Category: Weekly Commentary Page 3 of 21

Diversification with Portable Beta

On February 18, 2020

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

This post is available as a PDF download here.

Summary

A long/flat tactical equity strategy with a portable beta bond overlay – a tactical 90/60 portfolio – has many moving parts that can make attribution and analysis difficult.
By decomposing the strategy into its passive holdings (a 50/50 stock/bond portfolio and U.S. Treasury futures) and active long/short overlays (trend equity, bond carry, bond momentum, and bond value), we can explore the historical performance of each component and diversification benefits across each piece of the strategy.
Using a mean-variance framework, we are also able to construct an efficient frontier of the strategy components and assess the differences between the optimal portfolio and the tactical 90/60.
We find that the tactical 90/60 is relatively close to the optimal portfolio for its volatility level and that its drawdown risk profile is close to that of an unlevered 60/40 portfolio.
By utilizing a modest amount of leverage and pairing it will risk management in both equities and bonds, investors may be able to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk.

Portable beta strategies seek to enhance returns by overlaying an existing portfolio strategy with complementary exposure to diversifying asset classes and strategies. In overlaying exposure on an existing portfolio strategy, portable beta strategies seek to make every invested dollar work harder. This idea can create “capital efficiency” for investors, freeing up dollars in an investor’s portfolio to invest in other asset classes or investment opportunities.

At Newfound, we focus on managing risk. Trend following – or absolute momentum – is a key approach we employ do this, especially in equities. Trend equity strategies are a class of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following.

We wrote previously how a trend equity strategy can be decomposed into passive and active components in order to isolate different contributors to performance. There is more than one way to do this, but in the most symmetric formulation, a “long/flat” trend equity strategy (one that that either holds equities or cash; i.e. does not short equities) can be thought of as a 100% passive allocation to a 50/50 portfolio of stocks and cash plus a 50% overlay allocation to a long/short trend equity strategy that can move between fully short and fully long equities. This overlay component is portable beta.

We have also written previously about how a portable beta overlay of bonds can be beneficial to trend equity strategies – or even passive equity investments, for that matter. For example, 95% of a portfolio could be invested in a trend equity strategy, and the remaining 5% could be set aside as collateral to initiate a 60% overlay to 10-year U.S. Treasury futures. This approximates a 60/40 portfolio that is leveraged by 50%

Source: Newfound. Allocations are hypothetical and for illustrative purposes only.

Since this bond investment introduces interest rate risk, we have proposed ways to manage risk in this specific sleeve using factors such as value, carry, and momentum. By treating these factors as fully tactical long/short portfolios themselves, if we hold them in equal weight, we can also break down the tactical U.S. Treasury futures overlay into active and passive components, with a 30% passive position in U.S. Treasury futures and 10% in each of the factor-based strategies.

Source: Newfound. Allocations are hypothetical and for illustrative purposes only.

When each overlay is fully invested, the portfolio will hold 95% stocks, 5% cash, and 60% U.S. Treasury futures. When all the overlays are fully short, the strategy will be fully invested in cash with no bond overlay position.

While the strategy has not changed at all with this slicing and dicing, we now have a framework to explore the historical contributions of the active and passive components and the potential diversification benefits that they offer.

Diversification Among Components

For the passive portfolio 50/50 stock/cash, we will use a blend of the Vanguard Total U.S. stock market ETF (VTI) and the iShares Short-term Treasury Bond ETF (SHV) with Kenneth French data for market returns and the risk-free rate prior to ETF inception.

For the active L/S Trend Equity portfolio, we will use a long/short version of the Newfound U.S. Trend Equity Index.

The passive 10-year U.S. Treasury futures is the continuous futures contract with a proxy of the 10-year constant maturity Treasury index minus the cash index used before inception (January 2000). The active long/short bond factors can be found on the U.S. Treasuries section of our quantitative signals dashboard, which is updated frequently.

All data starts at the common inception point in May 1957.

As a technical side note, we must acknowledge that a constant maturity 10-year U.S. Treasury index minus a cash index will not precisely match the returns of 10-year U.S. Treasury futures. The specification of the futures contracts state that the seller of such a contract has the right to deliver any U.S. Treasury bond with maturity between 6.5 and 10 years. In other words, buyers of this contract are implicitly selling an option, knowing that the seller of the contract will likely choose the cheapest bond to deliver upon maturity (referred to as the “cheapest to deliver”). Based upon the specification and current interest rate levels, that current cheapest to deliver bond tends to have a maturity of 6.5 years.

This has a few implications. First, when you buy U.S. Treasury futures, you are selling optionality. Finance 101 will teach you that optionality has value, and therefore you would expect to earn some premium for selling it. Second, the duration profile between our proxy index and 10-year U.S. Treasury futures has meaningfully diverged in the recent decade. Finally, the roll yield harvested by the index and the futures will also diverge, which can have a non-trivial impact upon returns.

Nevertheless, we believe that for the purposes of this study, the proxy index is sufficient for broad, directional attribution and understanding.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

The 50/50 Stock/Cash portfolio is the only long-only holding. While the returns are lower for all the other strategies, we must keep in mind that they are all overlays that can add to the 50/50 portfolio rather than simply de-risk and cannibalize its return.

This is especially true since these overlay strategies have exhibited low correlation to the 50/50 portfolio.

The table below shows the full period correlation of monthly returns for all the portfolio components. The equity and bond sub-correlation matrices are outlined to highlight the internal diversification.

Not only do all of the overlays have low correlation to the 50/50 portfolio, but they generally exhibit low cross-correlations. Of the overlays, the L/S bond carry and L/S bond momentum strategies have the highest correlation (0.57), and the L/S bond carry and passive bond overlay have the next highest correlation (0.47).

The bond strategies have also exhibited low correlation to the equity strategies. This results in good performance, both absolute and risk-adjusted, relative to a benchmark 60/40 portfolio and a benchmark passive 90/60 portfolio.

Finding the Optimal Blend

Up to this point, we have only considered the fixed allocations to each of the active and passive strategies outlined at the beginning. But these may not be the optimal holdings.

Using a block-bootstrap method to simulate returns, we can utilize mean-variance optimization to determine the optimal portfolios for given volatility levels.¹ This yields a resampled historical realized efficient frontier.

