• The current outlook for stocks, bonds, and traditionally allocated portfolios is near all-time historical low levels.
• Even though short-term performance may vary, investors looking for long-term success may have to expand their investment palette to earn returns anywhere close to those realized in the past.
• A mean-variance optimal portfolio using the current market forecasts relies heavily on more unique asset classes such as U.S. Small Caps, Emerging Market Debt (Local Currency), and Levered Loans.
• While investors may not be willing to hold such a weird looking “60/40” portfolio, thinking outside the box may be necessary going forward.

Note: After recent podcasts with Meb Faber and Jeremy Schwartz, we received a large number of requests for our “Portfolios in Wonderland” presentation and the “weird” portfolio I discussed that was a result of the current market environment.  We thought we would take the content within the presentation and make it available as a commentary.

Portfolios in Wonderland

“Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.”

At the beginning of each year, many institutions publish their capital market assumptions, providing an outlook for expected returns, volatilities, and correlations.  These glossy brochures go well beyond data, however, and often veer wildly into what we like to call macro tourism: data-based market prognostications about macro-economic conditions and their implications for markets.

Unfortunately, for most investors, while macro tourism makes for an entertaining read, the track record of most predictors is quite poor.  Simply put, markets do not behave in the linear, domino-like fashion that most predictions are laid out as.  There are simply too many non-linear relationships to make accurate predictions; it is like trying to predict the exact weather in Boston a year out.

That said, if we are willing to restrain ourselves, meaningful forecasts can be made.  We may not be able to predict the exact weather, but there is a good chance the temperature will be between 65℉ and 80℉.

While exact predictions may be futile, evidence suggests that by taking a long-term view (7-10 years) and focusing on stable variables, we can make similar long-term forecasts for most major asset classes.  For U.S. investors, simply getting an understanding of what will likely happen with U.S. stocks and bonds can provide a tremendous amount of insight for the rest of our financial plan.

So, let’s begin with U.S. equities.  Here, we turn to the Shiller CAPE.  For those not familiar yet with this metric, it is a 10-year smoothed price-to-earnings measure for the U.S. equity market.  The aim of smoothing over 10-year periods is to get a measure that is less sensitive to market cycles, creating a “cyclically-adjusted” P/E (“CAPE”).

We can see that today’s CAPE is highly elevated compared to past measures.

The implication of a high CAPE reading is that stocks are expensive: you are paying more per unit of fundamental value.

In our piece Anatomy of a Bull Market, and the subsequent follow-up, we demonstrated that over the long-run, valuation changes have contributed little to U.S. equity performance.  While they can vary wildly in the short-run, they have historically exhibited mean-reverting behavior: cheap tends to get more expensive, and expensive tends to get cheaper.

In the short-run (7-10 year periods), however, valuation changes can have a very meaningful impact on returns.  Where the Shiller CAPE sits today, if real earnings grew at 2% a year, the market would have to return 0% for the next 13 years for the Shiller CAPE to revert back to its long-term average.  Even if earnings accelerate and grow at 4% a year, it would still take nearly a decade of 0% returns.

The other option, of course, is that we experience a bear market and price falls fast enough to cause the Shiller CAPE to revert.  A 30% decline in prices would just-about do it.

Now, we’re not here to forecast gloom and doom.  Rather, we believe there are a few simple, potential answers.  One is that Shiller CAPE is simply the wrong measurement of valuation.  Another is that this time really is different: valuations, for a variety of reasons, are simply structurally higher and will remain that way.  Or, we could simply argue that we expect market returns to be lower than average going forward, allowing earnings to catch up.

If we “hope for the best and prepare for the worst,” assuming the latter case is prudent.  Using earnings growth, dividend yield, and valuation figures, we can forecast expected equity returns over the next 7-10 years.  The current estimate – around 3.5% after inflation – is incredibly low by historical standards.

Estimating the expected future return for bonds is much easier.  Buying a bond today and holding it to maturity ensures that you lock in the yield-to-worst, regardless of what happens with interest rates.

What about bond funds?  For most funds – which are near constant maturity/duration in nature – changing rates have not made as large an impact as most people might assume.  This was the topic of our prior commentary Did Declining Rates Actually Matter?, whose results are depicted below.

What we find is that while declining rates did have an impact on bond index returns, the vast majority of the return was due to the actual coupon level itself.  In other words, what we should focus on, in the current environment, is not trying to accurately predict whether rates will go up or down, but rather the coupon yield we will be receiving.

Which is, today, incredibly low.

“Why, sometimes I've believed as many as six impossible things before breakfast.”

Believing that traditional core U.S. fixed income will deliver a return profile anything close to what they have historically delivered is misguided at best.  We can actually use a very simple rule – the “2x duration minus 1” rule – to forecast bond fund returns.  This rule is highly useful because it is derived to provide guidance regardless of what interest rates do.[1]

Simply, we take the current year and add to it 2x the duration of the bond fund and subtract one.  This provides us the forecast year.  The current yield-to-maturity – or, yield-to-worst – is then our estimate through that year.

AssetYield to MaturityDurationThroughPredicted Nominal ReturnPredicted Real 
ReturnU.S. Aggregate Bonds2.59%5.720282.59%0.29%1-3 Yr. Treasuries1.37%1.920201.37%-0.93%3-7 Yr. Treasuries1.91%4.520251.91%-0.39%7-10 Yr. Treasuries2.34%7.520312.34%0.04%10-20 Yr. Treasuries2.55%10.020362.55%0.25%20+ Yr. Treasuries3.00%17.320503.00%0.70%IG Corporates3.53%8.220323.53%1.23%

 Source: iShares.  Calculations by Newfound Research.  Figures as of June 2017.

It should be no surprise, then, that forecasted U.S. aggregate real returns are near all-time lows.

What makes the current market environment so strange is that while stock and bond valuations have historically been negatively correlated, they became simultaneously cheap in the 1980s and are now simultaneously expensive.

While the negative correlation allowed a traditionally constructed 60/40 stock/bond mix to provide a semi-constant expected return profile (or, at least, a reasonably floored one) from 1880-1970, the post 1970 period has seen the portfolio shift from very cheap to very expensive.

This means that the outlook for a 60/40 portfolio today is near the lowest it has ever been: our rough math puts the real-return near 2.2%.

“My dear, here we must run as fast as we can, just to stay in place. And if you wish to go anywhere you must run twice as fast as that.”

There is a significant danger of low expected returns for financial planning.  Old rules – using a 60/40 portfolio with a 4 or 5% withdrawal rate – may no longer be safe.  We highlighted this risk in our recent commentary Impact of High Equity Valuations on Safe Withdrawal Rates. Below are two graphs from that commentary.  In the first, the historical results of applying a 4% withdrawal rate to a 60/40 stock/bond allocation.  In the second, the same rules applied, but historical results are adjusted downward such that the long-term average return matches the future long-term expected returns.

We see that what was once safe may no-longer be.  There is no silver bullet to this problem.  Rather, a number of solutions will likely be necessary.  While we will be writing several follow-up articles in the coming weeks, some immediate ideas for dealing with this problem are:

• Increased savings rates during accumulation.
• Significantly reducing fees during retirement.
• Dynamic withdrawal plans.
• Active risk-management plans to address sequence risk.
• Looking outside traditional stocks and bonds for other return generators.

The Weird Portfolio

Fortunately, one of the many positive trends of the last two decades has been the down-stream movement of many asset classes and investment styles once relegated to the world of accredited investors, into low-cost, liquid fund packaging.  Exposures like levered loans and emerging market debt, and strategies like equity long/short and global macro, are now available for investor use to complement a traditionally allocated stock/bond portfolio.

If J.P. Morgan’s outlook is right, these types of positions may be more important today than ever before.

Plotting expected return versus risk allows us to see that positions like U.S. Large Cap equities and U.S. Aggregate Bonds may no longer be attractive.  Rather, positions like U.S. Small Caps, Emerging Market Debt (Local Currency), and Levered Loans may provide much more bang for the investment buck.

One of our favorite exercises is to take capital market assumptions like these and run them through a traditional mean-variance optimization, targeting the same risk profile of a standard 60/40 stock/bond mix.[2]  Unlike us, the optimizer has no attachment to a particular asset class: it simply looks to maximize return for our stated risk target.

The result, today, is a pretty weird looking portfolio.

(We should note that if we perform the same exercise using capital market assumptions from BNY Mellon, BlackRock, or Research Affiliates, the results are very similar).

