The Research Library of Newfound Research

Author: Corey Hoffstein Page 15 of 18

Corey is co-founder and Chief Investment Officer of Newfound Research.

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.

It’s Long/Short Portfolios All The Way Down

There is a PDF version of this post available for download here.

Summary­­

  • Long/short portfolios are helpful tools for quantifying the value-add of portfolio changes, especially for active strategies.
  • In the context of fees, we can isolate the implicit fee of the manager’s active decisions (active share) relative to a benchmark and ask ourselves whether we think that hurdle is attainable.
  • Bar-belling low fee beta with high active share, higher fee managers may actually be cheaper to incorporate than those managers found in the middle of the road.
  • However, as long as investors still review their portfolios on an itemized basis, this approach runs the risk of introducing greater behavioral foibles than a more moderated – yet ultimately more expensive – approach.

After a lecture on cosmology and the structure of the solar system, William James was accosted by a little old lady.

“Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it’s wrong. I’ve got a better theory,” said the little old lady.

“And what is that, madam?” Inquired James politely.

“That we live on a crust of earth which is on the back of a giant turtle,”

Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.

“If your theory is correct, madam,” he asked, “what does this turtle stand on?”

“You’re a very clever man, Mr. James, and that’s a very good question,” replied the little old lady, “but I have an answer to it. And it is this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him.”

“But what does this second turtle stand on?” persisted James patiently.

To this the little old lady crowed triumphantly. “It’s no use, Mr. James – it’s turtles all the way down.”

— J. R. Ross, Constraints on Variables in Syntax 1967

The Importance of Long/Short Portfolios

Anybody who has read our commentaries for some time has likely found that we have a strong preference for simple models.  Justin, for example, has a knack for turning just about everything into a conversation about coin flips and their associated probabilities.  I, on the other hand, tend to lean towards more hand-waving, philosophical arguments (e.g. The Frustrating Law of Active Management[1] or that every strategy is comprised of a systematic and an idiosyncratic component[2]).

While not necessarily 100% accurate, the power of simplifying mental models is that it allows us to explore concepts to their – sometimes absurd – logical conclusion.

One such model that we use frequently is that the difference between any two portfolios can be expressed as a dollar-neutral long/short portfolio.  For us, it’s long/short portfolios all the way down.

This may sound like philosophical gibberish, but let’s consider a simple example.

You currently hold Portfolio A, which is 100% invested in the S&P 500 Index.  You are thinking about taking that money and investing it entirely into Portfolio B, which is 100% invested in the Barclay’s U.S. Aggregate Bond Index.  How can you think through the implications of such a change?

One way of thinking through such changes is that recognizing that there is some transformation that takes us from Portfolio A to portfolio B, i.e. Portfolio A + X = Portfolio B.

We can simply solve for X by taking the difference between Portfolio B and Portfolio A.  In this case, that difference would be a portfolio that is 100% long the Barclay’s U.S. Aggregate Bond Index and 100% short the S&P 500 Index.

Thus, instead of saying, “we’re going to hold Portfolio B,” we can simply say, “we’re going to continue to hold Portfolio A, but now overlay this dollar-neutral long/short portfolio.”

This may seem like an unnecessary complication at first, until we realize that any differences between Portfolio A and B are entirely captured by X.  Focusing exclusively on the properties of X allows us to isolate and explore the impact of these changes on our portfolio and allows us to generalize to cases where we hold allocation to X that are different than 100%.

Re-Thinking Fees with Long/Short Portfolios

Perhaps most relevant, today, is the use of this framework in the context of fees.

To explore, let’s consider the topic in the form of an example.  The iShares S&P 500 Value ETF (IVE) costs 0.18%, while the iShares S&P 500 ETF (IVV) is offered at 0.04%.  Is it worth paying that extra 0.14%?

Or, put another way, does IVE stand a chance to make up the fee gap?

Using the long/short framework, one way of thinking about IVE is that IVE = IVV + X, where X is the long/short portfolio of active bets.

But are those active bets worth an extra 0.14%?

First, we have to ask, “how much of the 0.18% fee is actually going towards IVV and how much is going towards X?”  We can answer this by using a concept called active share, which explicitly measures how much of IVE is made up of IVV and how much it is made up of X.

Active share can be easily explained with an example.[3]  Consider having a portfolio that is 50% stocks and 50% bonds, and you want to transition it to a portfolio that is 60% stocks and 40% bonds.

In essence, your second portfolio is equal to your first plus a portfolio that is 10% long stocks and 10% short bonds.  Or, equivalently, we can think of the second portfolio as equal to the first plus a 10% position in a portfolio that is 100% long stocks and 100% short bonds.

Through this second lens, that 10% number is our active share.

Returning to our main example, IVE has a reported active share of 42% against the S&P 500[4].

Hence, we can say that IVE = 100% IVV + 42% X.  This also means that 0.14% of the 0.18% fee is associated with our active bets, X.  (We calculate this as 0.18% – 0.04% x 100%.)

If we take 0.14% and divide it by 42%, we get the implicit fee that we are paying for our active bets.  In this case, 0.333%.