Plotting the benchmark 60/40, benchmark 90/60, and the tactical 90/60 on this efficient frontier, we see that the tactical 90/60 lies very close to the frontier at about 11.5% volatility. The allocations for the frontier are shown below.

As expected, the lower volatility portfolios hold more cash and the high volatility portfolios hold more equity. For the 9% volatility level, these two allocations match, leading to the full allocation to a 50/50 stock/cash blend as in the tactical 90/60.

The passive allocation to the Treasury futures peaks at about 60%, while the L/S bond factor allocations are generally between 5% and 20% with more emphasis on Value and typically equal emphasis on Carry and Momentum.

The allocations in the point along the efficient frontier that matches the tactical 90/60 portfolio’s volatility are shown below.

In this portfolio, we see a higher allocation to passive equities, a smaller position in the tactical equity L/S, and a larger position in passive Treasury futures. However, given the resampled nature of the process, these allocations are not wildly far away from the tactical 90/60.

The differences in the allocations are borne out in the Ulcer Index risk metric, which quantifies the severity and duration of drawdowns.

The efficient frontier portfolio has a lower Ulcer Index than that of the tactical 90/60 even though their returns and volatility are similar. However, the Ulcer index of the tactical 90/60 is very close to that of the benchmark 60/40.

These differences are likely due to the larger allocation to the tactical equity long/short which can experience whipsaws (e.g. in October 1987), the lower allocation to passive U.S. equities, and the lower allocation to the Treasury overlay.

In an uncertain future, there can be significant risk in relying too much on the past, but having this framework can be useful for gaining a deeper understanding of which market environments benefit or hurt each component within the portfolio and how they diversify each other when held together.

Conclusion

In this research note, we explored diversification in a long/flat tactical equity strategy with a portable beta bond overlay. By decomposing the strategy into its passive holdings (50/50 stock/bond portfolio and U.S. Treasury futures) and active long/short overlays (trend equity, bond carry, bond momentum, and bond value), we found that each of the overlays has historically exhibited low correlation to the passive portfolios and low cross-correlations to each other. Combining all of these strategies using a tactical 90/60 portfolio has led to strong performance on both an absolute and risk-adjusted basis.

Using these strategy components, we constructed an efficient frontier of portfolios and also found that the “intuitive” tactical 90/60 portfolio that we have used in much of our portable beta research is close to the optimal portfolio for its volatility level. While this does not guarantee that this portfolio will be optimal over any given time period, it does provide evidence for the robustness of the multi-factor risk-managed approach.

Utilizing portable beta strategies can be an effective way for investors to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk. While leverage can introduce risks of its own, relying on diversification and robust risk-management methods (e.g. trend following) can mitigate the risk of large losses.

The fear of using leverage and derivatives may be an uphill battle for investors, and there are a few operational burdens to overcome, but when used appropriately, these tools can make portfolios work harder and lead to more flexibility for allocating to additional opportunities.

If you are interested in learning how Newfound applies the concepts of tactical portable beta to its mandates, please reach out (info@thinknewfound.com).

Payoff Diversification

By Corey Hoffstein

On February 10, 2020

In Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

At Newfound, we adopt a holistic view of diversification that encompasses not only what we invest in, but also how and when we make those investment decisions.
In this three-dimensional perspective, what is correlation-based, how is payoff-based, and when is opportunity-based.
In this piece, we provide an example of what we mean by payoff-based diversification, using a simple strategically rebalanced portfolio and a naïve momentum strategy.
We find that the strategically rebalanced portfolio exhibits a payoff structure that is concave in nature whereas the momentum-based approach exhibits a convex profile.
By combining the two approaches – being careful in how we size positions – we can develop a portfolio that is less sensitive to the co-movement of underlying assets.

At Newfound, we embrace a holistic view of diversification that covers not just what we invest in, but also how and when we make those decisions. What is the diversification most investors are well-versed in and covers traditional, correlation-based diversification between securities, assets, macroeconomic factors, and geographic regions.

We identify when as “opportunity diversification” because it captures the opportunities that are available when we make investment decisions. This often goes overlooked in public markets (which is why we spend so much time writing about rebalance timing luck) but is well acknowledged in private markets where investors often allocate to multiple fund “vintages” to create diversification.

How is generally easy to understand, but sometimes difficult to visualize. We call it “payoff diversification” to acknowledge that when viewed through he appropriate lens, every investment style creates a particular shape. For example, when the return of a call option is plotted against the return of the underlying security, it generates a hockey-stick-like payoff profile.

In this short research note, we are going to demonstrate the payoff profiles of a strategically allocated portfolio and a naïve momentum strategy. We will then show that by combining these two approaches we can create a portfolio that exhibits significantly less sensitivity to the co-movement of underlying assets.

The Payoff Profile of a Strategic Portfolio

Few investors consider a strategically allocated portfolio to be an active strategy. And it isn’t; at least not until we introduce rebalancing. Once we institute a process to systematically returning our drifted weights back to their original fixed mix, we create a strategy and a corresponding payoff profile.

But what does this payoff profile look like? As an example, consider a U.S. 60/40 portfolio comprised of broad U.S. equities and a constant maturity 10-year U.S. Treasury index. If equities out-perform bonds, our equity allocation will increase and our bond allocation will decrease. If equities continue to out-perform bonds, we will benefit relative to our original policy weights. Similarly, if equities under-perform bonds, then our relative equity allocation will decrease. Again, should they continue to underperform, we are well positioned.

However, if we were to rebalance back to our original 60/40 allocation, we would eliminate the opportunity to benefit from the continuation of the relative performance.

On the other hand, consider the case where equities out-perform, our relative allocation to equities increases due to drift, and then equities subsequently under-perform. Now allowing drift has hurt us and we would have been better off rebalancing.

We can visualize this relationship by plotting the return spread between stocks and bonds (x-axis) versus the return spread between a monthly-rebalanced portfolio and a buy-and-hold (drifted) approach (y-axis) over rolling 1-year periods.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The rebalanced variation is rebalanced at the end of each month whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

What we can see is a concave payoff function. When equities significantly out-perform bonds (far right side of the graph), the rebalanced portfolio under-performs the drifted portfolio. Similarly, when bonds significantly out-perform equities (far left side of the graph), the rebalanced portfolio under-performs the drifted portfolio. When the return spread between stocks and bonds is small– a case likely to be more indicative of mean-reversion than positive autocorrelation in the spread – we can see that rebalancing actually generates a positive return versus the drifted portfolio.