We see:

• Despite targeting the same risk profile of a 60/40 portfolio, traditional equities and bonds only make up about 1/3^rd.
• U.S. large-caps and U.S. aggregate bonds are almost nowhere to be found.
• Equity exposure is dominated by emerging market and U.S. small-cap exposure.
• Bond exposure is almost entirely long-dated U.S. Treasuries. This may seem odd, given that long-term Treasuries offer one of the worst risk-reward trade-offs according to J.P. Morgan’s outlook.  However, J.P. Morgan’s correlation assumptions make them an incredible diversifier to increased volatility of the equity sleeve.
• Traditional “return generators” are largely replaced by credit-like exposures (e.g. high yield bonds, levered loans, emerging market debt, and REITs).
• Traditional “risk mitigators” are largely replaced by diversifying alternative exposures.

We’ll be the first to admit that almost no investor would be willing to actually hold this portfolio.  With nearly 25% of the portfolio in gold and long-term U.S. Treasuries, the tracking error alone would drive most investors mad.

And all just for what amounts to a 1% bump in expected return.  While 1% may not seem like much, in a low-return world it is nearly a 25% increase from a traditional stock/bond mix.

While few would feel comfortable implementing this weird portfolio outright, we believe that this exercise provides at least a hint of guidance for investors today: thinking outside the box may be necessary going forward.

Conclusion

“But I don’t want to go among mad people," Alice remarked.

"Oh, you can’t help that," said the Cat: "we’re all mad here. I’m mad. You’re mad."

"How do you know I’m mad?" said Alice.

"You must be," said the Cat, "or you wouldn’t have come here.”

[1] See For Constant-Duration or Constant-Maturity Bond Portfolios, Initial Yield Forecasts Return Best near Twice Duration by Gabriel Lozada for technical details.

[2] Technically, we run a simulation-based mean-variance optimization in effort to account for estimation risk and come up with a more stable allocation profile.

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.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

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.

Copyright © Newfound Research

This blog post is available as a PDF download here.

• Limited attention drives us to focus on the big details of investment strategies.
• Small details can have an outsized impact on performance, especially if they can compound upon one another.
• To quote Aaron Brown, Head of Risk at AQR: “It takes a lot of compounding to turn a mistake into a disaster. There will never be any shortage of mistakes […].  So it’s the compounding you have to prevent, not the mistakes.”
• We believe details like how frequently to rebalance and when to rebalance are too often overlooked and can have a dramatic impact on investor results.

In the world of asset management, attention goes to the big details.  Details like: “what are we investing in?”  Or, “what is the process?”  And without a doubt these are very important things.

Yet our limited time and attention often leaves us to gloss over the small details.  Our expectation is that the big things should have a big impact and the small things should have a small impact.

That is not always the case.

In this commentary, we are going to discuss two small things – the frequency of rebalancing and when rebalancing occurs – to show that small things, done wrong, can have an outsized impact on long-term results.

How Frequently Should We Rebalance?

The standard protocol for most systematic strategies is to rank the investment universe based upon some sort of signal or score, with the assumption that a stronger signal forecasts a higher future return.  At each rebalance, the portfolio tilts towards those securities with the strongest signals and away from those with the weakest (or even sells them short).

Assuming our signals correlate strongly with forecasted returns, to maximize our expected return we would want to rebalance as frequently as possible so that we are always holding the securities with the strongest signals.

Solely maximizing expected return, however, with no consideration of risk, may not be prudent.  Consider that the optimal choice to maximize expected return would be to continuously rebalance into the single security with the strongest signal, subjecting the portfolio to a tremendous amount of idiosyncratic risk.

Maximizing expected returns may not result in maximized realized returns, however, as the returns we expect and the returns we realize can be quite different.  In the case where our investment decisions can compound upon themselves, variance can play a dramatic role in returns.

Rather, investors will likely prefer to maximize expected return subject to some risk level or tracking error threshold.  This added wrinkle means that diversification will play an important role in how frequently we need to rebalance, particularly in the face of transaction costs, taxes, operational costs, and whipsaw costs (we’ll shorthand these as “turnover costs”).

To get an idea for this, let’s pretend for a moment that we are managing a value portfolio.  (For simplicity’s sake, we’re going to assume that stocks within our portfolio are held in an equal-weight fashion.)

In the face of turnover costs, how frequently we will want to rebalance our portfolio will depend upon a number of factors:

1. How large is our portfolio?

If there are N stocks in our portfolio, then the average stock will have to fall N/2 positions before it needs to be removed.  Furthermore, the larger N is, the smaller the change is to the portfolio when a security is removed.  Turnover costs for small changes may exceed the increase in marginal risk-adjusted return, and thus we would only want to rebalance at a frequency when there are enough changes to warrant the costs.

All else held equal, larger portfolios will need to be rebalanced less frequently.

2. How fast do signals decay?

For some strategies, signals many months in the future correlate highly to signals today.  For example, value tends to be a strategy where signals decay slowly: having a high score today implies a high probability of having a high score in six to twelve months.  On the other hand, momentum scores decay quickly: a high momentum score today implies little about momentum scores a year from now.

All else held equal, strategies with faster decaying scores will need to be rebalanced more frequently.

3. How much diversification is available?

Let’s assume that it only makes sense to rebalance if M of our N stocks need to be replaced in the portfolio.  As the correlation between stocks in our portfolio increases, the odds of M stocks falling out between two periods will converge towards the probably of just a single stock falling out.  On the other hand, if the stocks are highly diversified from one another, the probably of M falling out will be the probability of a single policy falling out to the Mth power.

All else held equal, more internal diversification within the portfolio decreases the frequency with which we need to rebalance.

4. How noisy are our signals? 

If our score estimates contain an element of noise to them, more frequent rebalancing can needlessly increase turnover costs.That our signals include an element of noise is not an unrealistic assumption.  Consider that most value strategies rely upon some sort of reported fundamental metric (e.g. earnings or book value).  Since these figures are reported on a quarterly basis, when we rebalance will imply that some figures are more up-to-date than others.  In addition, accounting values are imperfect estimates of fundamental value and accounting treatment may vary across firms.

The danger here goes beyond just normal transaction costs, however.  Increasing the frequency of turnover can compound mistakes.  In some cases, the loss of sitting on the wrong signal for an extended period of time could actually be lower than the whipsaw costs incurred by rebalancing more frequently and compounding mistakes.

Consider the following example.  Let’s assume the market has a constant annualized expected return of 6% per year with a volatility of 14%.  We’ll assume we are running a market timing strategy, where we make long or short calls on the market.  To see how accuracy and rebalance frequency affects our risk profile, we can run simulations of what such a strategy might look like and look at the expected maximum drawdown.

Calculations by Newfound Research.  All results are hypothetical.

We can see that increased rebalance frequency can increase the number of errors we make.  Even while those errors may be small for more frequent rebalances, they can compound quickly.

To quote Aaron Brown (Head of Risk at AQR) from his book Red Blooded Risk: “It takes a lot of compounding to turn a mistake into a disaster.  There will never be any shortage of mistakes […].  So it’s the compounding you have to prevent, not the mistakes.”

In investing, it is prudent to hope for the best and prepare for the worst.  Model accuracy is less of a random coin-flip and more of a streaky process.  While long-run accuracy for a model may be 60%, that may be comprised of sub-periods where we have 100% accuracy and sub-periods where we have 0%.  Limiting rebalance frequency can help limit the impact of inaccuracy.

All else held equal, more noise in our signals implies a greater risk of compounding whipsaw in rebalance frequency.

Putting it Together

While these many considerations create a multi-dimensional problem for portfolio rebalancing, we can generally say:

1. More concentrated portfolios will need to be rebalanced more frequently.
2. Portfolios driven by signals that decay more quickly will need to be rebalanced more frequently.
3. Portfolios with greater internal diversification will need to be rebalanced less frequently.
4. If signals are noisier, the portfolio should be rebalanced less frequently to avoid compounding errors.

With tactical strategies, we often hear investors say that they want to rebalance more frequently.  Why wait a month between rebalances when we can wait a week?  Why wait a week when we can rebalance every day?  Yet what often goes unconsidered is that rebalancing frequency is a double-edged sword.  When the calls are correct, the benefits will compound more quickly.  However, when the calls are incorrect, so will the costs.  The frequency of rebalancing must be chosen so as to strike a balance between the portfolio objective and the risks of compounding mistakes.

When Should We Rebalance?

Once we’ve settled upon how frequently we want to rebalance, we next must consider when to rebalance.

For example, if we chose to rebalance a value strategy annually, we still need to choose whether this rebalance occurs at the end of the year, mid-year, or some other time entirely.  It seems reasonable to assume that the question of when should be largely irrelevant, unless we believe there is some sort of edge to exploit (e.g. turn-of-month effects).

However, we will see that the when can have a profound impact upon long-term returns.  Not because there are necessarily times of the year that are inherently better or worse, but because it can have a dramatic effect on the investment opportunity set.

To shed some light on this effect, we will explore two examples.

