seem confusing until we consider that a purposefully bad strategy could simply be inverted to create a purposefully good one.²

And, as above, we cannot simply diversify our way out of the problem. After all, if there were a magic combination of active strategies that earned the same expected alpha but reduced the risk, everybody would pursue that combination.

4. Investment versus Investor Returns

So is the answer here to just, “suck it up?” Do we simply look at periods like 2000-2010 and say, “it’s the price we pay for the opportunity to earn long-run returns?”

We would argue both “yes” and “no.”

It all depends upon where an investor falls within their lifecycle. Young investors who are pursuing growth mandates may simply need to accept that skew and fat tails are the cost of earning the long-run premium. Too much diversification may lead to “failing slow.”

For investors in the later stages of their lifecycle, however, the math changes. Indeed, this is true for any individual or institution where withdrawals are concerned. When we have a withdrawal-driven mandate, it is the risk of “failing fast” that we need to concern ourselves with.

The problem is that investment-centric thinking often makes diversification seem foolish. To quote Brian Portnoy, “diversification means always having to say you’re sorry.”

Not only do we have to contend with the fact that the relative performance of the investments in our portfolio will vary wildly from one another year-to-year, but evidence suggests that so will the investor’s utility function.

Consider the graphic below, where the investor’s utility oscillates between relative (“I didn’t do as well as my peers!”) and absolute returns (“I lost money!”), making the diversified profile a consistent loser.

Source: BlackRock.

(3/14/2019 Update: It was pointed out to me that based upon the numbers in the table above, the total return reported the Diversified Portfolio is actually understated. Total return should be 202.4%, with $100K turning into $302,420.)

However, if we actually think about investor returns, rather than investment returns, the picture changes. Below we plot the growth of $1,000,000 since 2000 with a fixed $40,000 withdrawal. In this highly simplified example, we can begin to see the benefits of increased diversification.

Despite the philosophical limits of diversification, we clearly should not forgo it entirely. But what is the right framework to think about diversification and how it can be introduced into a portfolio?

5. The Three Axes of Diversification

At Newfound, we talk about three potential axes of diversification that investors can try to exploit.

We call these axes the what, the how, and the when axes, and they aim to capture what we invest in (“correlation driven”), how we make the decisions (“pay-off driven”), and when we make those decisions (“opportunity driven”).

Below, we explore each axis individually and how to might be able to contribute to a portfolio’s overall diversification profile.

5.1 What Axis (“Correlation Diversification”)

The “what” axis asks the question, “what are we investing in?” It captures the traditional notions of asset class and geographic diversification. As we have explored in this commentary, it also implicitly captures risk-based diversification.

We can also think of this axis as being responsible for “correlation-driven” diversification. As we will see, however, the empirical evidence of the effectiveness of this type of diversification is limited.

5.1.1 It’s Hard to Allocate Our Way Out of a Bear Market

Empirical evidence suggests that correlation-driven diversification is not tremendously effective at limited losses in crisis events. Consider the returns plotted below for a number of asset classes during 2008. We can see that by the end of the year, almost all had fallen between -20% to -50%.

As it turns out, most of the risk reduction benefits seen in a traditional asset allocation are not actually due to diversification benefits, but rather simply due to outright de-risking.

In their 2016 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn and Robinson demonstrate that most of the risk reduction seen in moving from and all-stock portfolio to a balanced portfolio is simply due to the fact that bonds are less volatile than stocks.

That is not to say that de-risking is without its own merits. Outright de-risking a portfolio is simple way to reduce total loss potential and is one of the driving forces behind the benefits of glide-path investing’s ability to control sequence risk.

Investors looking to maintain a return profile while reducing risk through the benefits of diversification, however, may be disappointed.

In When Diversification Fails, Page and Panariello demonstrate that asset correlations tend to be bi-modal in nature. Unfortunately, the dynamics exhibited are the exact opposite of what we would like to see: diversification opportunity is ample in positive market states, but correlations tend to crash towards one during equity crises.

This does not make traditional diversification outright worthless, however, for growth-oriented investors.

Consider the table below from a paper titled, The Risk of Premiums, in which the author summarizes his findings about the statistical significance of different realized equity risk premia around the globe over different time horizons.

The five countries with stars on the left-hand side of the table have historically exhibited statistically significant risk premia across rolling 1-, 5-, 10-, and 20-year periods. Those with stars on the right did not exhibit statistically significant risk premia across any of the rolling periods.

It is important to remember that risk premia are expected, but by no means guaranteed. It is entirely possible that markets mis-estimate the frequency or magnitude with which risks manifest and fail to demand an adequately compensating premium.

