This post is available as a PDF download here.
Summary
- Recent research suggests that equity factors exhibit positive autocorrelation, providing fertile ground for the application of trend-following strategies.
- In this research note, we ask whether the same techniques can be applied to the active returns of long-only style portfolios.
- We construct trend-following strategies on the active returns of popular MSCI style indices, including Value, Size, Momentum, Minimum Volatility, and Quality.
- A naïve, equal-weight portfolio of style trend-following strategies generates an information ratio of 0.57.
- The interpretation of this result is largely dependent upon an investor’s pre-conceived views of style investing, as the diversified trend-following approach generally under-performs a naïve, equal-weight portfolio of factors except during periods of significant and prolonged factor dislocation.
There have been a number of papers published in the last several years suggesting that positive autocorrelation in factor returns may be exploitable through time-series momentum / trend following. For example,
- Ehsani and Linnainmaa (2017; revised 2019) document that “most factors exhibit positive autocorrelation with the average factor earning a monthly return of 2 basis points following a year of losses but 52 basis points following a positive year.”
- Renz (2018) demonstrates that “risk premiums are significantly larger (lower) following recent uptrends (downtrends) in the underlying risk factor.”
- Gupta and Kelly (2018; revised 2019) find that, “in general, individual factors can be reliably timed based on their own recent performance.”
- Babu, Levin, Ooi, Pedersen, and Stamelos (2019) find “strong evidence of time-series momentum” across the 16 long/short equity factors they study.
While this research focuses mostly only long/short equity factors, it suggests that there may be opportunity for long-only style investors to improve their realized results as well. After all, long-only “smart beta” products can be thought of as simply a market-cap benchmark plus a dollar-neutral long/short portfolio of active bets.
Therefore, calculating the returns due to the active bets taken by the style is a rather trivial exercise: we can simply take the monthly returns of the long-only style index and subtract the returns of the long-only market-capitalization-weighted benchmark. The difference in returns will necessarily be due to the active bets.1
Below we plot the cumulative active returns for five popular equity styles: Value (MSCI USA Enhanced Value), Size (MSCI USA SMID), Momentum (MSCI USA Momentum), Minimum Volatility (MSCI USA Minimum Volatility), and Quality (MSCI USA Quality).
The active returns of these indices certainly rhyme with, but do not perfectly replicate, their corresponding long/short factor implementations. For example, while Momentum certainly exhibits strong, negative active returns from 6/2008 to 12/2009, the drawdown is nowhere near as severe as the “crash” that occurred in the pure long/short factor.
This is due to two facts:
- The implied short side of the active bets is constrained by how far it can take certain holdings to zero. Therefore, long-only implementations tend to over-allocate towards top-quintile exposures rather than provide a balanced long/short allocation to top- and bottom-quintile exposures.
- While the active bets form a long/short portfolio, the notional size of that portfolio is often substantially lower than the academic factor definitions (which, with the exception of betting-against-beta, more mostly assumed to have a notional exposure of 100% per leg). The active bets, on the other hand, have a notional size corresponding to the portfolio’s active share, which frequently hovers between 30-70% for most long-only style portfolios.
- The implementation details of the long-only style portfolios and the long/short factor definitions may not perfectly match one another. As we have demonstrated a number of times in past research commentaries, these specification details can often swamp style returns in the short run, leading to meaningful cross-sectional dispersion in same-style performance.
Source: MSCI. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
Source: MSCI; AQR. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
Nevertheless, “rhymes but does not replicate” may be sufficient for long-only investors to still benefit from trend-following techniques.
In our test, we will go long the style / short the benchmark (i.e. long active returns) when prior N-month returns are positive and short the style / long the benchmark (i.e. short active returns) when prior N-month returns are negative. Portfolios are formed monthly at the end of each month. Performance results are reported in the table below for 1, 3, 6, 9, and 12-month lookback periods.