First, let’s consider a simple value-based sector-rotation strategy.  In this strategy, we will allocate to the nine primary GICS sectors of the S&P 500 based on a valuation score, tilting towards undervalued sectors and away from overvalued sectors.  The strategy will be rebalanced annually.[1]

To demonstrate the impact of timing luck, we create four different strategies, each rebalancing at the end of a different quarter.  For example, the first strategy will rebalance each December 31^st, while the second strategy will rebalance every March 31^st, et cetera.  Below, we plot the growth of a dollar in each of the strategies.

Data Source: CSI Analytics.  Results are purely hypothetic and gross of all fees.  Returns assume the reinvestment of all dividends.

While the difference may not seem like much, the annualized return spread between the worst performing (June) and the best performing (December) is 0.54%.  Over the full testing period, this balloons into a 13.5 percentage point difference: enough to get one manager fired and another hired.  In this case, the December manager got lucky while the June manager got unlucky.  There is nothing to say, however, that the results could not have been reversed.  Hence why we call this effect “timing luck.”

This effect can be magnified when the tracking error between the different strategy versions grows.  For our second example, let’s consider a market timing approach popularized by Faber (2006)[2], in which the author applies a simple 10-month moving average system to time market exposure.  Specifically, at the end of each month, the price of a security is compared to the 10-month moving average of its price.  If price is above its average, the security is held long; if price is below its average, the security is sold and cash is held.

While the strategy in the paper is applied at the end of each month, there is no reason the same strategy could not be applied mid-month, or even three-fourths of the way through each month.  To generalize the approach, we will assume there are 21 trading days in each month and use a 210-day moving average, allowing us to create 21 possible strategies.  We will test the approach on the SPDR S&P 500 ETF (“SPY”).

Data Source: CSI Analytics.  Results are purely hypothetic and gross of all fees.  Returns assume the reinvestment of all dividends.

The above graph shows the growth of $1 in each of the 21 possible strategies.  The spread between the best and worst performing strategies is 250bp per year, resulting in a cumulative return difference of 369 percentage points.   Just as importantly, as the strategy is focused on drawdown control, the best drawdown of the group was -17.96% while the worst was -28.76%.

Forget hired versus fired: this is the difference between staying and going out of business.  This is not a totally unrealistic example, either: there are a number of tactical strategies available today that rebalance on a monthly basis that dramatically shift the amount of equity market beta in the portfolio.

To deal with this timing luck, we introduce the concept of “overlapping portfolios” (also sometimes referred to as “tranching”).

The idea behind overlapping portfolios is simple: instead of investing in a single portfolio that rebalances in a discrete frequency, we invest in a several identically managed portfolios that rebalance with the same frequency, but at different times.

Consider the value-based sector rotation example above.  Let’s assume that each of the four return streams belong to a different manager.  A fifth manager comes along who decides to run a “fund-of-funds,” allocating to each of these managers equally.  Investing­ in this fund-of-funds creates the overlapping portfolio approach.

The table below demonstrates the idea.  Each portfolio is formed through an identical process and held for four periods, but when each is formed is offset by a period from the prior.

By spreading our capital out across the four portfolios, we diversify our exposure to the results of timing luck.  Positive returns in one portfolio due to good luck will be (eventually) be offset by negative returns due to bad luck in another.

In fact, under some simplifying assumptions, we can prove this is actually the optimal portfolio design choice to minimize timing luck.  We provide this proof in the Appendix.

Fortunately, the actual implementation of the overlapping portfolio technique can be much simpler than simulating the management of a number of underlying portfolios.  Instead, we can simply average our target weights over time.

Consider our four-manager example.  To implement this, at the end of each quarter we would:

• Run the portfolio process, identifying the most up-to-date target portfolio using current signals.
• Set our current portfolio to be the average of the portfolios calculated over the prior four quarters.

By setting our weights to the average of weights generated over the prior rolling four-quarter period, each quarterly generated portfolio is held for a year and given an equal amount of capital.  Hence, we get the overlapping portfolio effect with far less work![3]

The result of this effort is a portfolio that ultimately looks like the average of all the underlying portfolios.  The graph below shows this approach applied to the S&P 500 timing system discussed before.  We can see that timing luck has been eliminated from the equation.

Data Source: CSI Analytics.  Results are purely hypothetic and gross of all fees.  Returns assume the reinvestment of all dividends.

We want to take a moment to address one approach we have seen in the past to dealing with this problem that we believe is incorrect: signal smoothing.  If overlapping portfolios can be thought of running multiple portfolios and averaging the output, signal smoothing is all about averaging the input and running a single portfolio.

In some cases, there is no difference between signal smoothing and overlapping portfolios.  Consider our prior S&P 500 market timing example.  An overlapping portfolio approach would average the target portfolio weights of the prior 21 days.  A signal smoothing approach would average the signals over the prior 21 days.  However, since our signals are our target weights (“in” or “out”), we end up in the same place.

This is not always the case.  In fact, it is rarely the case.  For it to be true, the following equation must hold:

Where  is the vector of inputs at time  and  is the transformation function that takes inputs and returns portfolio weights.  This is a textbook case of a mathematical property known as Jensen’s inequality, which relates the expected value of a function (left-hand side of our equation) to the function of expected values (right-hand side).   

The figure below shows Jensen’s inequality in action.  The function applied to the average of x and y will fall on the bold black line, while the average of the function applied to each of x and y will fall on the lighter line.  We can see that which side of the equation is larger will depend on the nature of the function.  Only in the case that the function is a linear transformation will the two cases be equivalent.

Source: www.probabilitycourse.com

Let’s consider a simple two-asset example to highlight how the difference can play out between signal smoothing and overlapping portfolios.  In this example, we will assume each asset is given a score based on some quantitative model and the asset with the highest score is held by the portfolio.  We’ll assume that portfolio is rebalanced annually.

With an overlapping portfolio approach, we might re-evaluate scores quarterly and create a portfolio that averages weights from the prior four quarters.  A signal smoothing approach, on the other hand, would average signals over the prior four quarters and create a portfolio based upon those signals.

You may have already caught the problem.  In the overlapping portfolio case, portfolio weights can range between 0 and 100% for both assets.  In the signal smoothing case, weights must be either 0% or 100%.  Consider the hypothetical scores and the resulting weights in the tables below.

Hypothetical Signals

Resulting Weights

While the overlapping portfolio approach ended up with 75% allocated to Asset #1 and 25% to Asset #2, the signal smoothing approach ended up with 100% in Asset #1 and 0% in Asset #2.  These are very different results.

Conclusion

The little details in investing often go overlooked.  Yet the small things can have a big impact if not accounted for correctly.  While we often expect the big things to drive results, small things done wrong can have a dramatic compounding effect that can lead to poor performance.

Appendix

For the optimality proof of overlapping portfolios and the reduction of timing luck, please see the appendix in this PDF.

[1] The exact details of how the strategy works is not important for highlighting the impact of timing luck, and hence we have omitted it to avoid introducing unnecessary details.

[2] Faber, Meb, A Quantitative Approach to Tactical Asset Allocation (February 1, 2013). The Journal of Wealth Management, Spring 2007. Available at SSRN: https://ssrn.com/abstract=962461

[3] It is worth noting that this approach does not account for drift that may occur in a portfolio over time.  For higher volatility assets and longer holding periods, accounting for this drift in weights can be important.

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.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

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.

Copyright © Newfound Research

by Corey Hoffstein, Newfound Research

• Momentum-based sector rotation is a popular investment strategy.
• Recent academic studies have shown that alternative implementations of standard momentum – including risk-adjusted momentum, residual momentum, and “frog-in-the-pan” momentum – can significantly improve the risk-adjusted and total return potential of stock-based momentum systems.
• We explore whether these approaches create value for sector rotation systems.

Momentum is a system of investing that buys and sells securities based upon recent returns.  Momentum investors buy outperforming securities and avoid – or sell short – underperforming ones.

In the traditional academic implementation of momentum, hundreds of individual securities must be bought and sold.  One popular – albeit simplified – implementation of this approach is sector rotation, where investors implement a momentum strategy through industry groups or sectors.

In a past commentary[1], we demonstrated that sector rotation was entirely subsumed by the momentum factor (i.e. does not represent its own unique risk factor) and dampens total return potential.  We also found, however, that as the number of sectors utilized decreased, so did the risk of momentum crashes.  Risk-averse investors, therefore, still may find traditional sector rotation a valuable approach.

Since the momentum factor was identified and published by Jegadeesh and Titman in 1993, several other approaches have been explored and documented.  Most prominently have been risk-adjusted momentum, idiosyncratic momentum, and frog-in-the-pan momentum.

In this study, we explore whether these approaches are value-add in a traditional sector rotation approach.

Risk-Adjusted Momentum

Whereas traditional momentum looks at trading 12-1 month returns, risk-adjusted momentum scales this return figure by trailing realized volatility.