Things have worked out exceptionally well for U.S. investors, but the same cannot be said for investors around the globe.

With the exception of explicit de-risking, what diversification may not necessarily provide much support in managing the left-tails of systematic risk factors. Nevertheless, what diversification may be critical in helping reduce exposure to idiosyncratic risks associated with a specific geographic region or asset class.

5.2 The How Axis – Payoff Diversification

The how axis asks the question, “how are we making our investment decisions.”

How need not be complex. Low-cost, tax-efficient passive asset allocation is a legitimate how.

But this axis also captures the variety of other active investment styles that can create their own, and often independent, return streams.

One might go so far as to call them “synthetic assets,” but most popular literature simply refers to them as “styles.” Popular categories include: value, momentum, carry, defensive (quality / low-volatility), trend, and event-driven.

The how axis is able to take the same what and create what are potentially unique return streams. The return profile of a currency momentum portfolio may be inherently different than a commodity value portfolio, both of which may offer diversification from traditional, economic risk factors that drive currency and commodity beta.

If the what axis captures correlation driven diversification, we would argue that the how axis captures pay-off driven diversification.

5.2.1 Style Diversification

In When Diversification Fails, Page and Panariello also found that correlations for many styles are bi-modal, but some may offer significant diversification in equity crisis states.

2018, however, once again proved that there are philosophical limits to the benefits of diversification. For styles to work over the long run, not only do there have to be periods where they fail individually, but there have to be periods where they fail simultaneously.

If we want to keep earning reward, we have to bear some risk in some potential state of the world.

It is no surprise, then, that it appears that most major styles appear to offer compensation for their own negative skew. In their 2014 paper Risk Premia: Asymmetric Tail Risks and Excess Returns, Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud find that not only do most styles exhibit negative skew, but that there appears to be a positive relationship with skew and the style’s Sharpe ratio.

As with asset classes, return appears to be a compensation for bearing asymmetric risk.

The two exceptions in the graph are trend and equity value (Fama-French HML).

The authors of the paper note that the positive skew of equity value is somewhat problematic, as it implies it is an anomaly rather than a risk compensation. However, using monthly returns to recreate the above graph shifts the skew of equity value back to negative, implying perhaps that there is a somewhat regime-driven nature to value that needs to be further explored.

Trend, on the other hand, has long-been established to exhibit positive skew. Indeed, it may very well be a mathematical byproduct of the trading strategy itself rather than an anomaly.

5.2.2 Payoff Diversification

While the findings of Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud (2016) imply that style premia are not exceptions to the “no pain, no premium” rule, we should not be dissuaded from considering the potential benefits of their incorporation within a portfolio.

After all, not only might we potentially benefit from the fact that their negative states might be somewhat independent of economic risk factors (acknowledging, as always, the philosophical limits of diversification), but the trading strategies themselves create varying payoff profiles that differ from one another.

By combining different asset classes and payoff functions, we may be able to create a higher quality of portfolio return.

For example, when we overlay a naive trend strategy on top of U.S. equities, the result converges towards a distribution where we simply miss the best and worst years. However, because the worst years tend to be worse than the best years are good, it leads to a less skewed distribution.

In effect, we’ve fought negative skew with positive skew.

At Newfound, we often say that “risk cannot be destroyed, but only transformed.” We tend to think of risk as a blob that is spread across future states of the world. When we push down on that blob in one future state, in effect “reducing risk,” it simply displaces to another state.

Trend may have historically helped offset losses during crisis events, but it can create drawdowns during reversal markets. Similarly, style / alternative premia may be able to harvest returns when traditional economic factors are going sideways, but may suffer during coincidental drawdowns like 2018.

Source: PIMCO

That is why we repeat ad nauseam “diversify your diversifiers.”

5.2.3 Specification Risk

While the above discussion of how pertained to style risks, there is another form of risk worth briefly discussing: specification risk.

Specification risk acknowledges that two investors implementing two identical styles in theory may end up with very different results in practice. Style risk tells us that equity value managers struggled as a category in 2016; specification risk tells us how each manager did individually.

Whether we are compensated for bearing specification risk is up for debate and largely depends upon your personal view of a manager’s skill.

In the absence of a view of skill, what we find is that combining multiple managers tends to do little for a reduction in traditional portfolio volatility (except in highly heterogenous categories), but can tremendously help reduce portfolio skew as well as the dispersion in terminal wealth.

For example, below we generate a number of random 30-stock portfolios and plot their returns over the last decade.