So now we have to ask ourselves, “do we think that a long/short equity portfolio can return at least 0.333%?”  We might want to dive more into exactly what that long/short portfolio looks like (i.e. what are the actual active bets being made by IVE versus IVV), but it does not seem so outrageous.  It passes the sniff test.

What if IVE were actually 0.5% instead?  Now we would say that 0.46% of the 0.5% is going towards our 42% position in X.  And, therefore, the implicit amount we’re paying for X is actually 1.09%.

Am I confident that an equity long/short value portfolio can clear a hurdle of 1.09% with consistency?  Much less so.  Plus, the fee now eats a much more significant part of any active return generated.  E.g. If we think the alpha from the pure long/short portfolio is 3%, now 1/3rd of that is going towards fees.

With this framework in mind, it is no surprise active managers have historically struggled so greatly to beat their benchmarks.  Consider that according to Morningstar[5], the dollar-weighted average fee paid to passive indexes was 0.25% in 2000, whereas it was 1% for active funds.

If we assume a very generous 50% active share for those active funds, we can use the same math as before to find that we were, in essence, paying a 2.00% fee for the active bets.  That’s a high hurdle for anyone to overcome.

And the closet indexers?  Let’s be generous and assume they had an active share of 20% (which, candidly, is probably high if we’re calling them closet indexers).  This puts the implied fee at 4%!  No wonder they struggled…

Today, the dollar weighted average expense ratio for passive funds is 0.17% and for active funds, it’s 0.75%.  To have an implied active fee of less than 1%, active funds at that level will have to have an active share of at least 30%.[6]

Conclusion

As the ETF fee wars rage on, and the fees for standard benchmarks plummeting on a near-daily basis, the only way an active manager can continue to justify a high fee is with an exceptionally high active share.

We would argue that those managers caught in-between – with average fees and average active share – are those most at risk to be disintermediated.  Most investors would actually be better off by splitting the exposure into cheaper beta solutions and more expensive, high active share solutions.  Bar-belling low fee beta with high active share, higher fee managers may actually be cheaper to incorporate than those found the middle of the road.

The largest problem with this approach, in our minds, is behavioral.  High active share should mean high tracking error, which means significant year-to-year deviation from a benchmark.  So long as investors still review their portfolios on an itemized basis, this approach runs the risk of introducing greater behavioral foibles than a more moderated – yet ultimately more expensive – approach.

 


 

[1] https://blog.thinknewfound.com/2017/10/frustrating-law-active-management/

[2] https://twitter.com/choffstein/status/880207624540749824

[3] Perhaps it is “examples” all the way down.

[4] See https://tools.alphaarchitect.com

[5] https://corporate1.morningstar.com/ResearchLibrary/article/810041/us-fund-fee-study–average-fund-fees-paid-by-investors-continued-to-decline-in-2016/

[6] We are not saying that we need a high active share to predict outperformance (https://www.aqr.com/library/journal-articles/deactivating-active-share). Rather, a higher active share reduces the implicit fee we are paying for the active bets.

The Frustrating Law of Active Management

A PDF version of this post is available for download here.

Summary­­

  • In an ideal world, all investors would outperform their benchmarks. In reality, outperformance is a zero-sum game: for one investor to outperform, another must underperform.
  • If achieving outperformance with a certain strategy is perceived as being “easy,” enough investors will pursue that strategy such that its edge is driven towards zero.
  • Rather, for a strategy to outperform in the long run, it has to be hard enough to stick with in the short run that it causes investors to “fold,” passing the alpha to those with the fortitude to “hold.”
  • In other words, for a strategy to outperform in the long run, it must underperform in the short run. We call this The Frustrating Law of Active Management.

A few weeks ago, AQR published a piece titled Craftsmanship Alpha: An Application to Style Investing[1], to which Cliff Asness wrote a further perspective piece titled Little Things Mean a Lot[2].

We’ll admit that we are partial to the title “craftsmanship alpha” because portfolio craftsmanship is a concept we spend a lot of time thinking about.  In fact, we have a whole section titled Portfolio Craftsmanship on the Investment Philosophy section of our main website.[3]  We further agree with Cliff: little things do mean a lot.  We even wrote a commentary about it in May titled Big Little Details[4].

But there was one quote from Cliff, in particular, that inspires this week’s commentary:

Let’s just make up an example. Imagine there are ten independent (uncorrelated) sources of “craftsmanship alpha” and that each adds 2 basis points of expected return at the cost of 20 basis points of tracking error from each (against some idea of a super simple “non-crafted” alternative.)  Each is thus a 0.10 Sharpe ratio viewed alone. Together they are expected to add 20 basis points to the overall factor implementation inducing 63 basis points of tracking error (20 basis points times the square-root of ten). That’s a Sharpe ratio of 0.32 from the collective craftsmanship (in addition to the basic factor returns).

[…]

But, as many have noted in other contexts, a Sharpe ratio like 0.32 can be hard to live with. Its chance of subtracting from your performance in a given year is about 37%. Its chance of subtracting over five years is about 24%. And, wait for it… over twenty years the chance it subtracts is still about 8%. That’s right. There’s a non-trivial chance your craftsmanship is every bit as good as you think, and it subtracts over two full decades, perhaps the lion’s share of your career. Such is the unforgiving, uncaring math.