One argument for this approach is that it is secretly a multi-factor approach.  Here, we can think of 12-1 returns as our “momentum score” and inverse realized volatility as our “low volatility score.”  By multiplying them together to create a risk-adjusted momentum score, we are invoking a multi-factor scoring process somewhat similar to the “tilt-tilt” process advocated for by FTSE Russell.

Another potential argument for this approach is that by scaling by volatility, we overweight those sectors whose return has been more continuous in nature and less discrete (e.g. the return is driven by a large jump).  The rational inattention theory posits that since time is a scarce resource, investors may selectively ignore information or only obtain news on a limited frequency or with limited accuracy.  Chen and Yu (2014) found that portfolios constructed for stocks “more likely to grab attention” based on visual patterns induces investor overreaction.[2]  Indeed, momentum continuation could be induced by visually-based psychological biases.

Several studies have demonstrated the benefits of risk-adjusted momentum, including Shaik (2011) [3] and Soe (2016)[4], who find that risk-adjusted momentum creates excess risk-adjusted and total returns in large-cap U.S. equities, small-cap U.S. equities, and global equities.

Similarly, Ahti (2012)[5] finds that beta-adjusted momentum (where the anti-beta and low-volatility anomalies are close cousins) enhances global equity momentum by increasing total return and lowering volatility.

To test risk-adjusted momentum in a sector rotation context, we sort sectors based on their trailing 12-1 month risk-adjusted return.  We build an equal-weight portfolio of the top three sectors with the highest scores.  Similarly, for our short leg, we build an equal-weight portfolio of the bottom three sectors with the lowest scores.  Portfolios are rebalanced monthly (using overlapping portfolios).

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are hypothetical and are gross of all costs.

We can see that risk-adjusted momentum ends up being a drag on our sector rotation approach.  And without a commensurate reduction in volatility, we end up with a worse Sharpe ratio.

Of course, most investors implementing a sector rotation approach do so in a long-only capacity, so we believe it is important to distinguish between returns originating from the long and short legs of this analysis.  Specifically, we can plot the long-only legs to determine whether the short-leg was a drag on performance and we can still harvest some benefit in a long-only model.

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are purely hypothetical and are gross of all costs.

Again, we find no evidence that a risk-adjusted momentum approach is advantageous in a long-only sector rotation system.

Residual (Idiosyncratic) Momentum

One argument against the traditional approach to momentum is that the portfolios constructed have time-varying exposures to return factors such as market beta, value, and size.

In an effort to control for this effect, residual (or idiosyncratic) momentum first regresses a stock’s returns against these common risk factors and extracts only the residual, unexplained return stream.  The traditional 12-1 momentum approach is then applied to this idiosyncratic component.

Blitz, Huij, and Martens (2009) found that controlling for market beta, value, and size, risk-adjusted profits of their residual momentum process were about twice as large as those associated with total return momentum, with greater consistency.[6]

By correcting stocks for market returns, Chaves (2012) finds that momentum applied to idiosyncratic returns works better than traditional momentum in a sample of 21 developed countries.  Perhaps most importantly, the approach was successful in Japan, where traditional momentum has historically failed.[7]

More recently, Blitz, Hanauer, and Vidojevic (2017) found that residual momentum could not be subsumed by the conventional momentum factor and that traditional arguments of investor over-confidence and overreaction fail to explain the anomaly.[8]

In our sector rotation framework, we can explore this approach by employing the CAPM model, regressing sector returns against the market and extracting the idiosyncratic component.  Specifically, we will use rolling three year periods for calculating our residuals.  After residuals are calculated for each sector, we run a traditional 12-1 momentum approach.

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are purely hypothetical and are gross of all costs.

Unlike risk-adjusted momentum, idiosyncratic momentum does improve risk-adjusted returns for the long/short implementation – though just narrowly.  Again, however, we find the long-only implementation lacking.  In fact, the long-only momentum strategy has a Sharpe ratio of 0.47 while the idiosyncratic approach has a Sharpe ratio of just 0.44.

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are purely hypothetical and are gross of all costs.

Frog-in-the-Pan Momentum

Da, Gurun, and Warachka (2014) introduced a new concept in momentum: “frog in the pan” (FIP)[9].  The hypothesis behind FIP is that “investors are inattentive to information arriving continuously in small amounts. […] [A] series of frequent gradual changes attracts less attention than infrequent dramatic changes.”

To test this hypothesis, the authors double-sort stock returns, first on trailing 12-1 month total returns and then on an information discreteness (ID) score.  This ID score is calculated as the sign of the trailing 12-month return multiplied by the difference between the percentage of negative days and the percentage of positive days.  By construction, this figure will range from -1 to +1, with a lower score corresponding to greater return continuity.

The authors find that, consistent with their hypothesis, stocks exhibiting continuous information exhibit stronger momentum returns than those that exhibit information discreteness.

Unfortunately, with only 10 sectors, a double-sort approach is not possible.  To incorporate the concept of information discreteness, we create a new score: ID = (sign(PRET)[%pos - %neg] + 1) / 2.  Our information discreteness measure is bound between 0 and 1, with 0 being more discrete returns and 1 being more continuous.  We then multiply our traditional momentum score by this ID score, highly continuous returns retain their magnitude while discrete returns are pulled towards zero.

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are purely hypothetical and are gross of all costs.

Like the approaches before, FIP seems to fall short for sector rotation.  We see the same holds true for the long-only side as well.

Data from Kenneth French data library.  Calculations by Newfound Research.  All returns are purely hypothetical and are gross of all costs.

What’s going on here?  Why is FIP so close to momentum for sector rotation?  Quite simply, it is likely that with only ten sectors, there is not enough differential in the information discreteness score to significantly change the momentum score magnitude and cause relative ranks to shift.

Conclusion

It may seem, at the end of the day, all was for naught.  While we did not test every extension of momentum or combinations thereof (e.g. residual momentum using the Fama-French 3-factor model, risk-adjusted idiosyncratic momentum, etc), these initial tests were not promising for creating value-add in a sector rotation system.

To this, we would say two things.

First, we would argue that these adjustments to momentum general try to capture the concept of “consistency” and “smoothness.”  These tweaks may be relevant when dealing with individual securities that can exhibit a significant amount of jump risk in their returns.  However, much of this risk is diluted at the sector level, where we already benefit from a significant amount of diversification.  Therefore, the added steps to try to address this risk may not be necessary, and perhaps only harmful to returns.

Second, the mere fact that none of these variations broke sector rotation says something about momentum’s robustness.  These are not just minor variations either: idiosyncratic momentum, for example, is a significant change in methodology.  Nevertheless, evaluated in isolation, it would appear to be a statistically significant anomaly.  In other words, regardless of its form, momentum seems to persist.

The nature of research is that you are going to often find yourself at dead ends.  We believe, however, learning what doesn’t work, and why it doesn’t work, is just as, if not more important, than identifying what does.

[1] https://blog.thinknewfound.com/2017/03/sector-rotation-momentum-factor/

[2] Chen, Li-Wen and Yu, Hsin-Yi, Investor Attention, Visual Price Pattern, and Momentum Investing (August 12, 2014). 27th Australasian Finance and Banking Conference 2014 Paper. Available at SSRN: http://ssrn.com/abstract=2292895 or http://dx.doi.org/10.2139/ssrn.2292895

[3] Shaik, Rasool. 2011. “Risk-Adjusted Momentum: A Superior Approach to Momentum Investing.” Bridgeway Capital Management.

[4] Soe, Aye. 2016. “Momentum: Does Adjusting By Risk Matter?” S&P Dow Jones Indices.

[5] Ahti, Valterri.  2012.  “BAMM: MSCI World.”  Evli Bank.

[6] Blitz, David and Huij, Joop and Martens, Martin, Residual Momentum (August 1, 2009). Available at SSRN: https://ssrn.com/abstract=2319861 or http://dx.doi.org/10.2139/ssrn.2319861

[7] Chaves, Denis. 2012. “Eureka! A Momentum Strategy that Also Works in Japan.” Research Affiliates Working Paper (January 9).

[8] Blitz, David and Hanauer, Matthias X. and Vidojevic, Milan, The Idiosyncratic Momentum Anomaly (April 5, 2017). Available at SSRN: https://ssrn.com/abstract=2947044

[9] Da, Zhi and Gurun, Umit G. and Warachka, Mitch, Frog in the Pan: Continuous Information and Momentum (December 21, 2013). Available at SSRN: https://ssrn.com/abstract=2370931 or http://dx.doi.org/10.2139/ssrn.2370931

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.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

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.

Copyright © Newfound Research

This post is available as a PDF download here.

