Month: January 2018

Timing Bonds with Value, Momentum, and Carry

On January 29, 2018

In Carry, Momentum, Popular, Risk & Style Premia, Value, Weekly Commentary

This post is available as a PDF download here.

Summary

Bond timing has been difficult for the past 35 years as interest rates have declined, especially since bonds started the period with high coupons.
With low current rates and higher durations, the stage may be set for systematic, factor-based bond investing.
Strategies such as value, momentum, and carry have done well historically, especially on a risk-adjusted basis.
Diversifying across these three strategies and employing prudent leverage takes advantage of differences in the processes and the information contained in their joint decisions.

This commentary is a slight re-visit and update to a commentary we wrote last summer, Duration Timing with Style Premia[1]. The models we use here are similar in nature, but have been updated with further details and discussion, warranting a new piece.

Historically Speaking, This is a Bad Idea

Let’s just get this out of the way up front: the results of this study are probably not going to look great.

Since interest rates peaked in September 1981, the excess return of a constant maturity 10-year U.S. Treasury bond index has been 3.6% annualized with only 7.3% volatility and a maximum drawdown of 16.4%. In other words, about as close to a straight line up and to the right as you can get.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

With the benefit of hindsight, this makes sense. As we demonstrated in Did Declining Rates Actually Matter?[2], the vast majority of bond index returns over the last 30+ years have been a result of the high average coupon rate. High average coupons kept duration suppressed, meaning that changes in rates produced less volatile movements in bond prices.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

Ultimately, we estimate that roll return and benefits from downward shifts in the yield curve only accounted for approximately 30% of the annualized return.

Put another way, whenever you got “out” of bonds over this period, there was a very significant opportunity cost you were experiencing in terms of foregone interest payments, which accounted for 70% of the total return.

If we use this excess return as our benchmark, we’ve made the task nearly impossible for ourselves. Consider that if we are making “in or out” tactical decisions (i.e. no leverage or shorting) and our benchmark is fully invested at all times, we can only outperform due to our “out” calls. Relative to the long-only benchmark, we get no credit for correct “in” calls since correct “in” calls mean we are simply keeping up with the benchmark. (Note: Broadly speaking, this highlights the problems with applying traditional benchmarks to tactical strategies.) In a period of consistently positive returns, our “out” calls must be very accurate, in fact probably unrealistically accurate, to be able to outperform.

When you put this all together, we’re basically asking, “Can you create a tactical strategy that can only outperform based upon its calls to get out of the market over a period of time when there was never a good time to sell?”

The answer, barring some serious data mining, is probably, “No.”

**This Might Now be a Good Idea**

Yet this idea might have legs.

Since the 10-year rate peaked in 1981, the duration of a constant maturity 10-year U.S. bond index has climbed from 4.8 to 8.7. In other words, bonds are now 1.8x more sensitive to changes in interest rates than they were 35 years ago.

If we decompose bond returns in the post-crisis era, we can see that shifts in the yield curve have played a large role in year-to-year performance. The simple intuition is that as coupons get smaller, they are less effective as cushions against rate volatility.

Higher durations and lower coupons are a potential double whammy when it comes to fixed income volatility.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

With rates low and durations high, strategies like value, momentum, and carry may afford us more risk-managed access to fixed income.

Timing Bonds with Value

Following the standard approach taken in most literature, we will use real yields as our measure of value. Specifically, we will estimate real yield by taking the current 10-year U.S. Treasury rate minus the 10-year forecasted inflation rate from Philadelphia Federal Reserve’s Survey of Professional Forecasters.[3]

To come up with our value timing signal, we will compare real yield to a 3-year exponentially weighted average of real yield.

Here we need to be a bit careful. With a secular decline in real yields over the last 30 years, comparing current real yield against a trailing average of real yield will almost surely lead to an overvalued conclusion, as the trailing average will likely be higher.

Thus, we need to de-trend twice. We first subtract real yield from the trailing average, and then subtract this difference from a trailing average of differences. Note that if there is no secular change in real yields over time, this second step should have zero impact. What this is measuring is the deviation of real yields relative to any linear trend.

After both of these steps, we are left with an estimate of how far our real rates are away from fair value, where fair value is defined by our particular methodology rather than any type of economic analysis. When real rates are below our fair value estimate, we believe they are overvalued and thus expect rates to go up. Similarly, when rates are above our fair value estimate, we believe they are undervalued and thus expect them to go down.

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research.

Before we can use this valuation measure as our signal, we need to take one more step. In the graph above, we see that the deviation from fair value in September 1993 was approximately the same as it was in June 2003: -130bps (implying that rates were 130bps below fair value and therefore bonds were overvalued). However, in 1993, rates were at about 5.3% while in 2003 rates were closer to 3.3%. Furthermore, duration was about 0.5 higher in 2003 than it was 1993.

In other words, a -130bps deviation from fair value does not mean the same thing in all environments.

One way of dealing with this is by forecasting the actual bond return over the next 12 months, including any coupons earned, by assuming real rates revert to fair value (and taking into account any roll benefits due to yield curve steepness). This transformation leaves us with an actual forecast of expected return.

We need to be careful, however, as our question of whether to invest or not is not simply based upon whether the bond index has a positive expected return. Rather, it is whether it has a positive expected return in excess of our alternative investment. In this case, that is “cash.” Here, we will proxy cash with a constant maturity 1-year U.S. Treasury index.

Thus, we need to net out the expected return from the 1-year position, which is just its yield. [4]

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research.

While the differences here are subtle, had our alternative position been something like a 5-year U.S. Treasury Index, we may see much larger swings as the impact of re-valuation and roll can be much larger.

Using this total expected return, we can create a simple timing model that goes long the 10-year index and short cash when expected excess return is positive and short the 10-year index and long cash when expected excess return is negative. As we are forecasting our returns over a 1-year period, we will employ a 1-year hold with 52 overlapping portfolios to mitigate the impact of timing luck.

We plot the results of the strategy below.

Source: Federal Reserve of St. Louis. Philadelphia Federal Reserve. Calculations by Newfound Research. Results are hypothetical and backtested. Past performance is not a guarantee of future results. Returns are gross of all fees (including management fees, transaction costs, and taxes). Returns assume the reinvestment of all income and distributions.

The value strategy return matches the 10-year index excess return nearly exactly (2.1% vs 2.0%) with just 70% of the volatility (5.0% vs 7.3%) and 55% of the max drawdown (19.8% versus 36.2%).

Timing Bonds with Momentum

For all the hoops we had to jump through with value, the momentum strategy will be fairly straightforward.

We will simply look at the trailing 12-1 month total return of the index versus the alternative (e.g. the 10-year index vs. the 1-year index) and invest in the security that has outperformed and short the other. For example, if the 12-1 month total return for the 10-year index exceeds that of the 1-year index, we will go long the 10-year and short the 1-year, and vice versa.

Since momentum tends to decay quickly, we will use a 1-month holding period, implemented with four overlapping portfolios.

(Note that this backtest starts earlier than the value backtest because it only requires 12 months of returns to create a trading signal versus 6 years of data – 3 for the value anchor and 3 to de-trend the data – for the value score.)