Whether it is structural alpha, style premia, or craftsmanship alpha: we believe that the very uncertainty and risk that manifests as (expected) tracking error is a necessary component for the alpha to exist in the first place.

The “unforgiving, uncaring math” that is a result – the fact that you can do everything right and still get everything wrong – is a concept that in the past we have titled The Frustrating Law[5] of Active Management.

Defining The Frustrating Law of Active Management

We define The Frustrating Law of Active Management as:

For any disciplined[6] investment approach to outperform over the long run, it must experience periods of underperformance in the short run.

As if that were not frustrating enough a concept – that even if we do everything right, we still have to underperform from time-to-time – we add this corollary:

For any disciplined investment approach to underperform over the long run, it must experience periods of outperformance in the short run.

In other words, even if a competing manager does everything wrong, they should still be rewarded with outperformance at some point.  Talk about adding insult to injury.

For the sake of brevity, we will only explore the first half of the law in this commentary.  Note, however, that the second law is simply the inverse case of the first.  After all, if we found an investment strategy that consistently underperformed, we could merely inverse the signals and have a strategy that consistently outperforms.  If the latter is impossible, so must be the former.

For it to work, it has to be hard

Let’s say we approach you with a new investment strategy.  We’ve discovered the holy grail: a strategy that always outperforms.  It returns an extra 2% over the market, consistently, every year, after fees.

Ignoring reasonable skepticism for a moment, would you invest?  Of course you would.  This is free money we’re talking about here!

In fact, everyone we pitch to would invest.  Who wouldn’t want to be invested in such a strategy?  And here, we hit a roadblock.

Everyone can’t invest.  Relative performance is, after all, zero sum: for some to outperform, others must underperform.  Our extra return has to come from somewhere.

If we do continue to accept money into our strategy, we will begin to approach and eventually exceed capacity.  As we put money to work, we will create impact and inform the market, driving prices away from us.  As we try to buy, prices will be driven up and as we try to sell, prices will be driven down.  By chasing price, our outperformance will deteriorate.

And it needn’t even be us trading the strategy.  Once people learn about what we are doing – and how easy it is to make money – others will begin to employ the same approach.  Increasing capital flow will continue to erode the efficacy of the edge as more and more money chases the same, limited opportunities. The growth is likely to be exponential, quickly grinding our money machine quickly to a halt.

So, the only hope of keeping a consistent edge is in a mixture of: (1) keeping the methodology secret, (2) keeping our deployed capital well below capacity, and (3) having a structural moat (e.g. first-mover advantage, relationship-driven flow, regulatory edge, non-profit-seeking counter-party, etc).

While we believe that all asset managers have the duty to ensure #2 remains true (we highly recommend reading Alpha or Assets by Patrick O’Shaughnessy[7]), #1 pretty much precludes any manager actually trying to raise assets (with, perhaps, a few limited exceptions in the hedge fund world that can raise assets on brand alone).

The takeaway here is that if an edge is perceived as being easy to implement (i.e. not case #3 above) and easy to achieve, enough people will do it to the point that the edge is driven to zero.

Therefore, if an edge is known by many (e.g. most style premia like value, momentum, carry, defensive, trend, etc), then for it to persist over the long run, the outperformance must be difficult to capture.  Remember: for outperformance to exist, weak hands must at some point “fold” (be it for behavioral or risk-based reasons), passing the alpha to strong hands that can “hold.”

This is not just a case of perception, either.  Financial theory tells us that a strategy cannot always outperform its benchmark with certainty.  After all, if it did, we would have an arbitrage: we could go long the strategy, short the benchmark, and lock in certain profit.  As markets loathe (or, perhaps, love) arbitrage, such an opportunity should be rapidly chased away.  Thus, for a disciplined strategy to generate alpha over the long run, it must go through periods of underperformance in the short-run.

Can We Diversify Away Difficulty?

Math tells us that we should be able to stack the benefits of multiple, independent alpha sources on top of each other and simultaneously benefit from potentially reduced tracking error due to diversification.

Indeed, mathematically, this is true.  It is why diversification is known as the only free lunch in finance.

This certainly holds for beta, which derives its value from economic activity.  In theory, everyone can hold the Sharpe ratio optimal portfolio and introduce cash or leverage to hit their appropriate risk target.

Alpha, on the other hand, is explicitly captured from the hands of other investors.  Contrary to the Sharpe optimal portfolio, everyone cannot hold the Information ratio optimal portfolio at the same time[8]Someone needs to be on the other side of the trade.

Consider three strategies that all outperform over the long run: strategy A, strategy B, and strategy C.  Does our logic change if we learn that strategy C is simply 50% strategy A plus 50% strategy B?  Of course not!  For C to continue to outperform over the long run, it must remain sufficiently difficult to stick with in the short-run that it causes weak hands to fold.

Conclusion

For a strategy to outperform in the long run, it has to be perceived as hard: hard to implement or hard to hold.  For public, liquid investment styles that most investors have access to, it is usually a case of the latter.