• Market expectations are a key input in the portfolio construction process. These expectations can be either qualitative or quantitative.
• How to form expectations for more complex strategies (e.g. managed futures, covered calls, and alternatives) is often less straightforward than forming expectations for single asset classes (e.g. large-cap equities, gold, and long-term U.S. Treasuries).
• In the case of tactical equity strategies, periods of large absolute changes in the equity market and positive interest rate changes have historically created favorable performance versus a balanced stock/bond allocation. These factors can give context for setting expectations.
• While we cannot predict the future, we know that volatile markets happen frequently and that interest rates have already begun to increase.
• Having a robust, tactical equity solution can add value by equipping a portfolio for volatility and rising rates without sacrificing gains to whipsaw events.

Expectations are critical for any investment, and they can be expressed in many different forms.

For instance, when we construct our QuBe strategic portfolios, expectations for returns, volatilities, and correlations are critical input parameters.

We also expect that these inputs will not be 100% accurate. We account for this by using multiple data sources and stress testing the parameters to generate a rich array of market environments. The result is a robust portfolio that we would expect to weather more severe market scenarios, especially after further diversifying the processes within many asset classes in our final implementation.

Now let’s ask a more complicated question.

What is your expectation for a covered call strategy? Managed futures? Event driven alternatives?

These strategies have multiple components to consider, and complexity makes the exercise less straightforward. But with the emphasis on suitability of investments, having appropriate expectations is still essential.

Without appropriate expectations, how can we accurately gauge the risk of loss, the prospect of gains, or potential interaction effects with other investments?

With tactical equity strategies, the market environment can be a good indicator of what to expect.[1]

Tactical Equity in a Nutshell

To do some analysis, we will start simple.

Let’s construct a tactical equity strategy that invests in the S&P 500 when its 50-day simple moving average (SMA) is above its 200-day SMA. The strategy will invest in 1-3 month T-bills when the SMAs are reversed.

This simple, systematic strategy has historically exhibited strong positive returns with reduced risk relative to the S&P 500, as readers of this commentary are by now well aware. It has also done well versus a 50/50 blend of the S&P 500 Index and the Barclays Aggregate Bond Index (“balanced benchmark”).[2]

Source: Morningstar. Calculations by Newfound Research. Data from 11/15/1989 to 3/31/2017. Past performance is not a guarantee of future results.

However, the million dollar question is always, “how will this investment do in the future?”

The Context of the Market

There are many ways to categorize the market environment into different regimes. For investors with traditionally built portfolios of stocks and bonds, factors often at the forefront of their minds are returns in equities and changes in interest rates.

To evaluate how our toy tactical equity strategy performs, we can bucket these two variables into quintiles.  For equities, we will look at the one-year absolute returns of the S&P 500.  For interest rates, we will look at the one-year change in the 10-year U.S. Treasury rate.

The reason we look at absolute returns for equities is because we expect a tactical strategy to do well when there are large trends, regardless of direction.  On the other hand, in interest rates we take the sign of the change into account as we want to capture the headwind or tailwind it creates for the balanced benchmark portfolio.

Equity Moves

The chart below shows the one-year performance of the tactical equity strategy relative to that of the balanced benchmark for different magnitudes of 1-year S&P 500 moves.

Source: Morningstar. Calculations by Newfound Research. Data from 11/15/1989 to 3/31/2017. Past performance is not a guarantee of future results.

In low return (either positive or negative) environments for equities, the tactical strategy lags the balanced benchmark as whipsaw costs add up. As the equity moves become larger in magnitude, the tactical strategy outperforms the static stock/bond blend since the tactical strategy more effectively captures these moves with less whipsaw.

Interest Rate Moves

The following chart shows the one-year performance of the tactical equity strategy relative to that of the balanced benchmark for different 10-year U.S. Treasury changes.

Source: Morningstar and St. Louis Fed. Calculations by Newfound Research. Data from 11/15/1989 to 3/31/2017. Past performance is not a guarantee of future results.

In this graph, we see that the tactical equity strategy outperformed the balanced benchmark more when interest rates rose as the increasing interest rates were a headwind to core bonds.

Joint Equity and Interest Rate Moves

To dive deeper into these periods of outperformance, we can decompose each quintile in S&P 500 returns based on its overlap with changes in the 10-year U.S. Treasury rate.

First, we can look at the coverage of each quintile overlap. That is, have interest rate increases occurred more frequently in high or low absolute equity return environments, or vice versa?

Quintile Overlap of Rolling 1-Year S&P 500 Returns and Changes in the 10-Year U.S. Treasury Rate

Source: Morningstar and St. Louis Fed. Calculations by Newfound Research. Data from 11/15/1989 to 3/31/2017. Past performance is not a guarantee of future results.

Since there are 25 possible regimes in this two dimensional grid, 4% in each box would indicate a completely even distribution. We see that the overlap in the extremes of both variables (the four corner boxes) has been more frequent, as have middle-of-the-road changes, which have occurred together the most frequently.

The reasonable coverage in all of the regimes (i.e. none are less than 2%) allows us to assess the distribution of relative returns in each. The table below shows the median return in each regime.

Tactical Equity vs. Balanced Benchmark 1-Year Return by Quintiles of Rolling 1-Year S&P 500 Returns and Changes in the 10-Year U.S. Treasury Rate

Source: Morningstar and St. Louis Fed. Calculations by Newfound Research. Data from 11/15/1989 to 3/31/2017. Past performance is not a guarantee of future results.

As we saw previously, markets with small equity moves (left side of the table) are unfavorable to the tactical equity strategy.  When you have small equity moves and declining rates: watch out.

However, increasing interest rates, even in these small equity market move periods, can provide enough of a headwind to the balanced benchmark to push tactical equity back to the forefront.

A More Granular Tactical Equity Strategy

Going beyond the simple broad index-based tactical equity strategy, what would happen if we instead invest via sectors?

Below we show the results for a tactical equity strategy using the same moving average trend indicator, but now on each the nine primary S&P 500 sector indices. We construct the portfolio in a similar fashion to our Risk Managed Sector Series strategies, by equally weighting each sector with a positive momentum signal up to a 25% cap (which has the effect of building cash in the portfolio when three or fewer sectors are exhibiting positive trends).

Source: Morningstar. Calculations by Newfound Research. Data from 7/5/1990 to 3/31/2017.  Past performance is not a guarantee of future results.

For smaller absolute equity moves, we see an improvement in the sector based strategy versus the simpler strategy on only the S&P 500 as the nine sectors provide opportunities to manage model risk. That is, when a signal leads to whipsaw in one sector, an accurate signal in a different sector can mitigate the impact.

We can compare the benefits of this approach against the broad index approach by calculating the differences per quintile.

Source: Morningstar. Calculations by Newfound Research. Data from 7/5/1990 to 3/31/2017. Past performance is not a guarantee of future results.

We can see that the benefit decreases as the magnitude of the S&P 500 change increases.  In fact, the sector approach appears to be a drag compared to the single broad index approach for the largest moves.

Let’s now look at the impact of the sector-based design on returns versus 1-year changes in interest rates.

Source: Morningstar and St. Louis Fed. Calculations by Newfound Research. Data from 7/5/1990 to 3/31/2017. Past performance is not a guarantee of future results.

Again, we can see an improvement in the bottom quintiles.

Source: Morningstar and St. Louis Fed. Calculations by Newfound Research. Data from 7/5/1990 to 3/31/2017. Past performance is not a guarantee of future results.

For changes in interest rates, there was a benefit to using sectors relative to the strategy with only the S&P 500 across the board.

Conclusion

Including an asset in a portfolio without understanding which market environments will be favorable or not is a recipe for disaster. If losses occur, uncertainty can lead to poor decisions that compound losses, which can then lead to further emotion-driven decisions.

As Peter Lynch said, “Know what you own, and know why you own it.”

We own tactical equity strategies in an effort to manage the risk of large market drawdowns without sacrificing substantial gains during bull markets.

Tactical equity strategies have historically outperformed balanced portfolios during large swings in the equity markets and in rising rate environments. In sideways markets, whipsaw has typically led to underperformance.  However, there are ways to manage whipsaw risk and smooth out the ride even in tougher market environments.  For example, diversifying across the sectors has historically improved the outcome as whipsaw calls in one sector could be offset by accurate calls in another sector.

Knowing what to expect with tactical equity can lead to better long term results as investors learn how to better utilize tactical equity within their portfolios, both from a quantitative and behavioral perspective.

[1] We wrote a commentary entitled How Not to Ditch Your Investment Plan on setting expectations in a Multi-Asset Income portfolio. Many of the techniques we discussed there are applicable to any strategy.

^[2] This benchmark was chosen because it represents what an investor might replace with the tactical equity strategy. This swap acts as a dial for equity exposure. If we were instead evaluating the tactical strategy to see how well the momentum signals worked, we would benchmark it to a 50/50 mix of the S&P 500 and 1-3 month T-bills. Benchmarking can depend on what aspect of a strategy you are analyzing.