Compared to the buy-and-hold approach, the momentum strategy increases annualized return by 0.5% (1.7% versus 1.2%) while closely matching volatility (6.7% versus 6.9%) and having less than half the drawdown (20.9% versus 45.7%).

Of course, it cannot be ignored that the momentum strategy has largely gone sideways since the early 1990s. In contrast to how we created our bottom-up value return expectation, this momentum approach is a very blunt instrument. In fact, using momentum this way means that returns due to differences in yield, roll yield, and re-valuation are all captured simultaneously. We can really think of decomposing our momentum signal as:

10-Year Return – 1-Year Return = (10-Year Yield – 1-Year Yield) + (10-Year Roll – 1-Year Roll) + (10-Year Shift – 1-Year Shift)

Our momentum score is indiscriminately assuming momentum in all the components. Yet when we actually go to put on our trade, we do not need to assume momentum will persist in the yield and roll differences: we have enough data to measure them explicitly.

With this framework, we can isolate momentum in the shift component by removing yield and roll return expectations from total returns.

Source: Federal Reserve of St. Louis. Calculations by Newfound Research.

Ultimately, the difference in signals is minor for our use of 10-year versus 1-year, though it may be far less so in cases like trading the 10-year versus the 5-year. The actual difference in resulting performance, however, is more pronounced.

Ironically, by doing worse mid-period, the adjusted momentum long/short strategy appears to be more consistent in its return from the early 1990s through present. We’re certain this is more noise than signal, however.

Timing Bonds with Carry

Carry is the return we earn by simply holding the investment, assuming everything else stays constant. For a bond, this would be the yield-to-maturity. For a constant maturity bond index, this would be the coupon yield (assuming we purchase our bonds at par) plus any roll yield we capture.

Our carry signal, then, will simply be the difference in yields between the 10-year and 1-year rates plus the difference in expected roll return.

For simplicity, we will assume roll over a 1-year period, which makes the expected roll of the 1-year bond zero. Thus, this really becomes, more or less, a signal to be long the 10-year when the yield curve is positively sloped, and long the 1-year when it is negatively sloped.

As we are forecasting returns over the next 12-month period, we will use a 12-month holding period and implement with 52 overlapping portfolios.

Again, were we comparing the 10-year versus the 5-year instead of the 10-year versus the 1-year, the roll can have a large impact. If the curve is fairly flat between the 5- and 10-year rates, but gets steep between the 5- and the 1-year rates, then the roll expectation from the 5-year can actually overcome the yield difference between the 5- and the 10-year rates.

Building a Portfolio of Strategies

With three separate methods to timing bonds, we can likely benefit from process diversification by constructing a portfolio of the approaches. The simplest method to do so is to simply give each strategy an equal share. Below we plot the results.

Indeed, by looking at per-strategy performance, we can see a dramatic jump in Information Ratio and an exceptional reduction in maximum drawdown. In fact, the maximum drawdown of the equal weight approach is below that of any of the individual strategies, highlighting the potential benefit of diversifying away conflicting investment signals.

Strategy	Annualized Return	Annualized Volatility	Information Ratio	Max Drawdown
10-Year Index Excess Return	2.0%	7.3%	0.27	36.2%
Value L/S	2.0%	5.0%	0.41	19.8%
Momentum L/S	1.9%	6.9%	0.27	20.9%
Carry L/S	2.5%	6.6%	0.38	20.1%
Equal Weight	2.3%	4.0%	0.57	10.2%

One potential way to improve upon the portfolio construction is by taking into account the actual covariance structure among the strategies (correlations shown in the table below). We can see that, historically, momentum and carry have been fairly positively correlated while value has been independent, if not slightly negatively correlated. Therefore, an equal-weight approach may not be taking full advantage of the diversification opportunities presented.

	Value L/S	Momentum L/S	Carry L/S
Value L/S	1.0	-0.2	-0.1
Momentum L/S	-0.2	1.0	0.6
Carry L/S	-0.1	0.6	1.0

To avoid making any assumptions about the expected returns of the strategies, we will construct a portfolio where each strategy contributes equally to the overall risk profile (“ERC”). So as to avoid look-ahead bias, we will use an expanding window to compute our covariance matrix (seeding with at least 5 years of data). While the weights vary slightly over time, the result is a portfolio where the average weights are 43% value, 27% momentum, and 30% carry.

The ERC approach matches the equal-weight approach in annualized return, but reduces annualized volatility from 4.2% to 3.8%, thereby increasing the information ratio from 0.59 to 0.64. The maximum drawdown also falls from 10.2% to 8.7%.

A second step we can take is to try to use the “collective intelligence” of the strategies to set our risk budget. For example, we can have our portfolio target the long-term volatility of the 10-year Index Excess Return, but scale this target between 0-2x depending on how invested we are.

For example, if the strategies are, in aggregate, only 20% invested, then our target volatility would be 0.4x that of the long-term volatility. If they are 100% invested, though, then we would target 2x the long-term volatility. When the strategies are providing mixed signals, we will simply target the long-term volatility level.

Unfortunately, such an approach requires going beyond 100% notional exposure, often requiring 2x – if not 3x – leverage when current volatility is low. That makes this system less useful in the context of “bond timing” since we are now placing a bet on current volatility remaining constant and saying that our long-term volatility is an appropriate target.

One way to limit the leverage is to increase how much we are willing to scale our risk target, but truncate our notional exposure at 100% per leg. For example, we can scale our risk target between 0-4x. This may seem very risky (indeed, an asymmetric bet), but since we are clamping our notional exposure to 100% per leg, we should recognize that we will only hit that risk level if current volatility is greater than 4x that of the long-term average and all the strategies recommend full investment.

With a little mental arithmetic, the approach it is equivalent to saying: “multiply the weights by 4x and then scale based on current volatility relative to historical volatility.” By clamping weights between -100% and +100%, the volatility targeting really does not come into play until current volatility is 4x that of long-term volatility. In effect, we leg into our trades more quickly, but de-risk when volatility spikes to abnormally high levels.

Compared to the buy-and-hold model, the variable risk ERC model increases annualized returns by 90bps (2.4% to 3.3%), reduces volatility by 260bps (7.6% to 5.0%), doubles the information ratio (0.31 to 0.66) and halves the maximum drawdown (30% to 15%).

There is no magic to the choice of “4” above: it is just an example. In general, we can say that as the number goes higher, the strategy will approach a binary in-or-out system and the volatility scaling will have less and less impact.

Conclusion

Bond timing has been hard for the past 35 years as interest rates have declined. Small current coupons do not provide nearly the cushion against rate volatility that investors have been used to, and these lower rates mean that bonds are also exposed to higher duration.

These two factors are a potential double whammy when it comes to fixed income volatility.

This can open the door for systematic, factor-based bond investing.

Value, momentum, and carry strategies have all historically outperformed a buy-and-hold bond strategy on a risk adjusted basis despite the bond bull market. Diversifying across these three strategies and employing prudent leverage takes advantage of differences in the processes and the information contained in their joint decisions.

We should point out that in the application of this approach, there were multiple periods of time in the backtest where the strategy went years without being substantially invested. A smooth, nearly 40-year equity curve tells us very little about what it is actually like to sit on the sidelines during these periods and we should not underestimate the emotional burden of using such a timing strategy.