We can see that while the results are highly correlated, the terminal wealth achieved varies dramatically.

If instead of just picking one manager we pick several – say 3 or 4 – we find that the potential dispersion in terminal wealth drops dramatically and our achieved outcome is far more certain.

You can read more on this topic in our past commentary Is Multi-Manager Diversification Worth It?

5.3 When Axis

We believe that the when axis may be one of the most important, yet overlooked opportunities for diversification in portfolio construction. So much so, we wrote a paper about it titled Rebalance Timing Luck: The Difference Between Hired and Fired.

The basic intuition behind this axis is that our realized portfolio results will be driven by the opportunities presented to us at the time we rebalance.

In many ways, diversification along the when axis can be thought of as opportunity-diversification.

For example, Blitz, van der Grient, and van Vliet demonstrated in their 2010 paper Fundamental Indexation: Rebalancing Assumptions and Performance that the quarter in which an annually-rebalanced fundamental index is reconstituted can lead to significant performance disparity. For example, the choice to rebalance the portfolio in March versus September would have lead to a 1,000 basis point performance difference in 2009.

This difference was largely driven by the opportunities perceived by the systematic strategy at the time of rebalancing.

This risk is not limited to active portfolios. In the graph below we plot rolling 1-year return differences between two 60/40 portfolios, one of which is rebalanced at the end of each February and one that is rebalanced at the end of each August.

We can see that the rebalance in early 2009 lead to a 700 basis point gap in performance by spring 2010.

While we believe this has important implications for how research is conducted, benchmarks are constructed, and managers build portfolios, the more practical takeaway for investors is that they might benefit from choosing managers who rebalance on different schedules.

6. Summary

Investors often focus on returns, but it is important to keep in mind why we expect to earn those returns in the first place. We believe a risk-based mindset can help remind us that we expect to earn excess returns because we are willing to bear risk.

In many ways, we can think of ourselves and our portfolios as insurance companies: we collect premiums for bearing risk. Yet while we can we can seek to diversify the risks we insure, there are few truly independent risk factor and the premiums aren’t often large enough to offset large losses.

We also believe that there exist theoretical limits to diversification. If we eliminate risk through diversification, we also eliminate reward. In other words: no pain, no premium.

This does not inherently mean, however, we should just “suck it up.” The implications of risk-based thinking is dependent upon where we are in our investment lifecycle.

The primary risk of investors with growth mandates (e.g. investors early in their lifecycle) is “failing slow,” which is the failure to growth their capital sufficiently to outpace inflation or meet future liabilities. In this case, our aim should be to diversify as much as possible without overly de-risking the portfolio. With a risk-based mindset, it becomes clear why approaches like risk parity, when targeting an adequate volatility, may be philosophically superior to traditional asset allocation.

For investors taking withdrawals (e.g. those late in their lifecycle or endowments/pensions), the primary risk is “failing fast” from large drawdowns. Diversification is likely insufficient on its own and de-risking may be prudent. Diversifying payoff types and introducing positive skew styles – e.g. trend – may also benefit the investment plan by creating a more consistent return stream.

Yet we should acknowledge that even return opportunities available along the how axis appear to be driven largely by skew, re-emphasizing that without potential pain, there should be no premium.

Fragility Case Study: Dual Momentum GEM

By Corey Hoffstein

On January 14, 2019

In Craftsmanship, Momentum, Popular, Portfolio Construction, Risk Management, Trend

This post is available as a PDF download here.

Summary

Recent market volatility has caused many tactical models to make sudden and significant changes in their allocation profiles.
Periods such as Q4 2018 highlight model specification risk: the sensitivity of a strategy’s performance to specific implementation decisions.
We explore this idea with a case study, using the popular Dual Momentum GEM strategy and a variety of lookback horizons for portfolio formation.
We demonstrate that the year-to-year performance difference can span hundreds, if not thousands, of basis points between the implementations.
By simply diversifying across multiple implementations, we can dramatically reduce model specification risk and even potentially see improvements in realized metrics such as Sharpe ratio and maximum drawdown.

Introduction

Among do-it-yourself tactical investors, Gary Antonacci’s Dual Momentum is the strategy we tend to see implemented the most. The Dual Momentum approach is simple: by combining both relative momentum and absolute momentum (i.e. trend following), Dual Momentum seeks to rotate into areas of relative strength while preserving the flexibility to shift entirely to safety assets (e.g. short-term U.S. Treasury bills) during periods of pervasive, negative trends.