Those versed in options will note that this payoff looks incredibly similar to a 1-year strangle sold on the spread between stocks and bonds and struck at 0%. The seller captures the premium when the realized spread remains small but loses money when the spread is more extreme.

The Payoff Profile of Naïve Momentum Following

We can now take the exact same approach to evaluating the payoff profile of a naïve momentum strategy. Each month, the strategy will simply invest in either stocks or bonds based upon whichever had the highest trailing 12-month return

As this approach is explicitly trying to capture auto-correlation in the return spread between stocks and bonds, we would expect to see almost mirror behavior to the payoff profile we saw with strategic rebalancing.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

While the profile may not be as tidy as before, we can see a convex payoff profile that tends to profit when the return spread is more extreme and lose money when the spread is narrow. Again, those familiar with options will recognize this as similar to the payoff of a 1-year straddle based upon the return spread between stocks and bonds. The buyer pays a premium but captures the spread when it is extreme.

Note, however, the scale of the y-axis. Whereas the payoff profile for the rebalanced portfolio was between -3.0% and +2.0%, the payoff profile for this momentum approach is much larger, ranging between -30.0% and 40.0%.

Creating Payoff Diversification

We have seen that whether we strategically rebalance or adopt a momentum-based approach, both approaches create a payoff profile that is sensitive to the return spread in underlying assets. But what if we do not want to take such a specific payoff bet? One simple answer is diversification.

If we allocate to both the strategically rebalanced portfolio and the naïve momentum portfolio, we will realize both their payoff profiles simultaneously. As their profiles are close mirrors of one another, we may be able to achieve a more neutral outcome.

We have to be careful, however, as to size the allocations appropriate. Recall that the payoff profile of the strategically rebalanced portfolio was approximately 1/10^th the size of the naïve momentum strategy. For both profiles to contribute equally, we would want to allocate approximately 90% of our capital to the strategic rebalancing strategy and 10% of our capital to the momentum strategy.

Below we plot the payoff structure of such a mix.

Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index. The mixed portfolio is rebalanced monthly and is a 90% allocation to a rebalanced 60/40 and a 10% allocation to a naïve momentum strategy; whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results.

We can see that diversifying how we make decisions results in a payoff structure that is far more neutral to the co-movement of underlying securities in the portfolio. The holy grail, of course, is not just to find strategies whose combination neutralizes sensitivity to the spread in returns, but actually creates a higher likelihood of positive outcomes in all environments.

Conclusion

In this research note, we aimed to provide greater insight into the idea of payoff diversification, the how in our what-how-when diversification framework. To do so, we explored two simple examples: a strategically rebalanced 60/40 allocation and a naïve momentum strategy.

We found that the strategically rebalanced portfolio generates a payoff profile that is convex with respect to the spread in returns between stocks and bonds. In general, the larger the spread, the more likely that rebalancing generates a negative return versus a buy-and-hold approach. Conversely, the smaller the spread, the more likely that rebalancing generates a positive return.

The naïve momentum strategy – which simply bought the asset with the greatest prior 12-month returns – exhibited a convex profile. When the return spread between stocks and bonds was large, the naïve momentum strategy was more likely to out-perform buy-and-hold. Conversely, when the return spread was small, the naïve momentum strategy tended to under-perform.

Importantly, the magnitudes of the payoffs are significantly different, with the naïve momentum strategy generating returns nearly 10x larger than strategic rebalancing in the tails. This difference has important implications for strategy sizing, and we find a portfolio mixture of 90% strategic rebalancing and 10% naïve momentum does a reasonably good job of neutralizing portfolio payoff sensitivity to the spread in stock and bond returns.

Can Managed Futures Offset Equity Losses?

By Corey Hoffstein

On February 3, 2020

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

This post is available as a PDF download here.

Summary

Managed futures strategies have historically provided meaningful positive returns during left-tail equity events. Yet as a trading strategy, this outcome is by no means guaranteed.
While trend following is “mechanically convex,” the diverse nature of managed futures programs may actually prevent the strategy from offsetting equity market losses.
We generate a large number of random managed futures strategies by varying the asset classes included. We find that more diverse strategies have, historically, provided a larger offset to negative equity events.
This curious outcome appears to be caused by two effects: (1) diversification allows for increased total notional exposure; and (2) past crises saw coincidental trends across multiple markets simultaneously.
Therefore, for investors trying to offset equity market losses, an allocation to managed futures requires believing that future crises will be marked by a large number of simultaneous trends across multiple assets.
Less diversified strategies – such as just trading S&P 500 futures contracts – appear to work if the volatility target is removed.

Shortly after the 2008 crisis, the appetite for risk management strategies exploded. At the forefront of this trend was managed futures, which had already proven itself in the dot-com fallout. With the Societe Generale Trend Index¹ returning 20.9% in 2008, the evidence for CTAs to provide “crisis alpha”² seemed un-debatable. AUM in these strategies sky-rocketed, growing from $200 billion in 2007 to approximately $325 billion by 2012.

Source: http://managedfuturesinvesting.com

Subsequent performance has, unfortunately, been lack-luster. Since 12/31/2011, the SG Trend Index has returned just 14.2% compared to the S&P 500’s 200.8% total return. While this is an unfair, apples-to-oranges comparison, it does capture the dispersion the strategy has exhibited to the benchmark most investors measure performance against during a bull market.

Furthermore, the allocation to managed futures had to come from somewhere. If investors reduced exposure to equities to introduce managed futures, the spread in performance captures the opportunity cost of that decision. There is hope yet: if the S&P 500 fell 50% over the next year, managed futures would have to return just 32% for their full-period performance (2011-2020) to equalize.

Yet how certain are we that managed futures would necessarily generate a positive return in an S&P 500 left-tail environment? Hurst, Ooi, and Pedersen (2017)³ find that managed futures have generated anything from flat to meaningfully positive results during the top 10 largest drawdowns of a 60/40 portfolio since the late 1800s. This evidence makes a strong empirical case, but we should acknowledge the N=10 nature of the data.