This law is underpinned by two facts.  First, relative performance is zero-sum, requiring some investors to underperform for others to outperform.  Second, consistent outperformance violates basic arbitrage theories.

While coined somewhat tongue-in-cheek, we think this law provides an important reminder to investors about reasonable expectations.  As it turns out, the proof is not always in the eating of the pudding.  In fact, track records can be entirely misleading as validators of an investment process.  As Cliff pointed out, even if our alpha source has a Sharpe ratio of 0.32, there is an 8% chance that it subtracts from performance over the next 20-years.

Conversely, even negative alpha sources can show beneficial performance by chance.  An alpha source with a Sharpe ratio of -0.32 has an 8% chance that it adds to performance over the next 20-years.

And that’s why we call it The Frustrating Law of Active Management.  For investors and asset managers alike, there is little more frustrating than knowing that to continue working over the long run, good strategies have to do poorly, and poor strategies have to do well over shorter timeframes.

 


 

[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3034472

[2] https://www.aqr.com/cliffs-perspective/little-things-mean-a-lot

[3] https://www.thinknewfound.com/investment-philosophy

[4] https://blog.thinknewfound.com/2017/05/big-little-details/

[5] To be clear that we don’t mean a “law” in the sense of an inviolable, self-evident axiom.  In truth, our “law” is much closer to a “theory.”

[6] The disciplined component here is very important.  By this, we mean a strategy that applies a consistent set of rules.  We do not mean, here, a bifurcation of systematic versus discretionary.  Over the years, we’ve met a large number of discretionary managers who apply a highly disciplined approach.  Rather, we mean those aspects of an investment strategy that can be codified and turned into a set of systematically applied rules.

Thus, even a discretionary manager can be thought of as a systematic manager plus a number of idiosyncratic deviations from those rules.  The deviations must be idiosyncratic, by nature.  If there was a consistent reason for making the deviations, after all, the reason could be codified itself.  Thus, true discretion only applies to unique, special, and non-repeatable situations.

Note that the discipline does not preclude randomness.  You could, for example, flip a coin and use the result to make an investment decision every month.  So long as the same set of rules is consistently applied, we believe The Frustrating Law of Active Management applies.

[7] http://investorfieldguide.com/alpha-or-assets/

[8] Well, technically they can if everyone is a passive investor.  In this case, however, the information ratio would be undefined, with zero excess expected return and zero tracking error.

 

Tax-Managed Models & Asset Location

This post is available for download as a PDF here.

Summary­­

  • In a world of anemic asset returns, tax management may help significantly contribute to improving portfolio returns.
  • Ideally, asset location decisions would be made with full investor information, including goals, risk tolerances, tax rates, and distribution of wealth among account types.
  • Without perfect information, we believe it is helpful to have both tax-deferred and tax-managed model portfolios available.
  • We explore how tax-adjusted expected returns can be created, and how adjusting for taxes affects an optimized portfolio given today’s market outlook.

Before we begin, please note that we are not Certified Public Accountants, Tax Attorneys, nor do we specialize in tax management.  Tax law is complicated and this commentary will employ sweeping generalizations and assumptions that will certainly not apply to every individual’s specific situation.  This commentary is not meant as advice, simply research.  Before making any tax-related changes to your investment process, please consult an expert.

Tax-Managed Thinking

We’ve been writing a lot, recently, about the difficulties investors face going forward.[1][2][3]  It is our perspective that the combination of higher-than-average valuations in U.S. stocks and low interest rates in core U.S. bonds indicates a muted return environment for traditionally allocated investors going forward.

There is no silver bullet to this problem.  Our perspective is that investors will likely have to work hard to make many marginal, but compounding, improvements.  Improvements may include reducing fees, thinking outside of traditional asset classes, saving more, and, for investors in retirement, enacting a dynamic withdrawal plan.

Another potential opportunity is in tax management.

I once heard Dan Egan, Director of Behavioral Finance at Betterment, explain tax management as an orthogonal improvement: i.e. one which could seek to add value regardless of how the underlying portfolio performed.  I like this description for two reasons.

First, it fits nicely into our framework of compounding marginal improvements that do not necessarily require just “investing better.”  Second, Dan is the only person, besides me, to use the word “orthogonal” outside of a math class.

Two popular tax management techniques are tax-loss harvesting and asset location.  While we expect that tax-loss harvesting is well known to most (selling investments at a loss to offset gains taken), asset location may be less familiar.  Simply put, asset location is how investments are divided among different accounts (taxable, tax-deferred, and tax-exempt) in an effort to maximize post-tax returns.

Asset Location in a Perfect World

Taxes are a highly personal subject.  In a perfect world, asset location optimization would be applied to each investor individually, taking into account:

  • State tax rates
  • Federal tax rates
  • Percentage of total assets invested in each account type

Such information would allow us to run a very simple portfolio optimization that could take into account asset location.

Simply, for each asset, we would have three sets of expected returns: an after-tax expected return, a tax-deferred expected return, and a tax-exempt expected return.  For all intents and purposes, the optimizer would treat these three sets of returns as completely different asset classes.