Even with low rates and high rate movement sensitivity, bonds can still play a key role within a portfolio. Going forward, however, it may be prudent for investors to consider complementary risk-management techniques within their bond sleeve.

[1] https://blog.thinknewfound.com/2017/06/duration-timing-style-premia/

[2] https://blog.thinknewfound.com/2017/04/declining-rates-actually-matter/

[3] Prior to the availability of the 10-year inflation estimate, the 1-year estimate is utilized; prior to the 1-year inflation estimate availability, the 1-year GDP price index estimate is utilized.

[4] This is not strictly true, as it largely depends on how the constant maturity indices are constructed. For example, if they are rebalanced on a monthly basis, we would expect that re-valuation and roll would have impact on the 1-year index return. We would also have to alter the horizon we are forecasting over as we are assuming we are rolling into new bonds (with different yields) more frequently.

Quantifying Timing Luck

By Corey Hoffstein

On January 22, 2018

In Craftsmanship, Risk Management, Weekly Commentary

This blog post is available as a PDF download here.

Summary

When two managers implement identical strategies, but merely choose to rebalance on different days, we call variance between their returns “timing luck.”
Timing luck can easily be overcome by using a method of overlapping portfolios, but few firms do this in practice.
We believe the magnitude of timing luck impact is much larger than most believe, particularly in tactical strategies.
We derive a model to estimate the impact of timing luck, using only values that can be easily estimated from portfolios implemented without the overlapping portfolio technique.
We find that timing luck looms large in many different types of strategies.

As a pre-emptive warning, this week’s commentary is a math derivation. We think it is a very relevant derivation – one which we have not seen before – but a derivation nonetheless. If math is not your thing, this might be one to skip.

If math is your thing: consider this a request for comments. The derivation here will be rather informal sketch, and we think there are other improvements still lingering.

What is “Timing Luck?”

The basic concept of timing luck is that when we choose to rebalance can have a profound impact on our performance results. For example, if we rebalance an investment strategy once a month, the choice to rebalance at the end of the month will lead to different performance than had we elected to rebalance mid-month.

We call this performance differential “timing luck,” and we believe it is an overlooked, non-negligible portfolio construction risk.

As an example, consider a simple stock/cash timing model that rebalances monthly, investing in a broad U.S. equity index when its 12-1 month return is positive, and a constant maturity 1-year U.S. Treasury index otherwise. Depending on which day of the month you choose to rebalance (we will assume 21 variations to represent 21 trading days), your results may be dramatically different.

Source: Kenneth French Data Library, Federal Reserve of St. Louis. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.

The best performing strategy had an annualized return of 11.1%, while the worst returned just 9.6%. Compounded over 55 years, and that 150 basis point (“bps”) differential leads to an astounding difference in final wealth. With a standard deviation between 50-year annualized returns of 0.42%, the 1-year annualized estimate of performance variation due to timing luck is 314bps!

Again, an identical process is employed: the only difference between these results is the choice of what day of the month to rebalance.

That small choice, and the good luck or misfortune it realizes, can easily be the difference between “hired” and “fired.”

Is There a Solution to Timing Luck?

In the past, we have argued that overlapping portfolios can be utilized to minimize the impact of timing luck. The idea of overlapping portfolios is as follows: given an investment process and a holding period, we can invest across multiple managers that invest utilizing the same process but have offset holding periods.[1]

For example, below each manager has a four time-step holding period, and we utilize four managers to minimize timing luck from a single implementation.

The proof that this approach minimizes timing luck is as follows.

Assume that we have N managers, all following an identical investment process with identical holding period, but whose rebalance points are offset from one another by one period.

Consider that at any point in time, we can define the portfolio of Manager #2 to be the portfolio of Manager #1 plus a dollar-neutral long/short portfolio that captures the differences in holdings between them. Similarly, Manager #3’s portfolio can be thought of as Manager #2’s portfolio plus a dollar-neutral long/short portfolio. This continues in a circular manner, where Manager #1’s portfolio can be thought of as Manager #N’s portfolio plus a dollar-neutral long/short.

Given that the managers all follow an identical process, we would expect them to have the same long-term expected return. Thus, the expected return of the dollar-neutral long/short portfolios is zero.

However, the variance of the dollar-neutral long/short portfolios captures the risk of timing luck.

In allocating capital between the N portfolios, our goal is to minimize timing luck. Put another way, we want to find the allocation that results in the minimum variance portfolio of the long/short portfolios. Fortunately, there is a simple, closed form solution for calculating the minimum variance portfolio:

Here, w is our solution (an Nx1 vector of weights), Sigma is the covariance matrix and is an Nx1 vector of 1s. To solve this equation, we need the covariance matrix between the long/short portfolios. Since each portfolio is employing an identical process, we can assume that each of the long/short portfolios should have equal variance. Without loss of generality, we can assume variances are equal to 1 and replace our covariance matrix, Sigma, with a correlation matrix, C.

The correlations between long/short portfolios will largely depend on the process in question and the amount of overlap between portfolios. That said, because each manager runs an identical process, we would expect that the long-term correlation between Portfolio #2’s long/short and Portfolio #1’s long/short to be identical to the correlation between Portfolio #3’s long/short and Portfolio #2’s. Similarly, the correlation between Portfolio #3’s and Portfolio #1’s long/shorts should be the same as the correlation between Portfolio #N’s and Portfolio #2’s.

Following this logic (and remembering the circular nature of the rebalances), we can ignore exact numbers and fill in a correlation matrix using variables:

This correlation matrix has two special properties. First, being a correlation matrix, it is symmetric. Second, it is circulant: each row is rotated one element to the right of the preceding row. A special property of a symmetric circulant matrix is that its inverse – in this case C^-1 – is also symmetric circulant. This property guarantees that C^-11 is equal to k1 for some constant k.

Which means we can re-write our minimum variance solution as:

Since the constant will cancel out, we are left with:

Thus, our optimal solution is an equal-weight allocation to all N portfolios.

Highlighted in gold below, we can see the result of this approach using the same stock/cash example as before. Specifically, the gold portfolio uses each of the 21 variations as a different sub-portfolio.

Source: Kenneth French Data Library. Calculations by Newfound Research. Past performance is not an indicator of future results. Performance is backtested and hypothetical. Performance figures are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Performance assumes the reinvestment of all distributions.

While we have a solution for timing luck, a question that lingers is: “how much will timing luck affect my particular strategy?”

The Setup

We assume an active investment strategy with constant portfolio of variance (S²), constant and continuous annualized turnover (T; e.g. 0.5 for 50% annual turnover), and consistent rebalances at discrete frequency (f; e.g. 1/12 for monthly).

We will also assume that the portfolio contains no static components. This allows us to interpret 100% turnover as meaning that the entire portfolio was turned over, rather than that 50% of the portfolio was turn over twice.

To quantify the magnitude of timing luck, we will calculate the variance of a dollar-neutral, long/short portfolio that is long a discrete implementation (i.e. rebalancing at a fixed interval) of this strategy (D) and short the theoretically optimal infinite overlapping portfolio implementation (M – for “meta”).