| Annualized Return | Annualized Volatility | Information Ratio | Maximum Drawdown | Sample Size (Months) | ||
| 1 | Value | 1.7% | 6.1% | 0.28 | -15.1% | 261 |
| Size | -0.8% | 8.2% | -0.10 | -44.4% | 303 | |
| Momentum | -0.2% | 7.5% | -0.03 | -21.3% | 302 | |
| Minimum Volatility | -0.1% | 5.7% | -0.01 | -25.0% | 375 | |
| Quality | 1.3% | 3.8% | 0.35 | -8.9% | 302 | |
| 3 | Value | 3.3% | 6.0% | 0.55 | -15.5% | 261 |
| Size | 1.1% | 8.2% | 0.13 | -34.5% | 303 | |
| Momentum | -0.8% | 7.5% | -0.11 | -38.0% | 302 | |
| Minimum Volatility | 0.7% | 5.7% | 0.13 | -19.4% | 375 | |
| Quality | 0.9% | 3.8% | 0.24 | -10.1% | 302 | |
| 6 | Value | 2.9% | 6.0% | 0.48 | -21.0% | 261 |
| Size | 1.7% | 8.2% | 0.20 | -20.8% | 303 | |
| Momentum | 0.7% | 7.5% | 0.09 | -28.8% | 302 | |
| Minimum Volatility | 0.5% | 5.7% | 0.09 | -27.8% | 375 | |
| Quality | 0.6% | 3.9% | 0.16 | -14.6% | 302 | |
| 9 | Value | 3.4% | 6.0% | 0.57 | -14.8% | 261 |
| Size | 2.0% | 8.2% | 0.24 | -27.1% | 303 | |
| Momentum | 1.2% | 7.5% | 0.16 | -23.4% | 302 | |
| Minimum Volatility | 0.9% | 5.7% | 0.15 | -20.8% | 375 | |
| Quality | 0.3% | 3.9% | 0.07 | -14.7% | 302 | |
| 12 | Value | 3.2% | 6.0% | 0.54 | -11.2% | 261 |
| Size | 1.8% | 8.2% | 0.22 | -29.9% | 303 | |
| Momentum | 1.9% | 7.5% | 0.25 | -20.0% | 302 | |
| Minimum Volatility | 1.4% | 5.7% | 0.24 | -17.3% | 375 | |
| Quality | 1.3% | 3.8% | 0.34 | -11.0% | 302 |
Source: MSCI. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
Below we plot the equity curves of the 12-month time-series momentum strategy. We also plot a portfolio that takes a naïve equal-weight position across all five trend-following strategies. The naïve blend has an annualized return of 2.3%, an annualized volatility of 4.0%, and an information ratio of 0.57.
Source: MSCI. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
This analysis at least appears to provide a glimmer of hope for this idea. Of course, the analysis comes with several caveats:
- We assume that investors can simultaneously generate signals and trade at month end, which may not be feasible for most.
- We are analyzing index data, which may be different than the realized results of index-tracking ETFs.
- We do not factor in trading costs such as impact, slippage, or commissions.
It is also important to point out that the per-style results vary dramatically. For example, trend-following on the size style has been in a material drawdown since 2006. Therefore, attempting to apply time-series momentum onto of a single style to manage style risk may only invite further strategy risk; this approach may be best applied with an ensemble of factors (and, likely, trend signals).
What this commentary has conveniently ignored, however, is that the appropriate benchmark for this approach is not zero. Rather, a more appropriate benchmark would be the long-only active returns of the styles themselves, as our default starting point is simply holding the styles long-only.
The results, when adjusted for our default of buy-and-hold, is much less convincing.
Source: MSCI. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
What is clear is that the strategy can now only out-perform when the style is under-performing the benchmark. When the portfolio invests in the style, our relative return versus the style is flat.
When a diversified trend-following portfolio is compared against a diversified long-only factor portfolio, we see the general hallmarks of a trend-following approach: value-add during periods of sustained drawdowns with decay thereafter. Trend-following on styles, then, may be more appropriate as a hedge against prolonged style under-performance; but we should expect a cost to that hedge.
Source: MSCI. Calculations by Newfound Research. Results are hypothetical. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. You cannot invest in an index.
For some styles, like Minimum Volatility, this appears to have helped relative performance drawdowns in periods like the dot-com bubble without too much subsequent give-up. Size, on the other hand, also benefited during the dot-com era, but subsequently suffered from significant trend-following whipsaw.
Conclusion
Recent research has suggested that equity style premia exhibit positive autocorrelation that can be exploited by trend followers. In this piece, we sought to explore whether this empirical evidence could be exploited by long-only investors by isolating the active returns of long-only style indices.
We found that a naïve 12-month time-series momentum strategy proved moderately effective at generating a timing strategy for switching between factor and benchmark exposure. Per-style results were fairly dramatic, and trend-following added substantial style risk of its own. However, diversification proved effective and an equal-weight portfolio of style trend-following strategies offered an information ratio of 0.57.
However, if we are already style proponents, a more relevant benchmark may be a long-only style portfolio. When our trend-following returns are taken in excess of this benchmark, results deflate dramatically, as the trend-following strategy can now only exploit periods when the style under-performs a market-capitalization-weighted index. Thus, for investors who already implement long-only styles in their portfolio, a trend-following overlay may serve to hedge periods of prolonged style drawdowns but will likely come with whipsaw cost which may drag down realized factor results.
Thinking in Long/Short Portfolios
By Corey Hoffstein
On March 5, 2018
In Risk & Style Premia, Risk Management, Weekly Commentary
This post is available as a PDF download here.
Summary
Ask the average investor if they employ shorting in their portfolios and “no” is likely the answer.
Examine the average portfolio, however, and shorts abound. Perhaps not explicitly, but certainly implicitly. But what in the world is an implicit short?
As investors, if we held no particular views about the market, our default position would be a market-capitalization weighted portfolio. Any deviation from market-capitalization weighted, then, expresses some sort of view (intentional or not).
For example, if we hold a portfolio of 40 blue-chip stocks instead of a total equity market index, we have expressed a view. That view is in part determined by what we hold, but equally important is what we do not.