So, as a simple example, let’s assume we only want to build a portfolio of U.S. stocks and bonds.  For each, we would create three “versions”: Taxable, Tax-Deferred, and Tax-Exempt.  We would calculate expected returns for U.S. Stocks – Taxable, U.S. Stocks – Tax-Deferred, and U.S. Stocks – Tax-Exempt.  We would do the same for bonds.

We would then run a portfolio optimization.  To the optimizer, it would look like six asset classes instead of two (since there are three versions of stocks and bonds).  We would add the constraint that the sum of the weights to Taxable, Tax-Deferred, and Tax-Exempt groups could not exceed the percentage of our wealth in each respective account type.  For example, if we only have 10% of our wealth in Tax-Exempt accounts, then U.S. Stocks – Tax Exempt + U.S. Bonds – Tax Exempt must be equal to 10%.

Such an approach allows for the explicit consideration of an individual’s tax rates (which are taken into account in the adjustment of expected returns) as well as the distribution of their wealth among different account types.

Case closed.[4]

Asset Location in a Less Than Perfect World

Unfortunately, the technology – and expertise – required to enable such an optimization is not readily available for many investors.

As an industry, the division of labor can significantly limit the availability of important information.  While financial advisors may have access to an investor’s goals, risk tolerances, specific tax situation, and asset location break-down, asset managers do not.  Therefore, asset managers are often left to make sweeping assumptions, like infinite investment horizons, defined and constant risk tolerances, and tax indifference.

Indeed, we currently make these very assumptions within our QuBe model portfolios. Yet, we think we can do better.

For example, consider investors at either end of the spectrum of asset location.  On the one end, we have investors with the vast majority of their assets in tax-deferred accounts.  On the other, investors with the vast majority of their wealth in taxable accounts.  Even if two investors at opposite ends of the spectrum have an identical risk tolerance, their optimal portfolios are likely different.  Painting with broad strokes, the tax-deferred investor can afford to have a larger percentage of their assets in tax-inefficient asset classes, like fixed income and futures-based alternative strategies.  The taxable investor will likely have to rely more heavily on tax-efficient investments, like indexed equities (or active equities, if they are in an ETF wrapper).

Things get much messier in the middle of the spectrum.  We believe investors have two primary options:

  1. Create an optimal tax-deferred portfolio and try to shift tax-inefficient assets into the tax-deferred accounts and tax-efficient assets into taxable accounts. Investor liquidity needs need to be carefully considered here, as this often means that taxable accounts will be more heavily tilted towards more volatile equities while bonds will fall into tax-deferred accounts.
  2. Create an optimal tax-deferred portfolio and an optimal taxable portfolio, and invest in each account accordingly. This is, decidedly, sub-optimal to asset location in a perfect world, and should even under most scenarios be sub-optimal to Option #1, but it should be preferable to simply ignoring taxes.  Furthermore, it may be easier from an implementation perspective, depending on the rebalancing technology available to you.

With all this in mind, we have begun to develop tax-managed versions of our QuBe model portfolios, and expect them to be available at the beginning of Q4.

Adjusting Expected Returns for Taxes

To keep this commentary to a reasonable length (as if that has ever stopped us before…), we’re going to use a fairly simple model of tax impact.

At the highest level, we need to break down our annual expected return into three categories: unrealized, externally realized, and internally realized.

  • Unrealized: The percentage of the total return that remains un-taxed. For example, the expected return of a stock that is bought and never sold would be 100% unrealized (ignoring, for a moment, dividends and end-of-period liquidation).
  • Externally Realized: The percentage of total return that is taxed due to asset allocation turnover. For example, if we re-optimize our portfolio annually and incur 20% turnover, causing us to sell positions, we would say that 20% of expected return is externally realized.
  • Internally Realized: The percentage of total return that comes from internal turnover, or income generated, within our investment. For example, the expected return from a bond may be 100% internally realized.  Similarly, a very active hedge fund strategy may have a significant amount of internal turnover that realizes gains.

Using this information, we can fill out a table, breaking down for each asset class where we expect returns to come from as well as within that category, what type of tax-rate we can expect.  For example:

For example, in the table above we are saying we expect 70% of our annual U.S. equity returns to be unrealized while 30% of them will be realized at a long-term capital gains rate.  Note that we also explicitly estimate what we will be receiving in qualified dividends.

On the other hand, we only expect that 35% of our hedge fund returns to be unrealized, while 15% will be realized from turnover (all at a long-term capital gains rate) and the remaining 50% will be internally realized by trading within the fund, split 40% short-term capital gains and 60% long-term capital gains.For example, in the table above we are saying we expect 70% of our annual U.S. equity returns to be unrealized while 30% of them will be realized at a long-term capital gains rate.  Note that we also explicitly estimate what we will be receiving in qualified dividends.

Obviously, there is a bit of art in these assumptions.  How much the portfolio turns over within a year must be estimated.  What types of investments you are making will also have an impact.  For example, if you are investing in ETFs, even very active equity strategies can be highly tax efficient.  Mutual funds on the other hand, potentially less so.  Whether a holding like Gold gets taxed at a Collectible rate or a split between short- and long-term capital gains will depend on the fund structure.