As before, the expected return of this long/short is zero, but its variance captures the return differences created by timing luck.

Differences between the Discrete and Continuous Portfolios

The long/short portfolio is defined as (D – M). However, we would expect the holdings of D to overlap with the holdings of M. How much overlap will depend on both portfolio turnover and rebalance frequency.

Assume, for a moment, that M does not have infinite overlapping portfolios, but a finite number N, each uniformly spaced across the holding period.

If we assume 100% turnover that is continuous, we would expect that the first overlapping portfolio, implemented at t=1/N, to have (1 – 1/N) percent of its holdings identical to D (i.e. not “turned over”). On the other hand, the portfolio implemented at t = (N-1)/N will have just 1/N percent of its holdings identical to D.

Thus, we can say that if M contains N discrete overlapping portfolios, we can expect M and D to overlap by:

Which we can reduce,

If we take the limit as N goes to infinity – i.e. we have infinite overlapping portfolios – then we are simply left with:

Thus, the overlap we expect between our discretely implemented portfolio, D, and the portfolio with infinite overlapping portfolios, M, is a simple function of the expected turnover during the holding period.

We can then define our long/short portfolio:

Where Q is the portfolio of holdings in M that are not in D.

We should pause here, for a moment, as this is where our assumption of “no static portfolio elements” becomes relevant. We defined (1) to be the amount M and D overlap. Technically, if we allow securities to be sold and then repurchased, (1) represents a lower limit to how much M and D overlap. As an absurd example, consider a portfolio that creates 100% turnover by buying and selling the same 1% of the portfolio 100 times. Thus, Q in (6) need not necessarily be unique from D; part of D could be contained in Q.

By assuming that no part of the portfolio is static, we are assuming that over the (very) long run, the average turnover experience over a holding period does not include repurchase of sold securities, and thus (1) is the amount of overlap and D and Q are independent holdings.

This assumption is likely fairer for traditionally active portfolios that focus on security selection, but potentially less realistic for tactical strategies that often sell and re-purchase the same exposure. More on this later.

Defining,

We can re-write,

Solving for Timing Luck

We can then solve for the variance of the long/short portfolio,

Expanding:

As D and Q both represent viable allocation schemes for the portfolio, we will assume that they share the same long-term portfolio variance, S². This assumption may be fair, over the long run, for traditional stock-selection portfolios, but likely less fair for highly tactical portfolios that can meaningfully shift their portfolio risk exposures.

Thus,

Replacing back our definition for a, we are left with:

Or, that the annualized volatility due to timing luck (L) is:

What is Corr(D,Q)?

The least easily interpreted – or calculated – term in our equation is the correlation between our discrete portfolio, D, and the non-overlapping securities found in the infinite overlapping portfolios implementation, Q.

The intuitive interpretation here is that when the securities held in our discrete portfolio are highly correlated to those that are not held but the optimal strategy recommends we hold, then we would expect the difference to have less impact. On the other hand, if those securities are negatively correlated, then the discrete rebalance choice could lead to significant additional volatility.

Estimating this value, however, may be difficult to do empirically.

One potential answer is to use the intra-portfolio correlation (“IPC”) of an equal-weight portfolio of representative assets or securities. The intuition here is that we expect each asset to experience, on average, an equivalent amount of turnover due to our assumption that there are no static positions in the portfolio.

Thus, taking the IPC of an equal-weight portfolio of representative securities allows us to express the view that while we do not know which securities will be different at any given point in time, we expect over the long-run that all securities will be “missing” with equal frequency and magnitude, and therefore the IPC is representative of the long-term correlation between D and Q.

Estimating Timing Luck in our Stock/Cash Tactical Strategy

The assumptions required for our estimate of timing luck may work well with traditional security selection portfolios (or, at least, quantitative implementations of factors like value, momentum, defensive etc.), but will it work with tactical portfolios?

Using our prior stock/cash example, let’s estimate the expected magnitude of timing luck. Using one of the discrete implementations, we estimate that turnover is 67% per year. Our rebalance frequency is monthly (1/12) and the intra-portfolio correlation between stocks and bonds is assumed to be 0%. Finally, the long-term volatility of the strategy is about 12.2%.

Using these figures, we estimate:

This is a somewhat disappointing result, as we had calculated prior that the actual timing luck was 314bps. Our estimate is less than 1/6^th of the actual figure!

Part of the problem may be that many of the assumptions we outlined are violated with our example tactical strategy. We think the bigger problem is that our estimates for these variables, when using a highly tactical strategy, are simply wrong.

In our equation, we assumed that turnover would be continuous. This is because we are using turnover as a proxy for the decay speed of our alpha signal.

What does this mean? As an example, value strategies rely on value signals that tend to decay slowly. When a stock is identified as being a value stock, it tends to stay that way for some time. Therefore, if you build a portfolio off of these signals, you would expect low turnover. Momentum signals, on the other hand, tend to decay more quickly. A stock that is labeled as high momentum this month may no longer be high momentum in three months’ time. Thus, momentum strategies tend to be high turnover.

This relationship does not necessarily hold for tactical strategies.

In our tactical example, we rebalance monthly because we believe the time-series momentum has a short forecast horizon. However, with only two assets, the strategy can go years without turnover. Worse, the same strategy might miss a signal because it is only sampling in a discrete manner and therefore understate true turnover in a continuous framework.

If we were to look at the turnover of a tactical strategy implemented with the same rules but rebalanced daily, we would see a turnover rate over 300%. This would increase our estimate up to 215bps. Still well below the realized 314bps, but certainly high enough to raise eyebrows about the impact of timing luck in tactical portfolios not implemented using overlapping portfolios.

We should also remember that timing luck is determined by the difference in holdings between the discrete strategy and the meta strategy. We had assumed that the portfolios D and Q would have the same volatility, but in a strategy that shifts between stocks and bonds, this most certainly is not the case. This means that long-run volatility in such a tactical strategy can actually be misleadingly low.

Consider the situation when the tactical strategy goes to cash based upon a short-lived signal; i.e. the meta strategy will not build a significant cash position. The realized volatility of the strategy will dampen the perceived timing luck, when in reality the volatility difference between the two portfolios is quite large.

In our specific tactical example, we know that when D is stocks, Q is bonds and vice versa. With this insight, we can re-write equation (10):

Which we can simplify as:

Which is simply just a constant times the variance of a portfolio that is 100% long stocks and -100% short bonds (or vice versa; the variance will be the same).

If we use this equation and the variance of a long/short stock/bond portfolio and our prior estimate of 300% turnover, we get an estimate of timing luck volatility of 191bps.

Note that using this concept, there may be a more generic solution that is possible using some measure of active variance (likely scaled by active share).

Conclusion

In this piece we have demonstrated the potentially massive impact of timing luck, addressed how to solve for it, and derived a model that can be used to estimate the magnitude of timing luck risk in strategies that do not employ an overlapping portfolios technique.

While our derived approach is not perfect – as we saw in its application with our tactical example – we believe it is an important step forward in being able to quantify the potential risk that timing luck creates.

[1] In reality, we probably wouldn’t hire a different manager to implement the same strategy with different rebalance timing even if we could find such managers. A more feasible solution would be for a single manager to run different sleeves implementing each rebalance iteration.