In fact, we can capture this view – our active bets – by looking at the difference between what we hold in our portfolio and the market-capitalization weighted index. And we quite literally mean the difference. If we take the weights of our portfolio and subtract the weights of the index, we will be left with a dollar-neutral long/short portfolio. The long side will express those positions that we are overweight relative to the index, and the short side will express those positions we are underweight.
Below is a simple example of this idea.
“Dollar-neutral” simply means that the long and short legs will be of notional equal size (e.g. in the above example they are both 25%).
While our portfolio may appear to be long only, in reality it expresses a view that is captured by a long/short portfolio. As it turns out, our portfolio has an implicit short.
This framework is important because it allows us to go beyond evaluating what we hold and instead evaluate both the bets we are taking and the scale of those bets. Generically speaking, we can say:
Portfolio = Benchmark + b x Long/Short
Here, the legs of the Long/Short portfolio are assumed to have 100% notional exposure. Using the example above, this would mean that the long/short is 100% long Stock B, 100% short Stock A, and b is equal to 25%.
This step is important because it allows us to disentangle quantity from quality. A portfolio that is very overweight AAPL and a portfolio that is slightly overweight AAPL are expressing the same bet: it is simply the magnitude of that bet that is different.
So while the Long/Short portfolio captures our active bets, b measures our active share. In the context of this framework, it is easy to see that all active share determines is how exposed our portfolio is to our active bets.
We often hear a good deal of confusion about active share. Is more active share a good thing? A bad thing? Should we pay up for active share? Is active share correlated with alpha? This framework helps illuminate the answers.
Let’s slightly re-write our equation to more explicitly highlight the difference between our portfolio and the benchmark.
Portfolio – Benchmark = b x Long/Short
This means that the difference in returns between the portfolio and the benchmark will be entirely due to the return generated by the Long/Short portfolio of our active bets and how exposed we are to the active bets.
RPortfolio – RBenchmark = b x RLong/Short
Our expected excess return is then quite easy to think about: it is quite simply the expected return of our active bets (the Long/Short portfolio) scaled by how exposed we are to them (i.e. our active share):
E[RPortfolio – RBenchmark] = b x E[RLong/Short]
Active risk (also known as “tracking error”) also becomes quite easy to conceptualize. Active risk is simply the standard deviation of differences in returns between our Portfolio and the Benchmark. Or, as our framework shows us, it is just the volatility of our active bets scaled by how exposed we are to them.
s[RPortfolio – RBenchmark] = b x s[RLong/Short]
We can see that in all of these cases, both our active bets as well as our active share play a critical role. A higher active share means that the fee we are paying provides us more access to the active bets. It does not mean, however, that those active bets are necessarily any good. More is not always better.
Active share simply defines the quantity. The active bets, expressed in the long/short portfolio, will determine the quality. That quality is often captured by the Information Ratio, which is the expected excess return of our portfolio versus the benchmark divided by how much tracking error we have to take to generate that return.
IR = E[RPortfolio – RBenchmark] / s[RPortfolio – RBenchmark]
Re-writing these terms, we have:
IR = E[RLong/Short] / s[RLong/Short]
Note that the active share component cancels out. The information ratio provides us a pure measure of the quality of our active bets and ignores how much exposure our portfolio actually has to those bets.
Both quantity and quality are ultimately important in determining whether the portfolio will be able to overcome the hurdle rate set by the portfolio’s fee.
b x E[RLong/Short] > FeePortfolio – FeeBenchmark
The lower our active share, the higher our expectation for our active bets needs to be to overcome the fee spread. For example, if the spread in fee between our portfolio and the benchmark is 1% and our active share is just 25%, then we have to believe that our active bets can generate a return in excess of 4% to justify paying the fee spread. If, however, our active share is 75%, then the return needed falls to 1.33%.
Through this equation we can also understand the implications of fee pressure. If the cost of the active portfolio and the cost of the benchmark are equivalent, there is zero hurdle rate to overcome. We would choose active so long as we expect a positive return from our active bets.[1]
However, through its organizational structure and growth, Vanguard has been able to continually lower the fee of the passive benchmark over the last several decades. All else held equal, this means that the hurdle rate for active managers goes up.
Thus as the cost of passive goes down, active managers must lower their fee in a commensurate manner or boost the quality of their active bets.
Conclusion
For long-only “smart beta” and factor portfolios, we often see a focus on what the portfolio holds. While this is important, it is only a piece of the overall picture. Just as important in determining performance relative to a benchmark is what the portfolio does not hold.
In this piece, we explicitly calculate active bets as the difference between the active portfolio and its benchmark. This framework helps illuminate that our active return will be a function both of the quality of our active bets as well as the quantity of our exposure to them.
Finally, we can see that if our aim is to outperform the benchmark, we must first overcome the fee we are paying. The ability to overcome that fee will be a function of both quality and quantity. By scaling the fee by the portfolio’s active share, we can identify the hurdle rate that our active bets must overcome.
[1] More technically, theory tells us we would need a positive marginal expected utility from the investment in the context of our overall portfolio.