This post is available as a PDF download here.

• Quant is a broad word with many job descriptions in finance. In asset management, a quant is someone who applies mathematical (usually statistical) techniques to analyzing the securities market, usually with an eye towards identifying investment opportunities.
• Quants rely on factors: systematic investment approaches that capture and explain the return difference between different cohorts of securities.
• Factors are all about buying baskets of things; quants like to avoid idiosyncratic risk because we do not believe investors are compensated for bearing the additional risk.
• For a market to function, someone has to perform information discovery on individual stocks. Can this role be filled by quants or does the market require stock pickers to function?

“Quant” is a word of with many connotations.  For some, they are the numerical wizards conjuring new sources of alpha.  For others, the out-of-touch wonks who caused the financial crisis.

At the broadest, most sweeping generalization, quants specialize in applying mathematical techniques and methods – mostly statistical – to financial markets.

In finance, there are all sorts of quants.  Some work deriving new pricing theories for derivatives; others work managing and modeling risk; and still others – like us – work to identify empirical pricing relationships for building portfolios.

We’ll dedicate this commentary to our parents and significant others, who still have no idea what we do for a living.

More Risk, More Reward

In the 1960s, the Capital Asset Pricing Model (“CAPM”) was introduced.  CAPM provides a model for pricing an individual security.  Known as a “single factor” model, CAPM modeled a stock’s excess return as being one-part overall market return and one-part idiosyncratic return.

Here the Greek letter that looks like a "B" – known as “beta” – estimates the stock’s sensitivity to market returns.  The Greek letter that looks like an "E" at the end of the equation is the idiosyncratic component.

We’ve all heard the saying, “no risk, no reward.”  In the case of financial markets, the question is: “which risks earn reward?”

As the theory goes, not all of them do.  CAPM states that investors should only be compensated for bearing market risk but not for bearing idiosyncratic risk.  The argument is that beta is undiversifiable: build a portfolio of stocks and the beta component remains.  The idiosyncratic risk, on the other hand, can be diversified away.

For example, a portfolio of 30-40 stocks is typically sufficient to reduce idiosyncratic exposure enough that only the shared market risk remains.  If we did earn compensation for bearing the risk, we could create an arbitrage.  We would build a portfolio of 30-40 stocks to diversify away our idiosyncratic risk – but not the reward! – and then short the broad market to eliminate our market risk.  Hence, it holds that we should not be compensated for bearing idiosyncratic risk.

Here we’ll point out that CAPM stands in direct opposition to the practice of stock picking.  No amount of understanding of idiosyncratic, company specific risk should lead to an expectation of higher returns.

Being Compensated for Non-Market Risk

When a quant says, “risk factor,” what they mean is a characteristic that helps explain why one stock did one thing and another did something else.  In CAPM, the risk factor was the market.  If the market goes up, stocks with more market exposure should go up more while stocks with a lower exposure will go up less.

In 1974, Barr Rosenberg identified that stocks co-varied with a number of other non-market risk factors.  He found that firm-specific characteristics like balance sheet data and industry membership, as well as security characteristics like historical price behavior, were significant in explaining differences between stocks.  In quant terms, we call this “explaining cross-sectional returns.”

In 1977, Sanjoy Basu identified what would become known as the value factor: whether a stock was expensive or cheap (based on book-to-price) was a statistically significant explanatory variable in the cross section of security returns.  Later, Banz (1981) and Reinganum (1981) would discover the size factor, where a company’s capitalization held significant power in explaining cross-sectional returns.

This culminated in the early 1990s with what would become known as the Fama-French 3-Factor (“FF3”) model.  FF3 extends CAPM to introduce the value (“HML” for “high-minus-low”) and size (“SMB” for “small-minus-big”) factors as significant explanatory variables.

Here we need to take a step back and explain how a factor gets an associated “return.”  In CAPM, the answer was obvious: the market return is simply the return of the capitalization-weighted equity market.  But what is the return of the value factor?

Identifying important risk factors is all about identifying variables that explain differences.  For example, with the value factor, Basu found that companies with a high book-to-price value behaved differently than those with a low book-to-price.  To capture this effect, quants build a “long/short” portfolio to capture the return difference in the categories.  In the case of value, the portfolio shorts stocks with low book-to-price values and uses the proceeds to buy stocks with high book-to-price values.  With the expectation that the two legs will behave differently, the long/short portfolio captures this difference.

Risk Factor vs. Risk Premia vs. Anomaly

There is an important distinction in the world of quants between a risk factor, a risk premia, and an anomaly.

A risk factor is something that helps explain the cross-sectional differences in security returns.

A risk premia is the excess return we expect to earn for exposure to a certain risk factor.

For example, “market” exposure is the risk while the “equity risk premium” is the associated risk premium that compensates us for bearing the risk.

Not all risk factors necessarily have associated risk premia, however.  For example, it is well established that stocks tend to behave similarly to other stocks within the same industry group.  Industry classification, then, may be a risk factor that helps us explain why two stocks behave differently.  For example, if I know that a stock is an energy company, and I know how the energy sector does on a given day, I likely have some meaningful information about how that stock did.

We do not expect to earn a premium, however, for investing in a stock in one industry versus another.  Why?  Again, because this risk can be completely diversified away.  Industry classification only helps us decompose the idiosyncratic side of the equation; as we said before, we should not profit from idiosyncratic risk.

So why does FF3 highlight value and size instead of sweeping them into the idiosyncratic component?  At the time of publishing, value and size were both found to have statistically significant premia associated with them.  Historically, investing in small companies had earned you a premium over investing in large ones while investing in cheap companies had earned a premium over expensive ones.

These are called risk premia because the excess compensation can be tied to excess risk being taken.  For example, researchers posit that the value premium comes from being willing to bear the higher distress risk of the companies owned while the size premium might arise from illiquidity risk.[1]

An anomaly is slightly different: it is an excess return that cannot be explained by exposure to risk.  The momentum factor, for example, is the excess return that has been historically generated by short-selling recent underperformers and buying recent outperformers.  This strategy has historically generated significant excess premium, but no convincing argument has been made as to what risk the premium is compensation for.  Often these anomalies are attributed to behavioral biases exhibited by investors (i.e. irrational behavior) or market structure.

Not all investors can profit from these risk premia and anomalies simultaneously.  Rather, they arise because some investors are giving up the return that others capture.  For example, investors unwilling to bear distress risk may sell their stocks at a discount to intrinsic value to entice other investors to buy them.  Hence, value investors get access to these higher risk stocks at a discount.  If they diversify, they should earn a premium.  In a sense, they are acting as “insurer” against the distress risk for investors unwilling to bear it.

Depending on whom you ask, there are between 300-600 published “factors” (either risk premia or anomalies).  As we all know, past performance is not a guarantee of future results.  Unfortunately, past performance is really all we have to work with as quants.  However, as a million analysts pour over the same data, it is likely that a number of spurious factors will be discovered.  From the list of several hundred, there are just a handful that quants broadly accept as being significant: value, momentum, illiquidity, low-volatility, and quality.

That is, by no means, a comprehensive list.  We know at least a few quants who would disagree with our inclusion of low-volatility and quality.  But that’s what makes the market go ‘round.

Is Stock Picking Fundamentally Flawed?

While stock pickers tend to focus on what makes a company unique or a situation special – the highly idiosyncratic –theory tells us that we should not be compensated for idiosyncratic risk.

Hence, quants don’t pick stocks.  Rather, we buy big baskets of things in hopes to capture the common traits and characteristics (i.e. “factors,” which we think we’ll make money on) and eliminate the unique, idiosyncratic components.  Quants view the good stock pickers as those that are just actually closet factor-investors (whether they know it or not).  Warren Buffett?  He’s a value, quality, anti-beta guy with some leverage.[2]

That’s why we view the smart-beta revolution to be so important.  Nothing against stock pickers, but if you’re just providing factor exposure, we might as well commoditize you with rules-based, low-cost indices.

Of course, theory and reality have to meet somewhere.  Consider the following situation: the market goes 100% passive and index-based.  What happens?  Since everyone is buying the same stocks in the same relative proportion, there can be no relative price changes.  The market completely breaks: there can be no market with only price-takers.

Active investors are, therefore, necessary for functional markets.  This is captured by the Grossman-Stiglitz Paradox.  The paradox states:

1. For markets to be efficient (i.e. nobody can make excess profit), investors must participate in price discovery;
2. Because price discovery is expensive, investors must expect compensation for performing it;
3. Hence for markets to be efficient, someone must be expecting excess profit.

Someone has to perform price discovery.  Someone has to figure out why Coca-Cola is worth something different than Pepsi.  Is that not idiosyncratic information?  If stock pickers are providing this service, they should expect compensation for it: they can’t be so irrational as to do it for free (or worse, at a net loss after costs).