Perhaps we can lean into the mechanically convex nature of trend following. Trend following is a close cousin to the trading strategy that delta-hedges a strangle, generating the pay-off profile of a straddle (long an at-the-money put and call). Even without an anomalous premium generated by autocorrelation in the underlying security, the trading strategy itself should – barring trading frictions – generate a convex payoff.

Yet while mechanical convexity may be true on a contract-by-contract basis, it is entirely possible that the convexity we want to see emerge is diluted by trades across other contracts. Consider the scenario where the S&P 500 enters a prolonged and significant drawdown and our managed futures strategy goes short S&P 500 futures contract. While this trade may generate the hedge we were looking for, it’s possible that it is diluted by trades on other contracts such as wheat, the Japanese Yen, or the German Bund.

When we consider that many investors have portfolios dominated by equity risk (recall that equities have historically contributed 90% of the realized volatility for a 60/40 portfolio), it is possible that too much breadth within a managed futures portfolio could actually prevent it from providing negative beta during left-tail equity events.

Replicating Managed Futures

We begin our study by first replicating a generic trend-following CTA index. We adopt an ensemble approach, which is effectively equivalent to holding a basket of managers who each implement a trend-following strategy with a different model and parameterization.

Specifically, we assume each manager implements using the same 47 contracts that represent a diversified basket of equities, rates, commodities, and currencies.⁴

We implement with three different models (total return, price-minus-moving-average, and dual-moving-average-cross) and five potential lookback specifications (21, 42, 84, 168, and 336 days) for a total of 15 different implementations.

Each implementation begins by calculating an equal-risk contribution (“risk parity”) portfolio. Weights for each contract are then multiplied by their trend signal (which is simply either +1 or -1).

The weights for all 15 implementations are then averaged together to generate our index weights. Notional exposure of the aggregate weights is then scaled to target a 10% annualized volatility level. We assume that the index is fully collateralized using the S&P U.S. Treasury Bill Index.

Below we plot our index versus the SG Trend Index. The correlation of monthly returns between these two indices is 75% suggesting that our simple implementation does a reasonable job approximating the broad trend-following style of CTAs. We can also see that it captures the salient features of the SG Trend Index, including strong performance from 2001-2003, Q4 2008 and Q1 2009, and the 2014-2015 period. We can also see it closely tracks the shape the SG Trend Index equity curve from 2015 onward in all its meandering glory.

Source: Stevens Analytics. 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. These results do not reflect the returns of any strategy managed by Newfound Research.

Convexity versus Diversification

To explore the impact of diversification in managed futures versus convexity exhibited against the S&P 500, we will create a number of managed futures strategies and vary the number of contracts included. As we are attempting to create a convex payoff against the S&P 500, the S&P 500 futures contract will always be selected.

For example, a 2-contract strategy will always include S&P 500 futures, but the second contract could be 10-year U.S. Treasuries, the Nikkei, the Australian Dollar, Oil, or any of the other 42 futures contracts. Once selected, however, that pair defines the strategy.

For 2-, 4-, 8-, 16-, and 32- contract systems, we generate the performance of 25 randomly selected strategies. We then generate scatter plots with non-overlapping 6-month returns for the S&P 500 on the x-axis and non-overlapping 6-month returns for the managed futures strategies on the y-axis.⁵ We then fit a 2^nd-degree polynomial line to visualize the realized convexity.

(Note that for the single contract case – i.e. just the S&P 500 futures contract – we plot overlapping 6-month returns.)

Source: Stevens Analytics and Sharadar. 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. These results do not reflect the returns of any strategy managed by Newfound Research.

There are two particularly interesting artifacts to note.

First, as the number of contracts goes up, the best-fit model turns from a “smile” to a “smirk,” suggesting that diversification dilutes positive convexity relationships with the S&P 500. This outcome should have been expected, as we generally know how managed futures has done over the 20-year period we’re examining. Namely, managed futures did quite well offsetting losses in 2000-2003 and 2008-2009, but has failed to participate in the 2010s.

Perhaps more interestingly, however, is the increase in left-tail performance of managed futures, climbing from 20% when just trading the S&P 500 futures contract to 150% in the 32-contract case. The subtle reason here is diversification’s impact on total notional exposure.

Consider this trivial example: Asset A and Asset B have constant 10% volatility and are uncorrelated with one another. As they are uncorrelated, any combination of these assets will have a volatility that is less than 10%. Therefore, if we want to achieve 10%, we need to apply leverage. In fact, a 50-50 mix of these assets requires us to apply 1.41x leverage to achieve our volatility target, resulting in 70.7% exposure to each asset.

As a more concrete example, when trading just the S&P 500 futures contract, achieving 10% volatility position in 2008 requires diluting gross notional exposure to just 16%. For the full, 47-contract model, gross notional exposure during 2008 dipped to 90% at its lowest point.

Now consider that trend following tends to transform the underlying distributions of assets to generate positive skewness. Increasing leverage can help push those positive trades even further out in the tails.

But here’s the trade-off: the actual exposure to S&P 500 futures contracts, specifically, still remains much, much higher in the case where we’re trading it alone. In practice, the reason the diversified approach was able to generate increased returns during left-tail equity events – such as 2008 – is due to the fact correlations crashed to extremes (both positive and negative) between global equity indices, rates, commodities, and currencies. This allowed the total notional exposure of directionally similar trades (e.g. short equities, long bonds, and short commodities in 2008) to far exceed the total notional exposure achieved if we were just trading the S&P 500 futures contract alone.

Source: Stevens Analytics. Calculations by Newfound Research.

Our confidence in achieving negative convexity versus equity left-tail events, therefore, is inherently tied to our belief that we will see simultaneously trends across a large number of assets during such environments.

Another interpretation of this data is that because negative trends in the S&P 500 have historically coincided with higher volatility, a strategy that seeks to trade just the S&P 500 futures with constant volatility will lose convexity in those tail events. An alternative choice is to vary the volatility of the system to target the volatility of the S&P 500, whose convexity profile we plot below.

This analysis highlights a variety of trade-offs to consider:

What, specifically, are we trying to create convexity against?
Can diversification allow us to increase our notional exposure?
Will diversification be dilutive to our potential convexity?