Factor Investing & The Bets You Didn’t Mean to Make

By Corey Hoffstein

On January 16, 2018

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

Factor investing seeks to balance specificity with generality: specific enough to have meaning, but general enough to be applied broadly.
Diversification is a key tool to managing risk in factor portfolios. Imprecision in the factor definitions means that unintended bets are necessarily introduced.
This is especially true as we apply factors across securities that share fewer and fewer common characteristics. Left unmonitored, these unintended bets have the potential to entirely swamp the factor itself.
By way of example, we explore a simple value-based country model.
While somewhat counter-intuitive, constraints have the potential to lead to more efficient factor exposures.

In quantitative investing, we seek a balance between generality and specificity. When a model is too specific – designed to have meaning on too few securities or in too few scenarios – we lose our ability to diversify. When a model is too generic, it loses meaning and forecasting power.

The big quant factors – value, momentum, defensive, carry, and trend – all appear to find this balance: generic enough to be applied broadly, but specific enough to maintain a meaningful signal.

As we argued in our past commentary A Case Against Overweighting International Equity, the imprecision of the factors is a feature, not a bug. A characteristic like price-to-earnings may never fully capture the specific nuances of each firm, but it can provide a directionally accurate roadmap to relative firm valuations. We can then leverage diversification to average out the noise.

Without diversification, we are highly subject to the imperfections of the model. This is why, in the same piece, we argued that making a large regional tilt – e.g. away from U.S. towards foreign developed – may not be prudent: it is a single bet that can take decades to resolve. If we are to sacrifice diversification in our portfolio, we’ll require a much more accurate model to justify the decision.

Diversification, however, is not just measured by the quantity of bets we take. If diversification is too naively interpreted, the same imprecision that allows factors to be broadly applied can leave our portfolios subject to the returns of unintended bets.

Value Investing with Countries

If taking a single, large regional tilt is not prudent, perhaps value investing at a country level may better diversify our risks.

One popular way of measuring value is with the Shiller CAPE: a cyclically-smoothed price-to-earnings measure. In the table below, we list the current CAPE and historical average CAPE for major developed countries.

	CAPE	Mean CAPE	Effective Weight
Australia	18.5	17.2	2.42%
Belgium	25.0	15.4	0.85%
Canada	22.0	21.4	3.76%
Denmark	36.5	24.5	0.73%
France	20.9	21.9	4.85%
Germany	20.6	20.6	4.36%
Hong Kong	18.2	18.3	5.21%
Italy	16.8	22.1	1.33%
Japan	28.9	43.2	11.15%
Netherlands	23.5	14.8	1.45%
Singapore	13.9	22.1	1.09%
Spain	13.4	18.3	1.58%
Sweden	21.5	23.0	1.21%
Switzerland	25.9	21.9	3.15%
United Kingdom	16.5	15.3	6.55%
United States	30.5	20.3	50.30%

Source: StarCapital.de. Effective weight is market-capitalization weight of each country, normalized to sum to 100%. Mean CAPE figures use data post-1979 to leverage a common dataset.

While evidence[1] suggests that valuation levels themselves are enough to determine relative valuation among countries, we will first normalize the CAPE ratio by its long-term average to try to account for structural differences in CAPE ratios (e.g. a high growth country may have a higher P/E, a high-risk country may have a lower P/E, et cetera). Specifically, we will look at the log-difference between the mean CAPE and the current CAPE scores.

Note that we recognize there is plenty to criticize and improve upon here. Using a normalized valuation metric will mean a country like Japan, which experienced a significant asset bubble, will necessarily look under-valued. Please do not interpret our use of this model as our advocacy for it: we’re simply using it as an example.

Using this value score, we can compare how over and undervalued each country is relative to each other. This allows us to focus on the relative cheapness of each investment. We can then use these relative scores to tilt our market capitalization weights to arrive at a final portfolio.

	Value Score	Relative Z-Score	Scaled Z-Score	Scaled Weights
Australia	-0.07	-0.13	0.88	2.31%
Belgium	-0.48	-1.50	0.40	0.37%
Canada	-0.03	0.02	1.02	4.15%
Denmark	-0.40	-1.22	0.45	0.36%
France	0.05	0.27	1.27	6.65%
Germany	0.00	0.11	1.11	5.24%
Hong Kong	0.01	0.13	1.13	6.37%
Italy	0.27	1.02	2.02	2.92%
Japan	0.40	1.45	2.45	29.59%
Netherlands	-0.46	-1.43	0.41	0.65%
Singapore	0.46	1.65	2.65	3.14%
Spain	0.31	1.15	2.15	3.68%
Sweden	0.07	0.33	1.33	1.75%
Switzerland	-0.17	-0.45	0.69	2.36%
United Kingdom	-0.08	-0.14	0.88	6.22%
United States	-0.41	-1.25	0.45	24.26%

Source: StarCapital.de. Calculations by Newfound Research. “Value Score” is the log-difference between the country’s Mean CAPE and its Current CAPE. Relative Z-Score is the normalized value score of each country relative to peers. Scaled Z-Score applies the following function to the Relative Z-Score: (1+x) if x > 0 and 1 / (1+x) if x < 0. Scaled weights multiply the Scaled Z-Score against the Effective Weights of each country and normalize such that the total weights sum to 100%.

While the Scaled Weights represent a long-only portfolio, what they really capture is the Market Portfolio plus a dollar-neutral long/short factor tilt.

	Market Weight	+ Long / Short	= Scaled Weights
Australia	2.42%	-0.11%	2.31%
Belgium	0.85%	-0.48%	0.37%
Canada	3.76%	0.39%	4.15%
Denmark	0.73%	-0.37%	0.36%
France	4.85%	1.80%	6.65%
Germany	4.36%	0.88%	5.24%
Hong Kong	5.21%	1.16%	6.37%
Italy	1.33%	1.59%	2.92%
Japan	11.15%	18.44%	29.59%
Netherlands	1.45%	-0.80%	0.65%
Singapore	1.09%	2.05%	3.14%
Spain	1.58%	2.10%	3.68%
Sweden	1.21%	0.54%	1.75%
Switzerland	3.15%	-0.79%	2.36%
United Kingdom	6.55%	-0.33%	6.22%
United States	50.30%	-26.04%	24.26%

To understand the characteristics of the tilt we are taking – i.e. the differences we have created from the market portfolio – we need only look at the long/short portfolio.

Unfortunately, this is where our model loses a bit of interpretability. Since each country is being compared against its own long-term average, looking at the increase or decrease to the aggregate CAPE score is meaningless. Indeed, it is possible to imagine a scenario whereby this process actually increases the top-level CAPE score of the portfolio, despite taking value tilts (if value, for example, is found in countries that have higher structural CAPE values). We can, on the other hand, look at the weighted average change to value score: but knowing that we increased our value score by 0.21 has little interpretation.

One way of looking at this data, however, is by trying to translate value scores into return expectations. For example, Research Affiliates expects CAPE levels to mean-revert to the average level over a 20-year period.[2] We can use this model to translate our value scores into an annualized return term due to revaluation. For example, with a current CAPE of 30.5 and a long-term average of 20.3, we would expect a -2.01% annualized drag from revaluation.