Does it have to be stock pickers who perform this service, though?

To explore this question, we’ve built a market simulation.[3]  We’re going to assume that there are two sides to the market: passive investors and systematic value investors.

We’ll assume our market has 10 stocks in it.  At the beginning, the passive investors hold all the shares: 100,000 of each stock, to be exact.  Each share is priced at exactly $100 and has constant earnings per share.  For each stock, we randomly select an earnings per share level of between $0 and $5.  We assume these earnings are paid out, 100%, as a dividend to shareholders.

Now, if the passive investors never trade, nothing happens.  Fortunately, passive investors often trade for cash-flow reasons (not to mention share issuances, repurchases, index reconstitutions, et cetera – but we’ll ignore these).  In our simulation, we’ll assume that at each step the passive investors, collectively, make an aggregate trade: trying to purchase or sell some shares.  They will always look to transact in proportion to the current market capitalization.

Taking the other side of that trade will be our systematic value investors.  They will look at the dividend yield from each stock and look to buy the cheapest 30% and sell short the most expensive 30% (the middle 40% simply go untraded).  They start with $0, but can freely borrow shares to sell short.[4]

For simplicity, we assume $0.01 bid/ask spreads, meaning that the value investor always buys a penny above price and sells a penny below.[5]

At the end of each period, the stocks pay their dividend to shareholders.[6]

What happens to “valuations” (as measured, here, by dividend yield)?

Valuations converge.  With the publicly available information of price and dividends, our systematic value investors were able to converge prices to a place where investors are largely indifferent between the stocks they hold.

For this service, the value investor earns a premium.  Let’s look at what happens to the portfolio of the value investors:

We can see that the value investors made a significant profit during the repricing period, but once valuations became more-or-less constant to one another, their profit disappeared.  They arbitraged their way out of a job.

It is important to note here that this would not work if we simply introduced momentum investors.  Without an anchor to move towards (like “valuation”), if we seeded the system with some initial price velocity, prices would spiral out of control.  That said, we can see how a momentum trade could help a value trader converge prices in a faster manner.  In a sense, one might argue that momentum traders are leveraging information provided by value traders.

What we see, however, is that stock pickers are not necessary: a systematic value approach helps the market find equilibrium.  Whether that equilibrium is right or wrong, of course, depends on the value metric used.  We could argue, though, that valuation is always in the eye of the beholder.  So long as there are a number of different approaches being employed by the market, systematic value investors can play the role of stock pickers.

That is not to say that stock pickers cannot be successful.  Rather, there is just no expectation that they should earn a premium for bearing high levels of idiosyncratic risk.  We are not saying, however, that stock pickers cannot profit off of idiosyncratic information.

For example, in our simulation, a stock picker may be able to profit in a scenario where they have insight a company will be cutting or growing their dividend in the future (making the value proxy used by value investors invalid).  Ex-post, the value investors would pick up on that information, but information realized before the rest of the market is valuable.

By its very nature, this sort of information is idiosyncratic.  Each situation is unique, special, and must be analyzed individually.  The statement past performance is not a guarantee of future results really applies here.  What is being harvested is not a risk premium or an anomaly: it is pure alpha.

For some, alpha is the purest form of compensation.  It is profits earned for discovering information and providing it to the market.  It is also inconsistent: it requires investors to identify unique opportunities to profit from them.  After all, if a manager claims to have a disciplined process for identifying the alpha opportunities, then it can be systematized and factorized.

Which means that, in the eyes of quants, the approach is unscientific.  It does not give us a way to test and re-test our investment hypotheses.  While we all know past performance is not a guarantee of future results, past performance is really all we have to draw conclusions from when performing quant research.  Without a completely disciplined approach, there is no way to draw statistical conclusions.

For managers that focus on the idiosyncratic, this holds especially true.  Even the best track-record is statistically meaningless for basing our future confidence on if investment opportunities in the future are each unique.

We’d rather focus on areas where we have the expectation of earning a consistent reward.  For us, these are the theoretically and empirically proven risk premia and anomalies like value and momentum.  That’s why quants don’t pick stocks.

[1] It’s worth pointing out that since publishing, evidence for the size premium has waned.  Over the next several years, it may give up its title as a risk premium and be swept back into the category of a risk factor.

[2] See http://docs.lhpedersen.com/BuffettsAlpha.pdf

[3] Despite our usual disdain for simulations, we seem to be using them a lot recently.

[4] The lack of lending cost and margin requirement is obviously not realistic, but we don’t think it meaningfully detracts from the point here.

[5] We could argue that for providing liquidity, the active investors should be compensated and the passive investors should cross the bid/ask spread (see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2849071).  If this is the case, however, our simulation would break: prices would diverge further from fair value.

[6] We assume, for convenience, that “earnings” and “dividends” are accrued and paid instantaneously, so there is no change in share price.

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.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

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.

This post is available as a PDF download here.

• Research Affiliates published a new piece of research exploring mutual fund returns over the last 25 years and the implied ability for managers to capture popular factor premiums published by the academic community.
• They argue that several factors accepted in academia may not be implementable after real life frictions (e.g. transaction costs, cost of shorting, missed trades, et cetera).
• Their research finds significant shortfall between published factor premiums and realized factor premiums.
• We believe that a sufficient proportion of the shortfall can be explained by estimation error in their process and, therefore, we should refrain from drawing conclusive results until more evidence is published.
• As a larger point, we acknowledge the inherent biases people exhibit to defer to authority and accept as truth the things they read outside of their own areas of expertise.
• Financial research is, in many ways, like a backtest: it is rarely published unless it is interesting and supports the firm’s existing products or viewpoint. It should, therefore, be met with much the same skepticism.

Research Affiliates published a new piece this week titled The Incredible Shrinking Factor Return (Unabridged) (henceforth AKW for the authors’ last names: Arnott, Kalesnik, and Wu).[1]  A rather hefty and wonkish read, the ultimate conclusion they draw is that factor returns actually realized by investment managers are far below those purported to be available by long/short factor research.

While they do not provide evidence as to why the shortfall exists, they do put forth several potential reasons, including:

• The long/short portfolios ignore trading and transaction costs.
• The true cost of shorting may be prohibitively high.
• Trades may be missed (e.g. shorts may not be available).
• Fund fees may significantly erode captured alpha.

The huge disparity between realized and theoretical factor returns put forth in this piece draws into question the entire benefit of factor-based investing, particularly for high-turnover factors like momentum which may incur the brunt of the implementation cost.

Finding new ways to question broadly accepted beliefs is a laudable pursuit.  We believe, however, that there is reason to remain skeptical about these particular results.

Understanding the Research Affiliates Method

AKW employ a “two-stage” regression approach.

First, using fund data from the Morningstar Direct Mutual Fund Database, they compute monthly returns from January 1991 to December 2016.  For each fund, they regress the monthly returns against four factors: Market, Value, Size, and Momentum.  This regression process identifies how much exposure the fund has had to that factor over time.

This is a fairly standard way of creating a “factor lens” through which to identify where fund performance is derived.

The second stage of the process can be a bit confusing if you’ve never come across it before.

Each month, they take the actual fund returns and regress them against the factor betas they just calculated in the prior step.  The result is estimated returns for each factor for that month.  Or, more strictly, estimated returns for the factor as captured by the funds.

For each factor, the long-term average of these estimated monthly returns is compared to the long-term average of the true factor performance.  The difference between the two long-term averages is the “implementation shortfall.”

Now by AKW’s own admission, there are many potential shortfalls in this methodology, not the least of which includes the assumption that factor exposure is constant over time.  Furthermore, they note that the second-stage of the regression will bias estimates downward due to estimation error in the betas.

But just how much downward bias might be created?

Estimation Error in Betas

To explore how big a problem factor beta estimation might be, we wanted to take a look at an example fund that was live over the period and see how meaningfully full-period beta estimates differed from short-run, rolling estimates.  We chose to look at the Vanguard Wellington Fund (VWELX).

Full Period
EstimateMinimum Rolling EstimateMaximum Rolling EstimateMarket (“MKTexRF”)0.590.440.87Size (“SMB”)-0.14-0.290.02Value (“HML”)0.18-0.180.46Momentum (“UMD”)-0.02-0.200.06

Source: Yahoo! Finance and Kenneth French Data Library.  Calculations by Newfound Research.

With this one example, we can see that style drift should not go overlooked as a potentially significant source of error in estimating betas and, therefore, a source of error in the two-stage regression process.

Source: Yahoo! Finance and Kenneth French Data Library.  Calculations by Newfound Research.

Quant Note: Why Does Estimation Error Matter?

