Month: March 2019

Time Dilation

By Corey Hoffstein

On March 25, 2019

In Portfolio Construction, Weekly Commentary

This post is available as a PDF download here.

Summary

Information does not flow into the market at a constant frequency or with constant magnitude.

By sampling data using a constant time horizon (e.g. “200-day simple moving average”), we may over-sample during calm market environments and under-sample in chaotic ones.

As an example, we introduce a highly simplified price model and demonstrate that trend following lookback periods should be a dynamic function of trend and volatility in the time domain.

By changing the sampling domain slightly, we are able to completely eliminate the need for the dynamic lookback period.

Finally, we demonstrate a more complicated model that samples market prices based upon cumulative log differences, creating a dynamic moving average in the time domain.

We believe that there are other interesting applications of this line of thinking, many of which may already be in use today by investors who may not be aware of it (e.g. tracking-error-based rebalancing techniques).

In the 2014 film Interstellar, Earth has been plagued by crop blights and dust storms that threaten the survival of mankind. Unknown, interstellar beings have opened a wormhole near Saturn, creating a path to a distant galaxy and the potential of a new home for humanity.

Twelve volunteers travel into the wormhole to explore twelve potentially hospitable planets, all located near a massive black hole named Gargantua. Of the twelve, only three reported back positive results.

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

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

The close proximity of the planet to the gravitational forces of the supermassive black hole invites exponential time dilation effects. The positive beacon that had been tracked had perhaps been triggered just minutes prior on the planet. For the crew, the three hours spent on the planet amounted to over 23 years on Earth. The crew can only watch, devastated, as their loved ones age before their eyes in the video messages received – and never responded to – in their multi-decade absence.

Our lives revolve around the clock, though we do not often stop to reflect upon the nature of time.

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

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

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

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

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

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

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

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

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

Source: CSI Data. Calculations by Newfound Research.

If we believe that information flow is not static and constant, then sampling data on a constant, fixed interval will mean that during calm markets we might be over-sampling our data and during chaotic markets we might be under-sampling.

Let’s make this a bit more concrete.

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

Source: CSI Data. Calculations by Newfound Research.

The question we might want to ask ourselves is, why are looking at the prior 200 days? Or, more specifically, why is a day a meaningful unit of measure? We already demonstrated above that it very well may not be: one day might be packed with economically-relevant information and another entirely devoid.

Perhaps there are other ways in which we might think about sampling data. We could, for example, sample data based upon cumulative volume intervals. Another might be on a fixed number of cumulative ticks or trades. Yet another might be on a fixed cumulative volatility or variance.

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

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

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

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

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

Substituting our above definition of the simple moving average:

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

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

Re-arranging a bit, we get:

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

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

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

Despite being a highly simplified model, it illuminates that our lookback length should be a function of noise versus trend strength. The higher the ratio of noise to trend, the longer the lookback required to smooth out the noise. On the other hand, when the trend is very strong and the noise is weak, the lookback can be quite short.¹

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

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

Sampling at that frequency, how many of data points would we need to estimate our trend? We need not even work out the math as before; a bit of analytical logic will suffice. In this case, because we know the cumulative noise equals zero, we know that a point-to-point comparison will be affected only by the trend component. Thus, we only need n=1 in this new domain.

And this is true regardless of the parameterization of trend or noise. Goodbye! dynamic lookback function.

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

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

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

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

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

Conclusion

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

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

Even strategic portfolios are often rebalanced based upon the calendar. As we demonstrated in our paper Rebalance Timing Luck: The Difference Between Hired and Fired, fixed-schedule rebalancing can invite tremendous random impact in our portfolios.

Information does not flow into the market at a constant rate. While time may be a convenient measure, it may actually cause us to sample too frequently in some market environments and not frequently enough in others.

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

Trend Following in Cash Balance Plans

By Nathan Faber

On March 18, 2019

This post is available as a PDF download here.

Summary

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

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

Source: Investment Company Institute (ICI).

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

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

Source: Kravitz. 2018 National Cash Balance Research Report.

What is a cash balance plan?

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

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

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

What’s the appeal?

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

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

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

Source: Kravitz. 2018 National Cash Balance Research Report.

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

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

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

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

Source: Kravitz.

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

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

The Return Guarantee

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

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

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

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

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

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

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

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

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

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

Investing a Cash Balance Plan

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

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

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

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

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

The failure rate for the portfolios are shown below.³

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

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

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

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

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

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

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

Using Trend Following in a Cash Balance Plan

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

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

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

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

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

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

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

So which risks should a cash balance plan bear?

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

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

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

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

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

Conclusion

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

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

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

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

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

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

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

The Monsters of Investing: Fast and Slow Failure

By Corey Hoffstein

On March 11, 2019

In Risk Management, Trend

This post is available as a PDF download here.

Summary

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: BuzzFeed

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion

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

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

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

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

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

How Much Accuracy Is Enough?

By Nathan Faber

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 1/30^th 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:

The Plain Investor – This investor simply holds all 30 sectors, equally weighted, all the time.
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.
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 Return	Annualized Volatility	Maximum Drawdown
Plain Investor	10.5%	19.3%	83.9%
Perfect Investor	42.6%	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.

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.

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.

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.

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.

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?

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).

Month: March 2019

Time Dilation

Summary

Conclusion

Trend Following in Cash Balance Plans

Summary

The Return Guarantee

Investing a Cash Balance Plan

Using Trend Following in a Cash Balance Plan

Conclusion

The Monsters of Investing: Fast and Slow Failure

Summary

Conclusion

How Much Accuracy Is Enough?

Summary­

The (In)Accurate Investor

Accounting for Accuracy

Accuracy Schmaccuracy

Conclusion

Summary