By multiplying these return expectations against our long/short portfolio weights, we find that our long/short tilt is expected to create an annualized revaluation premium of +1.05%.

The Unintended Bet

Unfortunately, re-valuation is not the only bet the long/short portfolio is taking. The CAPE re-valuation is, after all, in local currency terms. If we look at our long/short portfolio, we can see a very large weight towards Japan. Not only will we be subject to the local currency returns of Japanese equities, but we will also be subject to fluctuations in the Yen / US Dollar exchange rate.

Therefore, to achieve the re-valuation premium of our long/short portfolio, we will either need to bear the currency risk or hedge it away.

In either case, we can use uncovered interest rate parity to develop an expected return for currency. The notion behind uncovered interest rate parity is that investors should be indifferent to sovereign interest rates. In theory, for example, we should expect the same return from investing in a 1-year U.S. Treasury bond that we expect from converting $1 to 1 euro, investing in the 1-year German Bund, and converting back after a year’s time.

Under uncovered interest rate parity, our expectation is that currency change should offset the differential in interest rates. If a foreign country has a higher interest rate, we should expect that the U.S. dollar should appreciate against the foreign currency.

As a side note, please be aware that this is a highly, highly simplistic model for currency returns. The historical efficacy of the carry trade clearly demonstrates the weakness of this model. More complex models will take into account other factors such as relative purchasing power reversion and productivity differentials.

Using this simple model, we can forecast currency returns for each country we are investing in.

	FX Rate	1-Year Rate	Expected FX Rate	Currency Return
Australia	1.2269	-0.47%	1.2546	-2.21%
Belgium	1.2269	-0.47%	1.2546	-2.21%
Canada	0.8056	1.17%	0.8105	-0.60%
Denmark	0.1647	-0.55%	0.1685	-2.29%
France	1.2269	-0.47%	1.2546	-2.21%
Germany	1.2269	-0.47%	1.2546	-2.21%
Hong Kong	0.1278	1.02%	0.1288	-0.75%
Italy	1.2269	-0.47%	1.2546	-2.21%
Japan	0.0090	-0.13%	0.0092	-1.88%
Netherlands	1.2269	-0.47%	1.2546	-2.21%
Singapore	0.7565	1.35%	0.7597	-0.42%
Spain	1.2269	-0.47%	1.2546	-2.21%
Sweden	0.1241	0.96%	0.1251	-0.81%
Switzerland	1.0338	-0.72%	1.0598	-2.46%
United Kingdom	1.3795	0.43%	1.3981	-1.33%
United States	1.0000	1.78%	1.0000	0.00%

Source: Investing.com, XE.com. Euro area yield curve employed for Eurozone countries on the Euro.

Multiplying our long/short weights against the expected currency returns, we find that we have created an expected annualized currency return of -0.45%.

In other words, we should expect that almost 50% of the value premium we intended to generate will be eroded by a currency bet we never intended to make.

One way of dealing with this problem is through portfolio optimization. Instead of blindly value tilting, we could seek to maximize our value characteristics subject to currency exposure constraints. With such constraints, what we would likely find is that more tilts would be made within the Eurozone since they share a currency. Increasing weight to one Eurozone country while simultaneously reducing weight to another can capture their relative value spread while remaining currency neutral.

Of course, currency is not the only unintended bet we might be making. Blindly tilting with value can lead to time varying betas, sector bets, growth bets, yield bets, and a variety of other factor exposures that we may not actually intend. The assumption we make by looking at value alone is that these other factors will be independent from value, and that by diversifying both across assets and over time, we can average out their impact.

Left entirely unchecked, however, these unintended bets can lead to unexpected portfolio volatility, and perhaps even ruin.

Conclusion

In past commentaries, we’ve argued that investors should focus on achieving capital efficiency by employing active managers that provide more pure exposure to active views. It would seem constraints, as we discussed at the end of the last section, might contradict this notion.

Why not simply blend a completely unconstrained, deep value manager with market beta exposure such that the overall deviations are constrained by position limits?

One answer why this might be less efficient is that not all bets are necessarily compensated. Active risk for the sake of active risk is not the goal: we want to maximize compensated active risk. As we showed above, a completely unconstrained value manager may introduce a significant amount of unintended tracking error. While we are forced to bear this risk, we do not expect the manager’s process to actually create benefit from it.

Thus, a more constrained approach may actually provide more efficient exposure.

That is all not to say that unconstrained approaches do not have efficacy: there is plenty of evidence that the blind application of value at the country index level has historically worked. Rather, the application of value at a global scale might be further enhanced with the management of unintended bets.

[1] For example, Predicting Stock Market Returns Using the Shiller CAPE (StarCapital Research, January 2016) and Value and Momentum Everywhere (Asness, Moskowitz, and Pedersen, June 2013)

[2] See Research Affiliate’s Equity Methodology for their Asset Allocation tool.

Levered ETFs for the Long Run?

By Corey Hoffstein

On January 8, 2018

In Portfolio Construction, Weekly Commentary

This blog post is available as a PDF download here.

Summary

We believe that capital efficiency should remain a paramount objective for investors.
The prudent use of leverage can help investors employ more risk efficient portfolios without necessarily sacrificing potential returns.
Many investors, however, do not have access to leverage (be it via borrowing or derivatives). They may, however, have access to leverage via Levered ETFs.
Levered ETFs are often dismissed as trading vehicles, not suited for buy-and-hold investors due to the so-called “volatility drag.” We show that the volatility drag is a component of all compounding returns, whether they are levered or not.
We explore the impact that the reset period can have on Levered ETFs and demonstrate how these ETFs may be used in the context of a portfolio to introduce diversifying, alternative exposures.

Early last month, we published a piece titled Portable Beta: Making the Most of the Returns You’re Already Getting, in which we outlined an argument whereby investors should focus on capital efficiency. We laid out four ways in which we believe that investors can achieve greater efficiency:

Reduce fees to take home more of what you earn.
Express active views more purely so that we are not caught paying active management prices for closet beta.
Focus on risk management by “diversifying your diversifiers” with strategies like trend following that can help increase exposure to higher return asset classes without necessarily increasing the overall portfolio risk profile.
Utilize modest leverage so that investors can create more risk-efficient portfolios without necessarily sacrificing potential return.

Unfortunately, for many investors, access to true leverage – either through borrowing or the use of derivatives – may be beyond their means. Fortunately, there are a number of ETFs available today that allow investors to access leverage in a packaged manner.

Wait, Aren’t Levered ETFs Dangerous?

Levered ETFs have quite a reputation, and not a good one at that. A quick search will result in numerous articles that tell you why they are a dangerous, bad idea. They are pejoratively dismissed as “trading vehicles,” unsuitable for “buy and hold.”