A fact of regression is that increasing estimation error in the “dependent” variables creates what is known as attenuation: a pull of estimates towards zero.  Why?  Consider a simple example:

Y = BX + E

It is assumed in basic regression that we know X (the “independent” variables) with certainty and that Y (the “dependent” variable) might have some estimation noise.  Our goal is then to identify B.  A critical requirement is that B and E, the error term, be independent.  Y is allowed to have estimation error because it can simply be swept into E.

If X has measurement noise, however, we end up with a scenario where the observed X’s will be positively correlated with the error term, e.g.

Y = BX* + E

Where X* is our measured X with estimation noise e (assumed to be normally distributed with zero mean):

X = X* + e

Re-arranging and substituting the true X back in the equation, we get:

Y = B(X - e) + E

Y = BX + (E - Be)

If B > 0, there is a negative correlation between X and (E – Be); if B < 0, there is a positive correlation.  Therefore, if the true B > 0, then the estimator for B will be biased downward.  If the true B < 0, the estimator for B will be biased upwards.

Which means that estimation error in the dependent variables creates a pull towards zero.

Introducing a Simulation-Based Approach

We should start by saying that we generally frown upon simulation-based approaches.  All too often, simulations require such a large number of unrealistic assumptions that results do little to give us statistical confidence in the results.

That said, where simulations can be useful is in situations where we want to try to isolate a particular effect.  In this case, with AKW’s two-step regression, we want to isolate the impact of estimation error in the initial betas.  What simulations can do, in this case, is give us a baseline to measure the final results against.

For example, in this case we can ask: is a nearly 50% shortfall in market beta reasonably explained by estimation error? 

To isolate and test the potential impact of this bias, we created a simulation-based replica of AKW’s process.  The process works as follows:

• For 1000 hypothetical funds, we create a random set of factor betas. We assume these betas are the true betas and are constant over time.  The betas are assumed to be normally distributed with mean zero and standard deviation of 0.15.  This means that 95% of factor betas should fall within +/- 0.3.  For the Market beta, we shift the mean to be around 1 (so 95% of market beta exposures will fall within 0.7 and 1.3).[2]
• Using these known betas, we create the fund returns by multiplying the betas against the factor returns. This is important because it means that our betas are not estimates: they are known and true.  For convenience we ignore idiosyncratic risk.
• We then introduce varying levels of error (distributed normally with varying levels of scale) on top of our betas to create “beta estimates,”
• We perform stage two of AKW’s regression process using the fund returns and the noisy beta estimates to extract the implied realized factor returns and compare those against the true factor returns.

That’s a Big Bias

To calibrate this process, we first assume there is no error in estimating the betas.  If built correctly, the implied realized factor capture exactly matches the true factor returns over time.

Before we analyze results, there is another expectation we can set based upon the data as well.

In the last section we mentioned that the error will create a pull towards zero.  E.g. if the real factor return is +1%, then we would expect a regression result between 0% and 1%.  Similarly, if the real factor return is -1%, then we would expect a regression result between -1% and 0%.

While all of the factors exhibit a positive long-run average, the percent of months that are positive versus negative differ for each.  For example, 60%+ of months for Market and Momentum factors are positive, while for Size and Value the figures are 52% and 49% respectively.

While estimation error will pull both positive and negative results towards zero, Market and Momentum exhibit a higher frequency of positive results than negative, and therefore should exhibit a greater negative drag.[3]

Which is exactly what we see in the AWK results, as well as our simulated results.

Scale of Errors / Scale of Beta (0.15) 0%25%50%100%125%150%Market0.00%-0.54%-1.62%-3.15%-4.13%-5.23%Size0.00%-0.07%-0.62%-0.95%-1.31%-1.82%Value0.00%-0.14%-0.68%-1.40%-1.54%-2.12%Momentum0.00%-0.32%-1.30%-2.40%-2.94%-3.57%

The question that remains is whether we believe estimation error could have the same distribution scale as the betas themselves.  While we should not draw too much evidence from a single data point, we can look back towards our VWELX for guidance.

In the prior VWELX example, the standard deviation in differences between full-period and rolling estimates ranges between 0.05 (Momentum) and 0.16 (Value).  In the above table, that would put the figures between 33% and just north of 100%: areas where significant downward bias exists.

That said, our results do not fully refute AKW’s evidence.

• AKW tests their results using look-back regressions instead of full-period regressions and find similar results. However, they appear to use an expanding window process, instead of a rolling window process, whereby as much historical data is utilized as possible.  In later periods, this will lead to estimates that asymptotically approach the full-period beta.
• The plots provided by AKW of factor returns captured by managers versus their observed returns exhibit linear relationships with slopes between 0.95 and 1.01. Downward biases created by estimation error would reduce the slope of these lines significantly.
• AKW reports that the Size premium captured by managers exceeds the theoretical long/short.

Nevertheless, style drift and estimation error in beta may be a significant contributor to the results put forth by AKW and, in our opinion, call into question the ability to draw any meaningful conclusion from their results at this time.

Addressing our Own Biases

We think it is worth taking a moment to take a step back and address a larger issue: biases when it comes to reading published research.

At Newfound, we have the quantitative aptitude to examine the hypothesis put forth by AKW.  Many industry professionals do not.  For those who cannot, all too often instead of addressing the research with a healthy dose of skepticism, it is accepted outright.  Why is that the case?

In a 1993 study by Daniel Gilbert, Romin Tafarodi, and Patrick Malone – titled “You Can’t Not Believe Everything You Read” – experiments found evidence that comprehension first requires an initial belief that is then followed by critical analysis.

In other words, if you read something, your natural inclination is to accept it as true.

We’re personally partial to a variant called the Murray Gell-Mann Amnesia effect, popularized by Michael Crichton in his 2002 essay, “Why Speculate?”:

Media carries with it a credibility that is totally undeserved. You have all experienced this, in what I call the Murray Gell-Mann Amnesia effect. (I call it by this name because I once discussed it with Murray Gell-Mann, and by dropping a famous name I imply greater importance to myself, and to the effect, than it would otherwise have.)

Briefly stated, the Gell-Mann Amnesia effect works as follows. You open the newspaper to an article on some subject you know well. In Murray’s case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward-reversing cause and effect. I call these the “wet streets cause rain” stories. Paper’s full of them.

In any case, you read with exasperation or amusement the multiple errors in a story-and then turn the page to national or international affairs, and read with renewed interest as if the rest of the newspaper was somehow more accurate about far-off Palestine than it was about the story you just read. You turn the page, and forget what you know.

That is the Gell-Mann Amnesia effect. I’d point out it does not operate in other arenas of life. In ordinary life, if somebody consistently exaggerates or lies to you, you soon discount everything they say. In court, there is the legal doctrine of falsus in uno, falsus in omnibus, which means untruthful in one part, untruthful in all.

But when it comes to the media, we believe against evidence that it is probably worth our time to read other parts of the paper. When, in fact, it almost certainly isn’t. The only possible explanation for our behavior is amnesia.

We’d argue these effects are compounded by our inherent authority bias, whereby we attribute greater accuracy to the opinion of an authority figure.

Rob Arnott and company are, without a doubt, authority figures.

Last year they made waves by arguing that not only should we be worried about a violent factor crash, but went so far as to say that many largely accepted factors were nothing but the result of sloppy data-mining.  (We’ll refrain from pointing out the irony that many of the factors identified as being data-mined are offered as RAFI indices…)

The big danger here is that, for many, what is published by big firms filled with PhDs – like Research Affiliates – is taken as gospel.

Cliff Asness, co-founder of AQR, took up the mantle to challenge Arnott’s claims, but Arnott has largely ignored the critiques.

Perhaps more importantly, Asness’s rebukes have been far more poorly covered in the media than Arnott’s initial outlandish claims.  For many, this creates a false perception that Arnott’s view is not only unchallenged, but broadly accepted by the industry.

We want to be clear: we are not saying Research Affiliates is doing anything malicious.  The reality is that we’re all human.  We all make mistakes.  We prefer to defer to Hanlon’s razor: “Don’t assume bad intentions over neglect and misunderstanding.”

That said, published research in finance is often like a backtest: rarely do you see any that does not support the firm’s products or existing views.

All that is to only say that we must be aware of our own biases that make it difficult for us to not blindly believe the things we read.  If we don’t understand the process behind something, it does little harm to apply a healthy dose of skepticism.

[1] https://www.researchaffiliates.com/en_us/publications/articles/604-the-incredible-shrinking-factor-return-unabridged.html

[2] We choose these levels largely based on anecdotal experience of running factor regressions.

[3] With this broad statement, we are (perhaps unfairly) assuming that monthly returns will be normally distributed.  Significant skew or kurtosis in these figures could meaningfully change these assumptions.

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.com, ETF Trends, and Forbes.com’s Great Speculations blog. He was named a 2014 ETF All Star by ETF.com.

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.