In our experience, the precise implementation of Dual Momentum tends to vary (with various bells-and-whistles applied) from practitioner to practitioner. The most popular benchmark model, however, is the Global Equities Momentum (“GEM”), with some variation of Dual Momentum Sector Rotation (“DMSR”) a close second.

Recently, we’ve spoken to several members in our extended community who have bemoaned the fact that Dual Momentum kept them mostly aggressively positioned in Q4 2018 and signaled a defensive shift at the beginning of January 2019, at which point the S&P 500 was already in a -14% drawdown (having peaked at over -19% on December 24^th). Several DIYers even decided to override their signal in some capacity, either ignoring it entirely, waiting a few days for “confirmation,” or implementing some sort of “half-and-half” rule where they are taking a partially defensive stance.

Ignoring the fact that a decision to override a systematic model somewhat defeats the whole point of being systematic in the first place, this sort of behavior highlights another very important truth: there is a significant gap of risk that exists between the long-term supporting evidence of an investment style (e.g. momentum and trend) and the precise strategy we attempt to implement with (e.g. Dual Momentum GEM).

At Newfound, we call that gap model specification risk. There is significant evidence supporting both momentum and trend as quantitative styles, but the precise means by which we measure these concepts can lead to dramatically different portfolios and outcomes. When a portfolio’s returns are highly sensitive to its specification – i.e. slight variation in returns or model parameters lead to dramatically different return profiles – we label the strategy as fragile.

In this brief commentary, we will use the Global Equities Momentum (“GEM”) strategy as a case study in fragility.

Global Equities Momentum (“GEM”)

To implement the GEM strategy, an investor merely needs to follow the decision tree below at the end of each month.

From a practitioner stand-point, there are several attractive features about this model. First, it is based upon the long-run evidence of both trend-following and momentum. Second, it is very easy to model and generate signals for. Finally, it is fairly light-weight from an implementation perspective: only twelve potential rebalances a year (and often much less), with the portfolio only holding one ETF at a time.

Despite the evidence that “simple beats complex,” the simplicity of GEM belies its inherent fragility. Below we plot the equity curves for GEM implementations that employ different lookback horizons for measuring trend and momentum, ranging from 6- to 12-months.

Source: CSI Analytics. Calculations by Newfound Research. Returns are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees except for underlying ETF expense ratios. 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.

We can see a significant dispersion in potential terminal wealth. That dispersion, however, is not necessarily consistent with the notion that one formation period is inherently better than another. While we would argue, ex-ante, that there should be little performance difference between a 9-month and 10-month lookback – they both, after all, capture the notion of “intermediate-term trends” – the former returned just 43.1% over the period while the latter returned 146.1%.

These total return figures further hide the year-to-year disparity that exists. The 9-month model, for example, was not a consistent loser. Below we plot these results, highlighting both the best (blue) and worst (orange) performing specifications. We see that the yearly spread between these strategies can be hundreds-to-thousands of basis points; consider that in 2010, the strategy formed using a 10-month lookback returned 12.2% while the strategy formed using a 9-month lookback returned -9.31%.

Same thesis. Same strategy. Slightly different specification. Dramatically different outcomes. That single year is likely the difference between hired and fired for most advisors and asset managers.

☞ Explore a diversified approach with the Newfound/ReSolve Robust Equity Momentum Index.

For those bemoaning their 2018 return, note that the 10-month specification would have netted a positive result! That specification turned defensive at the end of October.

Now, some may cry “foul” here. The evidence for trend and momentum is, after all, centuries in length and the efficacy of all these horizons is supported. Surely the noise we see over this ten-year period would average out over the long run, right?

The unfortunate reality is that these performance differences are not expected to mean-revert. The gambler’s fallacy would have us believe that bad luck in one year should be offset by good luck in another and vice versa. Unfortunately, this is not the case. While we would expect, at any given point in time, that each strategy has equal likelihood of experiencing good or bad luck going forward, that luck is expected to occur completely independently from what has happened in the past.

The implication is that performance differences due to model specification are not expected to mean-revert and are therefore expected to be random, but very permanent, return artifacts.¹

The larger problem at hand is that none of us have a hundred years to invest. In reality, most investors have a few decades. And we act with the temperament of having just a few years. Therefore, bad luck can have very permanent and very scarring effects not only upon our psyche, but upon our realized wealth.

But consider what happens if we try to neutralize the role of model specification risk and luck by diversifying across the seven different models equally (rebalanced annually). We see that returns closer in line with the median result, a boost to realized Sharpe ratio, and a reduction in the maximum realized drawdown.

These are impressive results given that all we employed was naïve diversification.