Most often, the negative publicity hinges on the concept of volatility decay (or, sometimes “volatility drag”). To illuminate this concept, let’s assume there is a stock that can only go up either +X% or down –X%. Thus, in any two-day period, we have the following growth in our wealth:

	Up	Down
Up	(1 + X%)(1 + X%)	(1 – X%)(1 + X%)
Down	(1 + X%)(1 – X%)	(1 – X%)(1 – X%)

If we expand out the returns, we are left with:

	Up	Down
Up	1 + 2X% + X%²	1 – X%²
Down	1 – X%²	1 – 2X% + X%²

Note that in the case where the stock went up +X% and then down -X% (or down –X% and then up +X%), we did not end up back at our starting wealth. Rather, we ended up with a loss of -X%².

On the other hand, we can see that when the stock goes the same direction, we actually outperform twice the daily return by +X%².

What’s going on here?

It is nothing more than the math of compound returns. The returns of the second day compound the returns of the first.

The effect earns the moniker volatility decay because in return environments that are mean-reversionary (e.g. positive returns follow negative returns, and vice versa), our capital decays due to the -X%² term.

Note, however, that we haven’t even introduced leverage into the scenario yet. This drag is not unique to levered ETFs: it is just the math of compounding returns. Why it gets brought up so frequently with respect to levered ETFs is because the leverage can accentuate it. Consider what happens if we introduce a daily leverage factor of L:

	Up	Down
Up	1 + 2LX% + L²X%²	1 – L²X%²
Down	1 – L²X%²	1 – 2LX% + L²X%²

When L=1, we have a standard long-only investment. When L=2, we have our 2X daily levered ETFs. What we see is that when L=1, our drag is simply –X%². When L=2, however, our drag is 4X%². When L=3, the drag skyrockets to 9X%². Of course, the so-called drag turns into a benefit in trending markets (whether positive or negative).

So why do we not see this same effect when we use traditional leverage? After all, are these ETFs not using leverage under the hood to achieve their returns?

The answer lies in the daily reset. Note that these ETFs aim to give you a multiple of returns every day. The same is not true if we simply lever our notional exposure and never reset it. By “reset,” we mean pay back what we owe and re-borrow capital in order to maintain our leverage ratio.

To achieve 2X daily returns, the levered ETFs basically borrow their NAV, invest in the asset class, and then pay back what they borrowed. Hence, every day they reset how much they borrow.

If we never reset, however, the proportion of our capital that is levered varies over time. Consider, for example, investing $10,000 of our own capital in the SPDR S&P 500 ETF and borrowing another $10,000 to invest alongside (for convenience, we’re going to assume zero borrowing cost). As the market has gone up over time, the initial $10,000 borrowed becomes a smaller and smaller proportion of our capital.

Source: CSI. Calculations by Newfound Research. Assumes portfolio applies 100% notional leverage applied to SPDR S&P 500 ETF (“SPY”) at inception of ETF. Assumes zero cost of leverage.

This happens because while we owe the initial $10,000 back, the returns made on that $10,000 are ours to keep. In the beginning, our portfolio will behave very much like a 2X daily levered ETF. As the market trends upward over time, however, we not only compound our own capital, but compound our gains on the levered capital. This causes our actual leverage to decline over time. As a result, our daily returns will gradually converge towards that of the market.

In practice, of course, there would be a cost associated with borrowing the $10,000. However, the same fact pattern applies so long as the growth of the portfolio exceeds the cost of leverage.

Resetting, therefore, is a necessary component of maintaining leverage. On the one hand, we have daily resets, which keeps our leverage proportion constant. On the other hand, we have “never reset,” which will decay the leverage proportion over time (assuming the portfolio grows faster than the cost of leverage). There are, of course, shades of gray as well. Consider a 1-year reset:

Source: CSI. Calculations by Newfound Research. Assumes portfolio applies 100% notional leverage applied to SPDR S&P 500 ETF (“SPY”) at inception of ETF and reset every 252-days thereafter. Assumes zero cost of leverage.

Note that in 2008, the debt proportion of our balance sheet spiked up to nearly 90% of our capital. What happened? This is reset timing risk. On 4/2008, the portfolio reset, borrowing $92,574 against our equity of $92,574. Over the next year, the market fell approximately 39%. Our total assets tumbled from $185,148 to $114,753 and we still owed the initial $92,574 we borrowed. Thus, our actual equity over this period fell an astounding -76.7%.

(It is worth pointing out that if we had considered a “never reset” portfolio that started on 4/2008, we’d have the same result.)

Frequent readers of our commentary may be wondering, “can this reset timing risk be controlled with overlapping portfolios just like other timing risks?” Yes … ish. On the one hand, there is not a whole lot we can do about the drawdown itself: 100% notional leverage plus a 37% drawdown means you’re going to have a bad time. Where overlapping portfolios can help is in ensuring that resets do not necessarily occur at the worst possible point (e.g. the bottom of the drawdown) and lock in losses.

As a general rule, we probably don’t want to apply N-times exposure over a time frame an asset class can experience a return of -1/N%. For example, if we want 2x equity exposure, we want to make sure we reset our leverage exposure well before equities have a chance to lose 50% (1/2). Similarly, if we want 3x exposure, we need to reset well before we can lose 33.3% (1/3).

So, Are They Evil or What?

We would argue that volatility decay takes the blame when it is not actually the culprit. Volatility decay is nothing more than the math of compounding returns: it happens whether you are levered or not.

The danger of most levered ETFs is more easily explained. If I told you I was going to take your investment, use it as collateral to gain 100% notional exposure to equities, and then invest that collateral in equities as well – an asset class than can easily lose 50% –what would you say? When put that way, it sounds a little nuts. It really isn’t much more complicated than that.

The reset effect really just introduces a few more nuanced wrinkles. The more frequently we reset, the less risk we run of going bust, as we take risk off the table as our debt-to-equity ratio climbs. That’s how we can avoid complete ruin with 100% leverage in an asset class that falls more than 50%.

On the other hand, the more frequently we reset, the closer we keep the portfolio to the target volatility level, increasing the drag from short-term mean reversion.

We’ve said it before and we’ll say it again: risk cannot be destroyed, only transformed.

But, these things might have their use yet…

Levered ETFs in a Portfolio

Held as 100% of our wealth, a 2X daily reset equity ETF may not be too prudent. In the context of a portfolio, however, things change.

Consider, for example, using 50% of our capital to invest in a 2x equity exposure and the remaining 50% to invest in bonds. In effect, we have created 150% exposure to a 67/33 stock/bond mixture. For example, we could hold 50% of our capital in the ProShares Ultra S&P 500 ETF (“SSO”) and 50% in the iShares Core U.S. Bond ETF (“AGG”).

To understand the portfolio exposure, we have to look under the hood. What we really have, in aggregate, is: 100% equity exposure and 50% bond exposure. To get to 150% total notional exposure, we have to borrow an amount equal to 50% of our starting capital. Indeed, at the portfolio level, we cannot differentiate whether we are using that 50% borrowing to lever up stocks, bonds, or the entire mixture!

In this context, levered ETFs become a lot more interesting.

The risk, of course, is in the resets. To really do this, we’d have to rebalance our portfolio back to a 50/50 mix of the 2x levered equity exposure and bonds on a daily basis. If we could achieve that, we’d have built a daily reset 1.5x 66/33 portfolio.

More realistically, investors may be able to rebalance their portfolio quarterly. How far does that deviate from the daily rebalance? We plot the two below.