Using this table, we can then adjust the expected return for each asset class using the following equations:

Where,

In English,

  • Take the pre-tax return and subtract out the amount we expect to come from qualified dividend yield.
  • Take the remainder and multiply it by the total blended tax rate we expect from externally and internally realized gains.
  • Add back in the qualified dividend yield, after adjusting for returns.

As a simple example, let’s assume U.S. equities have a 6% expected return.  We’ll assume a 15% qualified dividend rate and a 15% long-term capital gains rate.  We’ll ignore state taxes for simplicity.

Our post-tax expected return is, therefore 6% – (6%-2%)*(30%*15%) – 2%*15% = 5.52%.

We can follow the same broad steps for all asset classes, making some assumptions about tax rates and expected sources of realized returns.

(For those looking to take a deeper dive, we recommend Betterment’s Tax-Coordinated Portfolio whitepaper[5], Ashraf Al Zaman’s Tax Adjusted Portfolio Optimization and Asset Location presentation[6], and Geddes, Goldberg, and Bianchi’s What Would Yale Do If It Were Taxable? paper[7].)

 

How Big of a Difference Does Tax Management Make?

So how much of a difference does taking taxes into account really make in the final recommended portfolio?

We explore this question by – as we have so many times in the past – relying on J.P. Morgan’s capital market assumptions.  The first portfolio is constructed using the same method we have used in the past: a simulation-based mean-variance optimization that targets the same risk level as a 60% stock / 40% bond portfolio mix.

For the second portfolio, we run the same optimization, but adjust the expected return[8] for each asset class.

We make the following assumptions about the source of realized returns and tax rates for each asset class (note that we have compressed the above table by combining rates together after multiplying for the amount realized by that category; e.g. realized short below represents externally and internally realized short-term capital gains).

Again, the construction of the below table is as much art as it is science, with many assumptions embedded about the type of turnover the portfolio will have and the strategies that will be used to implement it.

 

CollectibleOrdinary IncomeRealized ShortRealized LongUnrealizedDividend
Alternative – Commodities0%0%10%20%70%0%
Alternative – Event Driven0%0%26%53%21%0%
Alternative – Gold30%0%0%0%70%0%
Alternative – Long Bias0%0%26%53%21%1%
Alternative – Macro0%0%26%53%21%0%
Alternative – Relative Value0%0%26%53%21%0%
Alternative – TIPS0%100%0%0%0%0%
Bond – Cash0%100%0%0%0%0%
Bond – Govt (Hedged) ex US0%100%0%0%0%0%
Bond – Govt (Not Hedged) ex US0%100%0%0%0%0%
Bond – INT Treasuries0%100%0%0%0%0%
Bond – Investment Grade0%100%0%0%0%0%
Bond – LT Treasuries0%100%0%0%0%0%
Bond – US Aggregate0%100%0%0%0%0%
Credit – EM Debt0%100%0%0%0%0%
Credit – EM Debt (Local)0%100%0%0%0%0%
Credit – High Yield0%100%0%0%0%0%
Credit – Levered Loans0%100%0%0%0%0%
Credit – REITs0%100%0%0%0%0%
Equity – EAFE0%0%10%20%70%2%
Equity – EM0%0%10%20%70%2%
Equity – US Large0%0%10%20%70%2%
Equity – US Small0%0%10%20%70%2%

We also make the following tax rate assumptions:

  • Ordinary Income: 28%
  • Short-Term Capital Gains: 28%
  • Long-Term Capital Gains: 28%
  • Qualified Dividend: 15%
  • Collectibles: 28%
  • Ignore state-level taxes.

The results of both optimizations can be seen in the table below.

 

Tax-DeferredTax-Managed
Equity – US Large3.9%5.3%
Equity – US Small5.9%7.0%
Equity – EAFE3.3%4.8%
Equity – Emerging Markets11.1%12.0%
Sum24.2%29.1%
Bond – US Aggregate0.1%0.1%
Bond – Int US Treasuries0.6%0.4%
Bond – LT US Treasuries12.4%12.2%
Bond – Investment Grade0.0%0.0%
Bond – Govt (Hedged) ex US0.3%0.1%
Bond – Govt (Not Hedged) ex US0.3%0.2%
Sum13.8%13.1%
Credit – High Yield6.2%3.9%
Credit – Levered Loans11.8%8.9%
Credit – EM Debt4.2%2.7%
Credit – EM Debt (Local)5.2%3.5%
Credit – REITs8.6%8.1%
Sum36.0%27.1%
Alternative – Commodities4.0%3.9%
Alternative – Gold11.3%13.9%
Alternative – Macro6.8%8.6%
Alternative – Long Bias0.1%0.1%
Alternative – Event Driven1.6%2.2%
Alternative – Relative Value0.5%1.3%
Alternative – TIPS1.6%0.8%
Sum26.0%30.8%

 

Broadly speaking, we see a shift away from credit-based asset classes (though, they still command a significant 27% of the portfolio) and towards equity and alternatives.

We would expect that if the outlook for equities improved, or we reduced the expected turnover within the portfolio, this shift would be even more material.