Conclusion

The odd thing about strategy diversification is that it guarantees we will be wrong. Each and every year, we will, by definition, allocate at least part of our capital to the worst performing strategy. The potential edge, however, is in being vaguely wrong rather than precisely wrong. The former is annoying. The latter can be catastrophic.

In this commentary we use the popular Dual Momentum GEM strategy as a case study to demonstrate how model specification choices can lead to performance differences that span hundreds, if not thousands, of basis points a year. Unfortunately, we should not expect these performance differences to mean revert. The realizations of good and bad luck are permanent, and potentially very significant, artifacts within our track records.

By simply diversifying across the different models, however, we can dramatically reduce specification risk and thereby reduce strategy fragility.

To be clear, no amount of diversification will protect you from the risk of the style. As we like to say, “risk cannot be destroyed, only transformed.” In that vein, trend following strategies will always incur some sort of whipsaw risk. The question is whether it is whipsaw related to the style as a whole or to the specific implementation.

For example, in the graphs above we can see that Dual Momentum GEM implemented with a 10-month formation period experienced whipsaw in 2011 when few of the other implementations did. This is more specification whipsaw than style whipsaw. On the other hand, we can see that almost all the specifications exhibited whipsaw in late 2015 and early 2016, an indication of style whipsaw, not specification whipsaw.

Specification risk we can attempt to control for; style risk is just something we have to bear.

At Newfound, evidence such as this informs our own trend-following mandates. We seek to diversify ourselves across the axes of what (“what are we investing in?”), how (“how are we making the decisions?”), and when (“when are we making those decisions?”) in an effort to reduce specification risk and provide the greatest style consistency possible.

Is Multi-Manager Diversification Worth It?

By Corey Hoffstein

On January 7, 2019

This post is available as a PDF download here.

Summary

Portfolio risk is traditionally quantified by volatility. The benefits of diversification are measured in how portfolio volatility is changed with the addition or subtraction of different investments.
Another measure of portfolio risk is the dispersion in terminal wealth: a measure that attempts to capture the potential difference in realized returns. For example, two equity managers that each hold 30 stock portfolios may exhibit similar volatility levels but will likely have very different realized results.
In this commentary we explore existing literature covering the potential diversification benefits that can arise from combining multiple managers together.
Empirical evidence suggests that in heterogeneous categories (e.g. many hedge fund styles), combining managers can reduce portfolio volatility. Yet even in homogenous categories (e.g. equity style boxes), combining managers can have a pronounced effect on reducing the dispersion in terminal wealth.
Finally, we address the question as to whether manager diversification leads to dilution, arguing that a combination of managers will reduce idiosyncratic process risks but maintain overall style exposure.

Introduction

In their 2014 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn, and Robinson draw a distinction between the risk reduction effects that occur due to de-risking and those that occur due to diversification benefits.

To illustrate the distinction, the authors compare the volatility of an all equity portfolio versus a balanced stock/bond mix. In the 1984-2014 sample period, they find that the all equity portfolio has an annualized volatility of 15.25% while the balanced portfolio has an annualized volatility of just 9.56%.

Over 75% of this reduction in volatility, however, is due simply to the fact that bonds were much less volatile than stocks over the period. In fact, of the 568-basis-point reduction, only 124 basis points was due to actual diversification benefits.

Why does this matter?

Because de-risking carries none of the benefits of diversification. If there is a commensurate trade-off between expected return and risk, then all we have done is reduced the expected return of our portfolio.¹

It is only by combining assets of like volatility – and, it is assumed, like expected return – that should allow us to enjoy the free lunch of diversification.

Unfortunately, unless you are willing to apply leverage (e.g. risky parity), the reality of finding such free lunch opportunities across assets is limited. The classic example of inter-asset diversification, though, is taught in Finance 101: as we add more stocks to a portfolio, we drive the contribution of idiosyncratic volatility towards zero.

Yet volatility is only one way to measure risk. If we build a portfolio of 30 stocks and you build a portfolio of 30 stocks, the portfolios may have nearly identical levels of volatility, but we almost assuredly will end up with different realized results. This difference between the expected and the realized is captured by a measure known as terminal wealth dispersion, first introduced by Robert Radcliffe in his book Investment: Concepts, Analysis, Strategy.

This form of risk naturally arises when we select between investment managers. Two managers may both select securities from the same universe using the same investment thesis, but the realized results of their portfolios can be starkly different. In rare cases, the specific choice of one manager over another can even lead to catastrophic results.

The selection of a manager reflects not only an allocation to an asset class, but also reflects an allocation to a process. In this commentary, we ask: how much diversification benefit exists in process diversification?

