Visualizing the Anxiety of Active Strategies

by Corey Hoffstein, Newfound Research

This post is available as a PDF here.


  • Prospect theory states that the pain of losses exceeds the pleasure of equivalent gains. An oft-quoted ratio for this pain-to-pleasure experience is 2-to-1.
  • Evidence suggests a similar emotional experience is true for relative performance when investors compare their performance to common reference benchmarks.
  • The anxiety of underperforming can cause investors to abandon approaches before they benefit from the long-term outperformance opportunity.
  • We plot the “emotional” experience investors might have based upon the active approach they are employing as well as the frequency with which they review results. The more volatile the approach, the greater the emotional drag.
  • Not surprisingly, diversifying across multiple active approaches can help significantly reduce anxiety.

Last week, Longboard Asset Management published blog post titled A Watched Portfolio Never PerformsWhat we particularly enjoyed about this post was a graphic found in the middle, which applied prospect theory to demonstrate actual results versus perceived investor results based upon emotional experience.

In prospect theory, investors tend to feel the pain of losses more than the pleasure of equivalent gains.  Investors that check their portfolio more frequently compound those negative emotions faster than those that check less frequently.  As a result,  they may perceive their experience as being riskier than it really is.

This is made worse by the fact that investors that check their portfolios more frequently are mathematically more likely to see periods of losses than those that check less frequently.

When prospect theory and mathematics are tied together, we get the following result:

Source: Longboard Asset Management.

While in actuality, the investors checking their portfolios daily, weekly, and monthly all had the same long-term performance result (assuming, of course, they were able to stick with their investment), the anxiety caused by checking performance more frequently caused the daily investor to feel like their long-term performance was much worse than it really was.

While prospect theory is most often applied to absolute gains and losses, we believe it also applies to relative portfolio performance.  Investors constantly compare their results to standard benchmarks.

In the remainder of this commentary, we want to extend Longboard’s example to explore how typical active strategies – expressed as factor tilts – feel to investors based upon how frequently they evaluate their portfolio.

Methodology & Data

To explore the idea of anxiety caused by relative performance in active strategies, we will look at the performance of long/short factor portfolios.

The idea here is that a long-only factor portfolio (e.g. a long-only value portfolio) can be made by overlaying a market portfolio with a long/short value portfolio.  Therefore, relative performance to the benchmark will be governed entirely by the size of the long/short portfolio overlay.

There are a variety of reasons why this framework is not true in practice, but we feel it adequately captures the concept we are looking to explore in this commentary.

The long/short factor portfolios we employ come from AQR’s factor library.  Specifically, we leverage their Size (“SMB”), Value (“HML Devil”), Momentum (“UMD”), Quality (“QMJ”), and anti-beta (“BAB”) factors data.

Factor portfolio returns are only available on a monthly basis, so we will recreate the above Longboard graphic for investors that review their portfolio on a monthly, quarterly, and annual basis.  Using monthly data allows us to go back as far as 1927 to evaluate performance for several factors.

To create “experience” returns, the return of the long/short portfolio is calculated over the investor’s evaluation period.  If the return over the period is negative, then the loss is doubled, to account for the fact that investors are reported to experiences the pain of a loss twice as much as the pleasure of an equivalent gain.

Size Factor

The size factor is the relative performance between small capitalization stocks and large capitalization stocks, with the idea being that small should outperform large over the long run.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.


What we can see is that while size has been a positive premium over the long run, even investors that only evaluate their portfolios on an annual basis have had a negative emotional experience.

Due to the asymmetric response to gains versus losses, we can see the pain of “volatility drag” in periods like the 1950s, where the size factor was largely flat in return, but the experience for investors was largely negative.


Value Factor

The value factor captures the relative performance of cheap stocks versus expensive ones.  Our anecdotal experience is that this is, by far and away, the most actively employed portfolio tilt for investors.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.

Unlike the size premium, we see that the long-term performance of the value factor is strong enough, and the historical frequency of underperformance limited enough, that an investor who checks their relative performance annually will feel like they ultimately ended up in the same place as the broad market.

At first review, this may seem disheartening.  After all, over the long run value has delivered significant outperformance.

However, what this tells us is that for investors that review their portfolios at most annually, a value tilt can be employed without creating too much long-term relative anxiety.  The investor will still feel like they are keeping up with the market benchmark, despite the emotional drags of prospect theory, and can in reality harvest long-term outperformance opportunities.


Momentum Factor

The momentum factor captures the relative performance of prior winners versus prior losers: investing in those stocks that have relatively outperformed their peers and shorting those that have underperformed.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.

While the value factor ended up nearly in the same place as the market for annual reviewers, the momentum factor ends up significantly positive.

Furthermore, the consistency of the momentum factor is so strong from the 1940s to the 2009s that even a monthly reviewer feels like they are treading water.

The trade-off appears in the dreaded momentum crashes (e.g. 1932 and 2009) when winners dramatically underperform losers.  The crashes have historically tended to occur during strong market rebounds.  From an emotional experience, this might as well be the apocalypse.

Even for an annual reviewer, we see that the emotional drawdown in from 3/2009 to 11/2009 is almost 80%.


Quality Factor

The quality factor captures the relative performance of “high quality” stocks versus “junk stocks,” as measured by a variety of financial and performance metrics.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.

While the absolute return of the quality factor is nowhere near the absolute return of the momentum factor (over the same period, momentum returned nearly 90x while quality returned nearly 10x), it is one of the few factors where a quarterly reviewer has close to a net neutral emotional experience.  This is likely due to the factor’s low volatility, which reduces the emotional drag caused by investors’ asymmetric response to positive and negative returns


Anti-Beta (“Low Volatility”) Factor

Anti-beta (often refered to as “low volatility”) captures the relative outperformance of lower beta stocks versus higher beta stocks.  Beta, in this case, is a measure of sensitivity to the overall market.  It quantifies a stock’s exposure to systematic market risk.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.

Anti-beta has the distinction of being the only factor where even a quarterly reviewer has had a net positive experience.

This is due to two effects: a strong absolute return level (with the actual performance trumping even the momentum factor) and limited drag from volatility (as can be seen by how closely the annual review tracks the actual performance from 1945 to 1998).


At Newfound, we often say that the optimal portfolio is first and foremost the one investors can stick with.  All too often, when it comes to active investing, we see investors go all in on a given approach without considering the emotional anxiety caused by relative underperformance.

The ability and discipline to stick with a strategy is just as important as the strategy itself when it comes to unlocking the potential of evidence-based active strategies.

What we find is that for each active approach, the strength of the anomaly versus its volatility and the frequency with which performance is reviewed will ultimately dictate the investor’s emotional experience.  Less volatile premia may cause less of an emotional drag.

Yet perhaps the most powerful take away can be found in the following graph.

Source: AQR.  Calculations performed by Newfound Research.  Past performance is not a guarantee of future results.

In the above chart, we construct a portfolio that holds an equal amount of each of the five factors, rebalanced monthly.

Not surprisingly, the benefits of diversification are so powerful that even an investor that evaluates their relative performance on a monthly basis is left with a positive emotional experience.

Once again, we find that diversification is hard to beat.

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients.

Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn.

Corey is a frequent speaker on industry panels and contributes to, ETF Trends, and’s Great Speculations blog. He was named a 2014 ETF All Star by

Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University.

You can connect with Corey on LinkedIn or Twitter.

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