Source: CSI. Calculations by Newfound Research. Returns for the Daily Rebalance and Quarterly Rebalance portfolios are backtested and hypothetical. Returns are gross of all fees except underlying ETF expense ratios. Returns assume the reinvestment of all distributions. Cost of leverage is assumed to be equal to the return of a 1-3 Year U.S. Treasury ETF (“SHY”). Past performance is not indicative of future results. The Daily Rebalance portfolio assumes 50% exposure to a hypothetical index providing 2x daily exposure of the SPDR S&P 500 ETF (“SPY”) and 50% exposure to the iShares US Core Bond ETF (“AGG”) and is rebalanced daily. The Quarterly Rebalance portfolio assumes the same exposure, but rebalances quarterly.

Indeed, for aggressive investors, a levered equity ETF mixed with bond exposure may not be such a bad idea after all. However – and to steal a line from our friends at Toroso Asset Management – levered ETFs are likely “buy-and-adjust” vehicles, not buy-and-hold. The frequency of adjusting, and the cost of doing so, will play an important role in results.

A Particular Application with Alternatives

Where levered ETFs may be particularly interesting is in the context of liquid alternatives.

In the past, we have said that many liquid alternatives, especially those offered as ETFs, have a volatility problem. Namely, they just don’t have enough volatility to be interesting.

Traditionally, allocating to a liquid alternative requires us removing capital from one investment to “make room” in our portfolio, which creates an implicit hurdle rate. If, for example, we sell a 5% allocation of our equity portfolio to make room for a merger arbitrage strategy, not only do we have to expect that the strategy can create alpha beyond its fees, but it also has to be able to deliver a long-term return that is at least in the same neighborhood of the equity risk premium. Otherwise, we should be prepared to sacrifice return for the benefit of diversification.

One solution to this problem with lower volatility alternatives is to fund their allocation by selling bonds instead of stocks. Bonds, however, are often our stable ballast in the portfolio. Regardless of how poorly we expect core fixed income to perform over the next decade, we have a high degree of certainty in their return. Asking us to sell bonds to buy alternatives is often asking us to throw certainty out the window.

By way of example, consider the Reality Shares DIVS ETF (“DIVY”). We wrote about this ETF back in August 2016 and think it is a particularly compelling story. The ETF buys the floating leg of dividend swaps, which in theory captures a premium from investors who want to insure their dividend growth exposure in the S&P 500.

For example, if the swap is priced such that the expected growth rate of S&P 500 dividends is 5% over the next year, but the realized growth is 6%, then the floating leg keeps the extra 1%. The “insurance” aspect comes in during years where realized growth is below the expected rate, and the floating leg has to cover the difference. To provide this insurance, the floating leg demands a premium.

A dividend swap of infinite length should, in theory, converge to the equity risk premium. Short-term dividend swaps (e.g. 1-year), however, seem to exhibit a potentially unique risk premium, making them an interesting diversifier within a portfolio.

While DIVY has performed well since inception, finding a place for it in a portfolio can be difficult. With low volatility, we have two problems. First, for the fund to make a meaningful difference, we need to make sure that our allocation is large enough. Second, we likely have to slot DIVY in for a low volatility asset – like core fixed income – so that we make sure that we are not creating an unreasonable hurdle rate for the fund.

Levered ETFs may allow us to have our cake and eat it too.

For example, ProShares offers an Ultra 7-10 Year Treasury ETF (“UST”), which provides investors with 2x daily return exposure to a 7-10 year U.S. Treasury portfolio. For investors who hold a large portfolio of intermediate-term U.S. Treasuries, they could potentially sell some exposure and replace it with 50% UST and 50% DIVY.

As before, the question of “when to reset” arises: but even with a quarterly [rebalance, we think it is a compelling concept.

Source: CSI. Calculations by Newfound Research. Returns for the S&P 500 Dividend Swaps Index and 50% 2x Daily 7-10 Year US Treasuries / 50% Dividend Swap Index portfolios are hypothetical and backtested. Returns are gross of all fees except underlying ETF expense ratios. Returns assume the reinvestment of all distributions. Cost of leverage is assumed to be equal to the return of a 1-3 Year U.S. Treasury ETF (“SHY”). Past performance is not indicative of future results. The 50% 2x Daily 7-10 Year US Treasuries / 50% Dividend Swap Index assumes a quarterly rebalance.

Conclusion

Leverage is a tool. When used prudently, it can help investors potentially achieve much more risk-efficient returns. When used without care, it can lead to complete ruin.

For many investors who do not have access to traditional means of leverage, levered ETFs represent one potential opportunity. While branded as a “trading vehicle” instead of a buy-and-hold exposure, we believe that if prudently monitored, levered ETFs can be used to help free up capital within a portfolio to introduce diversifying exposures.

Beyond the leverage itself, the daily reset process can introduce risk. While it helps maintain the leverage ratio – reducing risk after losses – it also re-ups our risk after gains and generally will increase long-term volatility drag from mean reversion.

This daily reset means that when used in a portfolio context, we should, ideally, be resetting our entire portfolio daily. In practice, this is impossible (and likely imprudent, once costs are introduced) for many investors. Thus, we introduce some tracking error within the portfolio.

We should note that there are monthly-reset leverage products that may partially alleviate this problem. For example, PowerShares and ETRACS offer monthly reset products and iPath offers “no reset” leverage ETNs that simply apply a leverage level at inception and never reset until the ETN matures.

Perhaps the most glaring absence in this commentary has been a discussion of fees. Levered ETP fees vary wildly, ranging from as low as 0.35% to as high as 0.95%. When considering using a levered ETP in a portfolio context, this fee must be added to our hurdle rate. For example, if our choice is between just holding the iShares 7-10 Year U.S. Treasury ETF (“IEF”) at 0.15%, or 50% in the ProShares Ultra 7-10 Year Treasury ETF (“UST”) and 50% in the Reality Shares DIVS ETF (“DIVY”) for a combined cost of 0.93%, the extra 0.78% fee needs to be added to our hurdle rate calculation.

Nevertheless, as fee compression marches on, we would expect fees in levered ETFs to come down over time as well, potentially making these products interesting for more than just expressing short-term trading views.

Month: January 2018

Timing Bonds with Value, Momentum, and Carry

Summary­­

Historically Speaking, This is a Bad Idea

This Might Now be a Good Idea

Timing Bonds with Value

Timing Bonds with Momentum

Timing Bonds with Carry

Building a Portfolio of Strategies

Conclusion

Quantifying Timing Luck

Summary­­

What is “Timing Luck?”

Is There a Solution to Timing Luck?

The Setup

Differences between the Discrete and Continuous Portfolios

Solving for Timing Luck

What is Corr(D,Q)?

Estimating Timing Luck in our Stock/Cash Tactical Strategy

Conclusion

Factor Investing & The Bets You Didn’t Mean to Make

Summary­­

Value Investing with Countries

The Unintended Bet

Conclusion

Levered ETFs for the Long Run?

Summary­­

Wait, Aren’t Levered ETFs Dangerous?

So, Are They Evil or What?

Levered ETFs in a Portfolio

A Particular Application with Alternatives

Conclusion

Summary

**This Might Now be a Good Idea**

Summary

Summary

Summary