The Theory Behind Manager Diversification

In Factors from Scratch, the research team at O’Shaughnessy Asset Management (OSAM), in partnership with anonymous blogger Jesse Livermore, digs into the driving elements behind value and momentum equity strategies.

They find that value stocks do tend to exhibit negative EPS growth, but this decay in fundamentals is offset by multiple expansion. In other words, markets do appear to correctly identify companies with contracting fundamentals, but they also exaggerate and over-extrapolate that weakness. The historical edge for the strategy has been that the re-rating – measured via multiple expansion – tends to overcompensate for the contraction in fundamentals.

For momentum, OSAM finds a somewhat opposite effect. The strategy correctly identifies companies with strengthening fundamentals, but during the holding period a valuation contraction occurs as the market recognizes that its outlook might have been too optimistic. Historically, however, the growth outweighed the contraction to create a net positive effect.

These are the true, underlying economic and behavioral effects that managers are trying to capture when they implement value and momentum strategies.

These are not, however, effects we can observe directly in the market; they are effects that we have to forecast. To do so, we have to utilize semi-noisy signals that we believe are correlated. Therefore, every manager’s strategy will be somewhat inefficient at capturing these effects.

For example, there are a number of quantitative measures we may apply in our attempt to identify value opportunities; e.g. price-to-book, price-to-earnings, and EBITDA-to-enterprise-value to name a few. Two different noisy signals might end up with different performance just due to randomness.

This noise between signals is further compounded when we consider all the other decisions that must be made in the portfolio construction process. Two managers may use the same signals and still end up with very different portfolios based upon how the signals are translated into allocations.

Consider this: Morningstar currently² lists 1,217 large-cap value funds in its mutual fund universe and trailing 1-year returns ranged from 1.91% to -22.90%. This is not just a case of extreme outliers, either: the spread between the 10^thand 90^thpercentile returning funds was 871 basis points.

It bears repeating that these are funds that, in theory, are all trying to achieve the same goal: large-cap value exposure.

Yet this result is not wholly surprising to us. In Separating Ingredients and Recipe in Factor Investing we demonstrated that the performance dispersion between different momentum strategy definitions (e.g. momentum measure, look-back length, rebalance frequency, weighting scheme, et cetera) was larger than the performance dispersion between the traditional Fama-French factors themselves in 90% of rolling 1-year periods. As it turns out, intra-factor differences can cause greater dispersion than inter-factor differences.

Without an ex-ante view as to the superiority of one signal, one process, or one fund versus another, it seems prudent for a portfolio to have diversified exposure to a broad range of signals that seem plausibly related to the underlying phenomenon.

Literature Review

While foundational literature on modern portfolio diversification extends back to the 1950s, little has been written in the field of manager diversification. While it is a well-established teaching that a portfolio of 25-40 stocks is typically sufficient to reduce idiosyncratic risk, there is no matching rule for how many managers to combine together.

One of the earliest articles on the topic was written by Edward O’Neal in 1997, titled How Many Mutual Funds Constitute a Diversified Mutual Fund Portfolio?

Published in the Financial Analysts Journal, this article explores risk across two different dimensions: the volatility of returns over time and the dispersion in terminal period wealth. Again, the idea behind the latter measure is that two investors with identical horizons and different investments will achieve different terminal wealth levels, even if those investments have the same volatility.

Exploring equity mutual fund returns from 1986 to 1997, the study adopts a simulation-based approach to constructing portfolios and tracking returns. Multi-manager portfolios of varying sizes are randomly constructed and compared against other multi-manager portfolios of the same size.

O’Neal finds that while combining managers has little-to-no effect on volatility (manager returns were too homogenous), it had a significant effect upon the dispersion of terminal wealth. To quote the article,

Holding more than a single mutual fund in a portfolio appears to have substantial diversification benefits. The traditional measure of volatility, the time-series standard deviation, is not greatly influenced by holding multiple funds. Measures of the dispersion in terminal-wealth levels, however, which are arguably more important to long-term investors than time-series risk measures, can be reduced significantly. The greatest portion of the reduction occurs with the addition of small numbers of funds. This reduction in terminal-period wealth dispersion is evident for all holding periods studied. Two out of three downside risk measures are also substantially reduced by including multiple funds in a portfolio. These findings are especially important for investors who use mutual funds to fund fixed-horizon investment goals, such as retirement and college savings.

Allocating to three managers instead of just one could reduce the dispersion in terminal wealth by nearly 50%, an effect found to be quite consistent across the different time horizons measured.