It is important to note that at least some of this difference can be attributed to the simulation-based optimization engine.  Percentages can be misleading in their precision: the basis point differences between assets within the bond category, for example, are not statistically significant changes.

And how much difference does all this work make?  Using our tax-adjusted expected returns, we estimate a 0.20% increase in expected return between tax-managed and tax-deferred versions right now.  As we said: no silver bullets, just marginal improvements.

What About Municipal Bonds?

You may have noticed municipal bonds are missing from the above example.  What gives?

Part of the answer is theoretical.  Consider the following situation.  You have two portfolios that are identical in every which way (e.g. duration, credit risk, liquidity risk, et cetera), except one is comprised of municipal bonds and one of corporate bonds.  Which one do you choose?

The one with the higher post-tax yield, right?

This hypothetical highlights two important considerations.  First, the idea that municipal bonds are for taxable accounts and corporate bonds are for tax-deferred accounts overlooks the fact that investors should be looking to maximize post-tax return regardless of asset location.  If municipal bonds offer a better return, then put them in both accounts!  Similarly, if corporate bonds offer a more attractive return after taxes, then they should be held in taxable accounts.

For example, right now the iShares iBoxx $ Investment Grade Corporate Bond ETF (LQD) has a 30-day SEC yield of 3.16%.  The VanEck Vectors ATM-Free Intermediate Municipal Index ETF (ITM) has a 30-day SEC yield of just 1.9%.  However, this is the taxable equivalent to an investor earning a 3.15% yield at a 39.6% tax rate.

In other words, LQD and ITM offer a nearly identical return within in a taxable account for an investor in the highest tax bracket.  Lower tax brackets imply lower taxable equivalent return, meaning that LQD may be a superior investment for these investors.  (Of course, we should note that municipal bonds are not corporate bonds.  They often are often less liquid, but of higher credit quality.)

Which brings up our second point: taxes are highly personal.  For a wealthy investor, an ordinary income tax of 35% could make municipal bonds far more attractive than they are for an investor only paying a 15% ordinary income tax rate.

Simply put: solving the when and where of municipal bonds is not always straight forward.  We believe the best approach is account for them as a standalone asset class within the optimization, letting the optimizer figure out how to maximize post-tax returns.

Conclusion

We believe that a low-return world means that many investors will have a tough road ahead when it comes to achieving their financial goals.  We see no silver bullet to this problem.  We do see, however, many small steps that can be taken that can compound upon each other to have a significant impact.  We believe that asset location provides one such opportunity and is therefore a topic that deserves far more attention in a low-return environment.

 


 

[1] See The Impact of High Equity Valuations on Safe Withdrawal Rates –   https://blog.thinknewfound.com/2017/08/impact-high-equity-valuations-safe-retirement-withdrawal-rates/

[2] See Portfolios in Wonderland & The Weird Portfolio – https://blog.thinknewfound.com/2017/08/portfolios-wonderland-weird-portfolio/

[3] See The Butterfly Effect in Retirement Planning – https://blog.thinknewfound.com/2017/09/butterfly-effect-retirement-planning/

[4] Clearly this glosses over some very important details.  For example, an investor that has significant withdrawal needs in the near future, but has the majority of their assets tied up in tax-deferred accounts, would significantly complicate this optimization.  The optimizer will likely put tax-efficient assets (e.g. equity ETFs) in taxable accounts, while less tax-efficient assets (e.g. corporate bonds) would end up in tax-deferred accounts.  Unfortunately, this would put the investor’s liquidity needs at significant risk.  This could be potentially addressed by adding expected drawdown constraints on the taxable account.

[5] https://www.betterment.com/resources/research/tax-coordinated-portfolio-white-paper/

[6] http://www.northinfo.com/documents/337.pdf

[7] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2447403

[8] We adjust volatility as well.

Building an Unconstrained Sleeve

We’re often asked about how to build an unconstrained sleeve in a portfolio.

Our view is that your mileage will largely vary by where you are trying to go.  With that in mind, we focus on three objectives:

  • Sleeves that seek to hedge equity losses.
  • Sleeves that seek significant equity upside capture while reducing downside.
  • Sleeves that seek an absolute return profile.

We explore how these sleeves can be built using common strategies such as tactical equity, minimum volatility equity, managed futures, risk parity, global contrarian, alternative income, and traditional U.S. Treasuries.

You can find the full presentation below.

 

(If the above slideshow is not working, you can view an online version here or download a PDF version here.)

 

Combining Tactical Views with Black-Litterman and Entropy Pooling

This post is available as a PDF download here

Summary­­

  • In last week’s commentary, we outline a number of problems faced by tactical asset allocators in actually implementing their views.
  • This week, we explore popular methods for translating a combination of strategic views and tactical views into a single, comprehensive set of views that can be used as the foundation of portfolio construction.
  • We explore Black-Litterman, which can be used to implement views on returns as well as the more recently introduced Entropy Pooling methodology of Meucci, which allows for more flexible views.
  • For practitioners looking to implement tactical views into a number of portfolios in a coherent manner, the creation of posterior capital market assumptions via these methods may be an attractive process.