Perhaps, then, we should consider approaching the problem from another angle: given exposure to managed futures, what would be a better core portfolio to hold? Given that most managed futures portfolios start from a risk parity core, the simplest answer is likely risk parity.

As an example, we construct a 10% target volatility risk parity index using equity, rate, and commodity contracts. Below we plot the convexity profile of our managed futures strategy against this risk parity index and see the traditional “smile” emerge. We also plot the equity curves for the risk parity index, the managed futures index, and a 50/50 blend. Both the risk parity and managed futures indices have a realized volatility of level of 10.8%; the blended combination drops this volatility to just 7.6%, achieving a maximum drawdown of just -10.1%.

Conclusion

Managed futures have historically generated significant gains during left-tail equity events. These returns, however, are by no means guaranteed. While trend following is a mechanically convex strategy, the diversified nature of most managed futures programs can potentially dilute equity-crisis-specific returns.

In this research note, we sought to explore this concept by generating a large number of managed futures strategies that varied in the number of contracts traded. We found that increasing the number of contracts had two primary effects: (1) it reduced realized convexity from a “smile” to a “smirk” (i.e. exhibited less up-side participation with equity markets); and (2) meaningfully increased returns during negative equity markets.

The latter is particularly curious but ultimately the byproduct of two facts. First, increasing diversification allows for increased notional exposure in the portfolio to achieve the same target volatility level. Second, during past crises we witnessed a large number of assets trending simultaneously. Therefore, while increasing the number of contracts reduced notional exposure to S&P 500 futures specifically, the total notional exposure to trades generating positive gains during past crisis events was materially higher.

While the first fact is evergreen, the second may not always be the case. Therefore, employing managed futures specifically as a strategy to provide offsetting returns during an equity market crisis requires the belief that a sufficient number of other exposures (i.e. equity indices, rates, commodities, and currencies) will be exhibiting meaningful trends at the same time.

Given its diversified nature, it should come as no surprise that managed futures appear to be a natural complement to a risk parity portfolio.

Investors acutely sensitive to significant equity losses – e.g. those in more traditional strategic allocation portfolios – might therefore consider strategies designed more specifically with such environments in mind. At Newfound, we believe that trend equity strategies are one such solution, as they overlay trend-following techniques directly on equity exposure, seeking to generate the convexity mechanically and not through correlated assets. When overlaid with U.S. Treasury futures – which have historically provided a “flight-to-safety” premium during equity crises – we believe it is a particularly strong solution.

Should I Stay or Should I Growth Now?

By Corey Hoffstein

On January 21, 2020

In Value, Weekly Commentary

This post is available as a PDF download here.

Summary

Naïve value factor portfolios have been in a drawdown since 2007.
More thoughtful implementations performed well after 2008, with many continuing to generate excess returns versus the market through 2016.
Since 2017, however, most value portfolios have experienced a steep drawdown in their relative performance, significantly underperforming glamour stocks and the market as a whole.
Many investors are beginning to point to the relative fundamental attractiveness of value versus growth, arguing that value is well poised to out-perform going forward.
In this research note, we aim to provide further data for the debate, constructing two different value indices (a style-box driven approach and a factor-driven approach) and measuring the relative attractiveness of fundamental measures versus both the market and growth stocks.

“Should I stay or should I go now?
If I go, there will be trouble
And if I stay it will be double”

— The Clash

It is no secret that quantitative value strategies have struggled as of late. Naïve sorts – like the Fama-French HML factor – peaked around 2007, but most quants would stick their noses up and say, “See? Craftsmanship matters.” Composite metrics, industry-specific scoring, sector-neutral constraints, factor-neutral constraints, and quality screens all helped quantitative value investors stay in the game.

Even a basket of long-only value ETFs didn’t peak against the S&P 500 until mid-2014.

Source: Sharadar. 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 Value ETF basket is an equal-weight portfolio of FVAL, IWD, JVAL, OVLU, QVAL, RPV, VLU, and VLUE, with each ETF being included when it is first available. Performance of the long/short portfolio is calculated as the monthly return of the Value ETF Basket minus the monthly return of the S&P 500 (“SPY”).

Many strategies were able to keep the mojo going until 2016 or so. But at that point, the wheels came off for just about everyone.

A decade of under-performance for the most naïve approaches and three-plus years of under-performance for some of the most thoughtful has many people asking, “is quantitative value an outdated idea? Should we throw in the towel and just buy growth?”

Of course, it should come as no surprise that many quantitative value managers are now clamoring that this is potentially the best time to invest in value since the dot-com bubble. “No pain, no premium,” as we like to say.

Nevertheless, the question of value’s attractiveness itself is muddied for a variety of reasons:

How are we defining value?
Are we talking about long/short factors or long-only implementations?
Are we talking about the style-box definition or the factor definition of value?

By no means will this commentary be a comprehensive evaluation as to the attractiveness of Value, but we do hope to provide some more data for the debate.

Replicating Style-Box Growth and Value

If you want the details of how we are defining Growth and Value, read on. Otherwise, you can skip ahead to the next section.

Morningstar invented the style box back in the early 1990s. Originally, value was simply defined based upon price-to-book and price-to-earnings. But somewhere along the line, things changed. Not only was the definition of value expanded to include more metrics, but growth was given an explicit set of metrics to quantify it, as well.

The subtle difference here is rather than measuring cheap versus expensive, the new model more explicitly attempted to capture value versus growth. The problem – at least in my opinion – is that the model makes it such that the growth-iest fund is now the one that simultaneously ranks the highest on growth metrics and the lowest on value metrics. Similarly, the value-iest fund is the one that ranks the highest on value metrics and the lowest on growth metrics. So growth is growing but expensive and value is cheap but contracting.

The index providers took the same path Morningstar did. For example, while MSCI originally defined value and growth based only upon price-to-book, they later amended it to include not only other value metrics, but growth metrics as well. S&P Dow Jones and FTSE Russell follow this same general scheme. Which is all a bit asinine if you ask me.¹

Nevertheless, it is relevant to the discussion as to whether value is attractive or not, as value defined by a style-box methodology can differ from value as defined by a factor methodology. Therefore, to dive under the hood, we created our own “Frankenstein’s style-box” by piecing together different components of S&P Dow Jones’, FTSE Russell’s, and MSCI’s methodologies.