In 1999, O’Neal teamed up with L. Franklin Fant to publish Do You Need More than One Manager for a Given Equity Style? Adopting a similar simulation-based approach, Fant and O’Neal explored multi-manager equity portfolios in the context of the style-box framework.

And, as before, they find that taking a multi-manager approach has little effect upon portfolio volatility.

It does, however, again prove to have a significant effect on the deviation in terminal wealth.

To quote the paper,

Regardless of the style category considered, the variability in terminal wealth levels is significantly reduced by using more managers. The first few additional managers make the most difference, as terminal wealth standard deviation declines at a decreasing rate with the number of managers. Concentrating on the variability of periodic portfolio returns fails to document the advantage of using multiple managers within style categories.
Second, some categories benefit more from additional managers than others. Plan sponsors would do well to allocate relatively more managers to the styles that display the greatest diversification benefits. Growth styles and small-cap styles appear to offer the greatest potential for diversification.

In 2002, François-Serge Lhabitant and Michelle Learned pursued a similar vein of research in the realm of hedge funds in their article Hedge Fund Diversification: How Much is Enough? They employ the same simulation-based approach but evaluate diversification effects within the different hedge fund styles.

They find that while diversification does little to affect the expected return for a given style, it does appear to help reduce portfolio volatility: sometimes quite significantly so. This somewhat contradictory result to the prior research is likely due to the fact that hedge funds within a given category exhibit far more heterogeneity in process and returns than do equity managers in the same style box.

(Note that while the graphs below only show the period 1990-1993, the paper explores three time periods: 1990-1993, 1994-1997, and 1998-2001 and finds a similar conclusion in all three).

Perhaps most importantly, however, they find a rather significant reduction in risk characteristics like a portfolio’s realized maximum drawdown.

To quote the article,

We find that naively adding more funds to a portfolio tends to leave returns stable, decrease the standard deviation, and reduce downside risk. Thus, diversification should be increased as long as the marginal benefits of adding a new asset to a portfolio exceeds the marginal cost.
…
If a sample of managers is relatively style pure, then a fewer number of managers will minimize the unsystematic risk of that style. On the contrary, if the sample is really heterogeneous, increasing the number of managers may still provide important diversification benefits.

Taken together, this literature paints an important picture:

Diversifying across managers in the same category will likely do little to reduce portfolio volatility, except in the cases where categories are broad enough to capture many heterogeneous managers.
Diversifying across managers appears to significantly reduce the potential dispersion in terminal wealth.

But why is minimizing “the dispersion of terminal wealth” important? The answer is the same reason why we diversify in the first place: risk management.

The potential for high dispersion in terminal wealth means that we can have dramatically different outcomes based upon the choices we are making, placing significant emphasis on our skill in manager selection. Choosing just one manager is more right style thinking rather than our preferred less wrong.

But What About Dilution?

The number one response we hear when we talk about manager diversification is: “when we combine managers, won’t we just dilute our exposure back to the market?”

The answer, as with all things, is: “it depends.” For the sake of brevity, we’re just going to leave it with, “no.”

No?

No.

If we identify three managers as providing exposure to value, then it makes little logical sense that somehow a combination of them would suddenly remove that exposure. Subtraction through addition only works if there is a negative involved; i.e. one of the managers would have to provide anti-value exposure to offset the others.

Remember that an active manager’s portfolio can always be decomposed into two pieces: the benchmark and a dollar-neutral long/short portfolio that isolates the active over/under-weights that manager has made.

To “dilute back to the benchmark,” we’d have to identify managers and then weight them such that all of their over/under-weights net out to equal zero.

Candidly, we’d be impressed if you managed to do that. Especially if you combine managers within the same style who should all be, at least directionally, taking similar bets. The dilution that occurs is only across those bets which they disagree on and therefore reflect the idiosyncrasies of their specific process.

What a multi-manager implementation allows us to diversify is our selection risk, leading to a return profile more “in-line” with a given style or category. In fact, Lhabitant and Learned (2002) demonstrated this exact notion with a graph that plots the correlation of multi-manager portfolios with their broad category. While somewhat tautological, an increase in manager diversification leads to a return profile closer to the given style than to the idiosyncrasies of those managers.

We can also see this with a practical example. Below we take several available ETFs that implement quantitative value strategies and plot their rolling 52-week return relative to the S&P 500. We also construct a multi-manager index (“MM_IDX”) that is a naïve, equal-weight portfolio. The only wrinkle to this portfolio is that ETFs are not introduced immediately, but rather slowly over a 12-month period.³

Source: CSI Analytics. Calculations by Newfound Research. It is not possible to invest in an index. Returns are total returns (i.e. assume the reinvestment of all distributions) and are gross of all fees except for underlying expense ratios of ETFs. Past performance does not guarantee future results.