The parent universe is the S&P 500.
Growth metrics are 3-year earnings-per-share growth, 3-year revenue-per-share growth, internal growth rate², and 12-month price momentum.³
Value metrics are book-to-price⁴, earnings-to-price⁵, free-cash-flow-to-price, and sales-to-enterprise-value⁶.
Metrics are all winsorized at the 90^th percentile.
Z-scores for each Growth and Value metric are calculated using market-capitalization weighted means and standard deviations.
An aggregate Growth and Value score is calculated for each security as the sum of the underlying style z-scores.

From this point, we basically follow MSCI’s methodology. Each security is plotted onto a “style space” (see image below) and assigned value and growth inclusion factors based upon the region it falls into. These inclusion factors represent the proportion of a security’s market cap that can be allocated to the Value or Growth index.

Securities are then sorted by their distance from the origin point. Starting with the securities that are furthest from the origin (i.e. those with more extreme style scores), market capitalizations are proportionally allocated to Value and Growth based upon their inclusion factors. Once one style hits 50%, the remaining securities are allocated to the other style regardless of inclusion factors.

Source: MSCI.

The result of this process is that each style represents approximately 50% of the total market capitalization of the S&P 500. The market capitalization for each security will be fully represented in the combination of growth and value and may even be represented in both Value and Growth as a partial weight (though never double counted).

Portfolios are rebalanced semi-annually using six overlapping portfolios.

How Attractive is Value?

To evaluate the relative attractiveness of Growth versus Value, we will evaluate two approaches.

In the first approach, we will make the assumption that fundamentals will not change but prices will revert. In this approach, we will plot the ratio of price-to-fundamental measures (e.g. price-to-earnings of Growth over price-to-earnings of Value) minus 1. This can be thought of as how far price would have to revert between the two indices before valuations are equal.

As an example, consider the following two cases. First, Value has an earnings yield of 2% and Growth has an earnings yield of 1%. In this case, both are expensive (Value has a P/E of 50 and Growth has a P/E of 100), but the price of Value would have to double (or the price of Growth would have to get cut in half) for their valuations to meet. As a second case, Value has an earnings yield of 100% and Growth has an earnings yield of 50%. Both are very cheap, but we would still have to see the same price moves for their fundamentals to meet.

For our second approach, we will assume prices and fundamentals remain constant and ask the question, “how much carry do I earn for this trade?” Specifically, we will measure shareholder yield (dividend yield plus buyback yield) for each index and evaluate the spread.

In both cases, we will decompose our analysis into Growth versus the Market and the Market versus Value to gain a better perspective as to how each leg of the trade is influencing results.

Below we plot the relative ratio for price-to-book, price-to-earnings, price-to-free-cash-flow, and price-to-sales.

Source: Sharadar. Calculations by Newfound Research.

A few things stand out:

The ratio of Growth’s price-to-book versus the S&P 500’s price-to-book appears to be at 2000-level highs. Even the ratio of the S&P 500’s price-to-book versus Value’s price-to-book appears extreme. However, the interpretation of this data is heavily reliant upon whether we believe price-to-book is still a relevant valuation metric. If not, this result may simply be a byproduct of naïve value construction loading up on financials and ignoring technology companies, leading to an artificially high spread. The fact that Growth versus the S&P 500 has far out-stripped the S&P 500 versus Value in this metric might suggest that this result might just be caused Growth loading up on industries where the market feels book value is no longer relevant.
The ratio of price-to-earnings has certainly increased in the past year for both Growth versus the S&P 500 and the S&P 500 versus Value, suggesting an even larger spread for Growth versus Value. We can see, however, that we are still a far way off from 2000 highs.
Ratios for free cash flows actually look to be near 20-year lows.
Finally, we can see that ratios in price-to-sales have meaningfully increased in the last few years. Interestingly, Growth versus the S&P 500 has climbed much faster than the S&P 500 versus Value, suggesting that moving from Growth to the S&P 500 may be sufficient for de-risking against reversion. Again, while these numbers sit at decade highs, they are still well below 2000-era levels.

Below we plot our estimate of carry (i.e. our return expectation given no change in prices): shareholder yield. Again, we see recent-era highs, but levels still well below 2000 and 2008 extremes.

Source: Sharadar. Calculations by Newfound Research.

Taken all together, value certainly appears cheaper – and a trade we likely would be paid more to sit on than we had previously – but a 2000s-era opportunity seems a stretch.

Growth is not Glamour

One potential flaw in the above analysis is that we are evaluating “Value 1.0” indices. More modern factor indices drop the “not Growth” aspect of defining value, preferring to focus only on valuation metrics. Therefore, to acknowledge that investors today may be evaluating the choice of a Growth 1.0 index versus a modern Value factor index, we repeat the above analysis using a Value strategy more consistent with current smart-beta products.

Specifically, we winsorize earnings yield, free-cash-flow yield, and sales yield and then compute market-cap-weighted z-scores. A security’s Value score is then equal to its average z-score across all three metrics with no mention of growth scores. The strategy selects the securities in the top quintile of Value scores and weights them in proportion to their value-score-scaled market capitalization. The strategy is rebalanced semi-annually using six overlapping portfolios.

Source: Sharadar. Calculations by Newfound Research.

We can see:

In the Value 1.0 approach, moving from Growth appeared much more expensive versus the S&P 500 than the S&P 500 did versus Value. With a more concentrated approach, the S&P 500 now appears far more expensive versus Value than Growth does versus the S&P 500.
Relative price-to-book (despite price-to-book no longer being a focus metric) still appears historically high. While it peaked in Q3 2019, meaningful reversion could still occur. All the same caveats as before apply, however.
Relative price-to-earnings did appear to hit multi-decade highs (excluding the dot-com era) in early 2019. If the prior 6/2016-to-2/2018 reversion is the playbook, then we appear to be halfway home.
Relative price-to-free-cash-flow and price-to-sales are both near recent highs, but both below 2008 and dot-com era levels.

Plotting our carry for this trade, we do see a more meaningful divergence between Value and Growth. Furthermore, the carry for bearing Value risk does appear to be at decade highs; however it is certainly not at extreme levels and it has actually reverted from Q3 2019 highs.

Source: Sharadar. Calculations by Newfound Research.

Conclusion

In this research note, we sought to explore the current value-of-value. Unfortunately, it proves to be an elusive question, as the very definition of value is difficult to pin down.

For our first approach, we build a style-box driven definition of Value. We then plot the relative ratio of four fundamental measures – price-to-book, price-to-earnings, price-to-sales, and price-to-free-cash-flow – of Growth versus the S&P 500 and the S&P 500 versus Value. We find that both Growth and the S&P 500 look historically expensive on price-to-book and price-to-earnings metrics (implying that Value is very, very cheap), whereas just Growth looks particularly expensive for price-to-sales (implying that Value may not be cheap relative to the Market). However, none of the metrics look particularly cheap compared to the dot-com era.

We also evaluate Shareholder Yield as a measure of carry, finding that Value minus Growth reached a 20-year high in 2019 if the dot-com and 2008 periods are excluded.

Recognizing that many investors may prefer a more factor-based definition of value, we run the same analysis for a more concentrated value portfolio. Whereas the first analysis generally pointed to Growth versus the S&P 500 being more expensive than the S&P 500 versus Value trade, the factor-based approach finds the opposite conclusion. Similar to the prior results, Value appears historically cheap for price-to-book, price-to-earnings, and price-to-sales metrics, though it appears to have peaked in Q3 2019.

Finally, the Shareholder Yield spread for the factor approach also appears to be at multi-decade highs ignoring the dot-com and 2008 extremes.

Directionally, this analysis suggests that Value may indeed be cheaper-than-usual. Whether that cheapness is rational or not, however, is only something we’ll know with the benefit of hindsight.

For further reading on style timing, we highly recommend Style Timing: Value vs Growth (AQR). For more modern interpretations: Value vs. Growth: The New Bubble (QMA), It’s Time for a Venial Value-Timing (AQR), and Reports of Value’s Death May Be Greatly Exaggerated (Research Affiliates).

Pursuing Factor Purity

By Corey Hoffstein

On January 6, 2020

In Risk & Style Premia, Weekly Commentary

This post is available as a PDF download here.

Summary

Factors play an important role for quantitative portfolio construction.
How a factor is defined and how a factor portfolio is constructed play important roles in the results achieved.
Naively constructed portfolios – such as most “academic” factors – can lead to latent style exposures and potentially large unintended bets.
Through numerical techniques, we can seek to develop pure factors that provide targeted exposure to one style while neutralizing exposure to the rest.
In this research note, we implement a regression-based and optimized-based approach to achieving pure factor portfolios and report the results achieved.

Several years ago, we penned a note titled Separating Ingredients and Recipe in Factor Investing (May 21, 2018). In the note we discussed why we believe it is important for investors and allocators to consider not just what ingredients are going into their portfolios – i.e. securities, styles, asset classes, et cetera – but the recipe by which those ingredients are combined. Far too often the ingredients are given all the attention, but mistake salt for sugar and I can guarantee that you’re not going to enjoy your cake, regardless of the quality of the salt.

As an example, the note focused on constructing momentum portfolios. By varying the momentum measure, lookback period, rebalance frequency, portfolio construction, weighting scheme, and sector constraints we constructed over 1,000 momentum strategies. The resulting dispersion between the momentum strategies was more-often-than-not larger than the dispersion between generic value (top 30% price-to-book) and momentum (top 30% by 12-1 prior returns).

Yet having some constant definition for factor portfolios is desirable for a number of reasons, including both alpha signal generation and return attribution.

One potential problem for naïve factor construction – e.g. a simple characteristic rank-sort – is that it can lead to time-varying correlations between factors.

For example, below we plot the correlation between momentum and value, size, growth, and low volatility factors. We can see significant time-varying behavior; for example, in 2018 momentum and low volatility exhibited moderate negative correlation, while in 2019 they exhibited significant positive correlation.

The risk of time-varying correlations is that they can potentially leading to the introduction of unintended bets within single- or multi-factor portfolios or make it more difficult to determine with accuracy a portfolio’s sensitivity to different factors.

More broadly, low and stable correlations are preferable – assuming they can be achieved without meaningfully sacrificing expected returns – because they should allow investors to develop portfolios with lower volatility and higher information ratios.

Naively constructed equity styles can also exhibit time-varying correlations to traditional economic factors (e.g. interest rate risk), risk premia (e.g. market beta) or risk factors (e.g. sector or country exposure).

But equity styles can even exhibit time-varying sensitivities to themselves. For example, below we multiply the weights of naively constructed long/short style portfolios against the characteristic z-scores for the underlying holdings. As the characteristics of the underlying securities change, so does the actual weighted characteristic score of the portfolio. While some signals stay quite steady (e.g. size), others can vary substantially; sometimes value is just more value-y.

Source: Sharadar. Calculations by Newfound Research. Factor portfolios self-financing long/short portfolios that are long the top quintile and short the bottom quintile of securities, equally weighted and rebalanced monthly, ranked based upon their specific characteristics (see below).

In the remainder of this note, we will explore two approaches to constructing “pure” factor portfolios that can be used to generate a factor portfolio that neutralizes exposure to risk factors and other style premia.

Using the S&P 500 as our parent universe, we will construct five different factors defined by the security characteristics below:

Value (VAL): Earnings yield, free cash flow yield, and revenue yield.
Size (SIZE): Negative log market capitalization.
Momentum (MOM): 12-1 month total return.
Quality (QUAL): Return on equity¹, negative accruals ratio, negative leverage ratio².
Low Volatility (VOL): Negative 12-month realized volatility.

All characteristics are first cross-sectionally winsorized at the 5^th and 95^th percentiles, then cross-sectionally z-scored, and finally averaged (if a style is represented by multiple scores) to create a single score for each security.

Naively constructed style benchmarks are 100% long the top-ranked quintile of securities and 100% short the bottom-ranked quintile, with securities receiving equal weights.

Factor Mimicry with Fama-MacBeth

Our first approach to designing “pure” factor portfolios is inspired by Fama-MacBeth (1973)³. Fama-MacBeth regression is a two-step approach:

Regress each security against proposed risk factors to determine the security’s beta for that risk factor;
Regress all security returns for a fixed time period against the betas to determine the risk premium for each factor.