We can see that while the multi-manager blend is never the best performing strategy, it is also never the worst. Never the hero; never a zero.

It should be noted that while manager diversification may be able to reduce the idiosyncratic returns that result from process differences, it will not prevent losses (or relative underperformance) of the underlying style itself. In other words, we might avoid the full brunt of losses specific to the Sequoia Fund, but no amount of diversification would prevent the relative drag seen by the quantitative value style in general over the last decade.

We can see this in the graph above by the fact that all the lines generally tend to move together. 2015 was bad for value managers. 2016 was much better. But we can also see that every once in a while, a specific implementation will hit a rough patch that is idiosyncratic to that approach; e.g. IWD in 2017 and most of 2018.

Multi-manager diversification is the tool that allows us to avoid the full brunt of this risk.

Conclusion

Taken together, the research behind manager diversification suggests:

In heterogeneous categories (e.g. many hedge fund styles), manager diversification may reduce portfolio volatility.
In more homogenous categories (e.g. equity style boxes), manager diversification may reduce the dispersion in terminal wealth.
Multi-manager implementations appear to reduce realized portfolio risk metrics such as maximum drawdown. This is likely partially due to the reduction in portfolio volatility, but also due to a reduction in exposure to funds that exhibit catastrophic losses.
Multi-manager implementations do not necessarily “dilute” the portfolio back to market exposure, but rather “dilute” the portfolio back to the style exposure, reducing exposure idiosyncratic process risk.

For advisors and investors, this evidence may cause a sigh of relief. Instead of having to spend time trying to identify the best manager or the best process, there may be significant advantages to simply “avoiding the brain damage”⁴ and allocating equally among a few. In other words, if you don’t know which low-volatility ETF to pick, just buy a couple and move on with your life.

But what are the cons?

A multi-manager approach may be tax inefficient, as we will need to rebalance allocations back to parity between the exposures.
A multi-manager approach may lead to fund bloat within a portfolio, doubling or tripling the number of holdings we have. While this is merely optical, except possibly in small portfolios, we recognize there exists an aversion to it.
By definition, performance will be middling: the cost of avoiding the full brunt of losers is that we also give up the full benefit of winners. We’re reluctant to label this as a con, as it is arguably the whole point of diversification, but it is worth pointing out that the same behavioral biases that emerge in portfolio reviews of asset allocation will likely re-emerge in reviews of manager selection, especially over short time horizons.

For investment managers, a natural interpretation of this research is that approaches blending different signals and portfolio construction methods together should lead to more consistent outcomes. It should be no surprise, then, that asset managers adopting machine learning are finding significant advantages with ensemble techniques. After all, they invoke the low-hanging fruit of manager diversification.

Perhaps most interesting is that this research suggests that fund-of-funds really are not such bad ideas so long as costs can be kept under control. As the asset management business continues to be more competitive, perhaps there is an edge – and a better client result – found in cooperation.

Category: Popular Page 2 of 3

Taxes and Trend Equity

Summary

The Risk in Taxes

Tax Impacts in Trend Equity

Improving the Tax Profile Within Trend Equity

Conclusion

Trend Following in Cash Balance Plans

Summary

The Return Guarantee

Investing a Cash Balance Plan

Using Trend Following in a Cash Balance Plan

Conclusion

No Pain, No Premium

Summary

1. Is it About Risk or Return?

1.1 Stocks for the Long Run

1.2 “Funding Secured”

1.2 Well ‘Skews Me

2. You’re An Insurance Company

2.1 Diversifying with Bonds

3. The Philosophical Limits of Diversification

3.1 The Frustrating Law of Active Management

4. Investment versus Investor Returns

5.1 What Axis (“Correlation Diversification”)

5.1.1 It’s Hard to Allocate Our Way Out of a Bear Market

5.2 The How Axis – Payoff Diversification

5.2.1 Style Diversification

5.2.2 Payoff Diversification

5.2.3 Specification Risk

5.3 When Axis

6. Summary

Fragility Case Study: Dual Momentum GEM

Summary­

Introduction

Global Equities Momentum (“GEM”)

Conclusion

Is Multi-Manager Diversification Worth It?

Summary­

Introduction

The Theory Behind Manager Diversification

Literature Review

But What About Dilution?

Conclusion

Summary

Summary