Similarly, we will assume a factor model where the return for a given security can be defined as:

Where R_m is the return of the market and RF_j is the return for some risk factor. In this equation, the betas define a security’s sensitivity to a given risk factor. However, instead of using the Fama-MacBeth two-step approach to solve for the factor betas, we can replace the betas with factor characteristic z-scores.

Using these known scores, we can both estimate the factor returns using standard regression⁴ and extract the weights of the factor mimicking portfolios. The upside to this approach is that each factor mimicking portfolios will, by design, have constant unit exposure to its specific factor characteristic and zero exposure to the others.

Here we should note that unless an intercept is added to the regression equation, the factor mimicking portfolios will be beta-neutral but not dollar-neutral. This can have a substantial impact on factors like low volatility (VOL), where we expect our characteristics to be informative about risk-adjusted returns but not absolute returns. We can see the impact of this choice in the factor return graphs plotted below.⁵

Furthermore, by utilizing factor z-scores, this approach will neutralize characteristic exposure, but not necessarily return exposure. In other words, correlations between factor returns may not be zero. A further underlying assumption of this construction is that an equal-weight portfolio of all securities is style neutral. Given that equal-weight portfolios are generally considered to embed positive size and value tilts, this is an assumption we should be cognizant of.

Attempting to compare these mimic portfolios versus our original naïve construction is difficult as they target a constant unit of factor exposure, varying their total notional exposure to do so. Therefore, to create an apples-to-apples comparison, we adjust both sets of factors to target a constant volatility of 5%.

We can see that neutralizing market beta and other style factors leads to an increase in annualized return for value, size, momentum, and quality factors, leading to a corresponding increase in information ratio. Unfortunately, none of these results are statistically significant at a 5% threshold.

Nevertheless, it may still be informative to take a peek under the hood to see how the weights shook out. Below we plot the average weight by security characteristic percentile (at each rebalance, securities are sorted into percentile score bins and their weights are summed together; weights in each bin are then averaged over time).

Before reviewing the weights, however, it is important to recall that each portfolio is designed to capture a constant unit exposure to a style and therefore total notional exposure will vary over time. To create a fairer comparison across factors, then, we scale the weights such that each leg has constant 100% notional exposure.

As we would generally expect, all the factors are over-weight high scoring securities and underweight low scoring securities. What is interesting to note, however, is that the shapes by which they achieve their exposure are different. Value, for example leans strongly into top decile securities whereas quality leans heavily away (i.e. shorts) the bottom decile. Unlike the other factors which are largely positively sloped in their weights, low volatility exhibits fairly constant positive exposure above the 50^th percentile.

What may come as a surprise to many is how diversified the portfolios appear to be across securities. This is because the regression result is equivalent to minimizing the sum of squared weights subject to target exposure constraints.

Source: Sharadar. Calculations by Newfound Research.

While we focused specifically on neutralizing style exposure, this approach can be extended to also neutralize industry / sector exposure (e.g. with dummy variables), region exposure, and even economic factor exposure. Special care must be taken, however, to address potential issues of multi-collinearity.

Pure Quintile Portfolios with Optimization

Liu (2016)⁶ proposes an alternative means for constructing pure factor portfolios using an optimization-based approach. Specifically, long-only quintile portfolios are constructed such that:

They minimize the squared sum of weights;
Their weighted characteristic exposure for the target style is equal to the weighted characteristic exposure of a naïve, equally-weighted, matching quintile portfolio; and
Weighted characteristic exposure for non-targeted styles equals zero.

While the regression-based approach was fast due to its closed-form solution, an optimization-based approach can potentially allow for greater flexibility in objectives and constraints.

Below we replicate the approach proposed in Liu (2016) and then create dollar-neutral long/short factor portfolios by going long the top quintile portfolio and short the bottom quintile portfolio. Portfolios are re-optimized and rebalanced monthly. Unlike the regression-based approach, however, these portfolios do not seek to be beta-neutral.

We can see that the general shapes of the factor equity curves remain largely similar to the naïve implementations. Unlike the results reported in Liu (2016), however, we measure a decline in return among several factors (e.g. value and size). We also find that annualized volatility is meaningfully reduced for all the optimized portfolios; taken together, information ratio differences are statistically indistinguishable from zero.

As with the regression-based approach, we can also look at the average portfolio exposures over time to characteristic ranks. Below we plot these results for both the naïve and optimized Value quintiles. We can see that the top and bottom quintiles lean heavily into top- and bottom-decile securities, while 2^nd, 3^rd, and 4^th quintiles had more diversified security exposure on average. Similar weighting profiles are displayed by the other factors.

Source: Sharadar. Calculations by Newfound Research.

Conclusion

Factors are easy to define in general but difficult to define explicitly. Commonly accepted academic definitions are easy to construct and track, but often at the cost of inconsistent style exposure and the risk of latent, unintended bets. Such impure construction may lead to time-varying correlations between factors, making it more difficult for managers to manage risk as well as disentangle the true source of returns.

In this research note we explored two approaches that attempt to correct for these issues: a regression-based approach and an optimization-based approach. With each approach, we sought to eliminate non-target style exposure, resulting in a pure factor implementation.

Despite a seemingly well-defined objective, we still find that how “purity” is defined can lead to different results. For example, in our regression-based approach we targeted unit style exposure and beta-neutrality, allowing total notional exposure to vary. In our optimization-based approach, we constructed long-only quintiles independently, targeting the same weighted-average characteristic exposure as a naïve, equal-weight factor portfolio. We then built a long/short implementation from the top and bottom quintiles. The results between the regression-based and optimization-based approaches were markedly different.

And, statistically, not any better than the naïve approaches.

This is to say nothing of other potential choices we could make about defining “purity.” For example, what assumptions should we make about industry, sector, or regional exposures?

More broadly, is “purity” even desirable?

In Do Factors Market Time? (June 5, 2017) we demonstrated that beta timing was an unintentional byproduct of naïve value, size, and momentum portfolios and had actually been a meaningful tailwind for value from 1927-1957. Some factors might actually be priced across industries rather than just within them (Vyas and van Baren (2019)⁷). Is the chameleon-like nature of momentum to rapidly tilt towards whatever style, sector, or theme has been recently outperforming a feature or a bug?

And this is all to say nothing of the actual factor definitions we selected.

While impurity may be a latent risk for factor portfolios, we believe this research suggests that purity is in the eye of the beholder.