Note: Last week’s commentary was fairly qualitative – and hopefully applicable for practitioners and non-practitioners alike.  This week’s is going to be a bit wonkier and is primarily aimed at those looking to express tactical views in an asset allocation framework.  We’ll try to keep the equations to a minimum, but if the question, “how do I create a posterior joint return distribution from a prior and a rank view of expected asset class returns?” has never crossed your mind, this might be a good week to skip.

In last week’s commentary, we touched upon some of the important details that can make the actual implementation and management of tactical asset allocation a difficult proposition.[1]  Specifically, we noted that:

  1. Establishing consistent measures across assets is hard (e.g. “what is fair value for a bond index and how does it compare to equities?”);
  2. There often are fewer bets being made, so position sizing is critical;
  3. Cross-asset dynamics create changing risk profiles for bets placed.
  4. Tactical decisions often explicitly forego diversification, increasing the hurdle rate.

We’ll even add a fifth, sixth, and seventh:

  1. Many attractive style premia (e.g. momentum, value, carry, and trend) trades require leverage or shorting. Many other tactical views (e.g. change in yield curve curvature or change in credit spreads) can require leverage and shorting to neutralize latent risk factors and allocate risk properly.
  2. Combining (potentially conflicting) tactical views is not always straight forward.
  3. Incorporating tactical views into a preexisting policy portfolio – which may include long-term strategic views or constraints – is not obvious.

This week, we want to address how points #2-7 can be addressed with a single comprehensive framework.[2]

What is Tactical Asset Allocation?

As we hinted in last week’s commentary, we’re currently smack dab in the middle of writing a book on systematic tactical asset allocation.

When we sat down to write, we thought we’d start at an obvious beginning: defining “what is tactical asset allocation?”

Or, at least, that was the plan.

As soon as we sat down to write, we got a case of serious writer’s block.  Which, candidly, gave us deep pause.  After all, if we struggled to even write down a succinct definition for what tactical asset allocation is, how in the world are we qualified to write a book about it?

Fortunately, we were eventually able to put digital ink to digital paper.  While our editor would not let us get away with a two sentence chapter, our thesis can be more or less boiled down to:

Strategic asset allocation is the policy you would choose if you thought risk premia were constant; tactical asset allocation is the changes you would make if you believe risk premia are time-varying.[3]

We bring this up because it provides us a mental framework for thinking about how to address problems #2 – 7.

Specifically, given prior market views (e.g. expected returns and covariances) that serve as the foundation to our strategic asset allocation, can our tactical views be used to create a posterior view that can then serve as the basis of our portfolio construction process? 

Enter Black-Litterman

Fortunately, we’re not the first to consider this question.  We missed that boat by about 27 years or so.

In 1990, Fischer Black and Robert Litterman developed the Black-Litterman model while working at Goldman Sachs. The model provides asset allocators with a framework to embed opinions and views about asset class returns into a prior set of return assumptions to arrive at a bespoke asset allocation.

Part of what makes the Black-Litterman model unique is that it does not ask the allocator to necessarily come up with a prior set of expected returns.  Rather, it relies on equilibrium returns – or the “market clearing returns” – that serve as a neutral starting point.  To find these returns, a reverse optimization method is utilized.

Here, R is our set of equilibrium returns, c is a risk aversion coefficient, S is the covariance matrix of assets, and w is the market-capitalization weights of those assets.

The notion is that in the absence of explicit views, investors should hold the market-capitalization weighted portfolio (or the “market portfolio”).  Hence, the return views implied by the market-capitalization weights should be our starting point.

Going about actually calculating the global market portfolio weights is no small feat.  Plenty of ink has been spilled on the topic.[4]  For the sake of brevity, we’re going to conveniently ignore this step and just assume we have a starting set of expected returns.

The idea behind Black-Litterman is to then use a Bayesian approach to combine our subjective views with these prior equilibrium views to create a posterior set of capital market assumptions.

Specifically, Black-Litterman gives us the flexibility to define:

  • Absolute asset class return views (e.g. “I expect U.S. equities to return 4%”)
  • Relative asset class return views (e.g. “I expect international equities to outperform U.S. equities by 2%”)
  • The confidence in our views

Implementing Black-Litterman

We implement the Black-Litterman approach by constructing a number of special matrices.

  • P: Our “pick matrix.” Each row tells us which asset classes we are expressing a view on.  We can think of each row as a portfolio.
  • Q: Our “view vector.” Each row tells us what our return view is for the corresponding row in the pick matrix.
  • O: Our “error matrix.” A diagonal matrix that represents the uncertainty in each of our views.

Given these matrices, our posterior set of expected returns is:

If you don’t know matrix math, this might be a bit daunting.

At the highest level, our results will be a weighted average of our prior expected returns (R) and our views (Q).  How do compute the weights?  Let’s walk through it.

  • t is a scalar. Generally, small.  We’ll come back to this in a moment.
  • S is the prior covariance matrix. Now, the covariance matrix represents the scale of our return distribution: i.e. how far away from the expectation that we believe our realized returns could fall. What we need, however, is some measure of uncertainty of our actual expected returns.  g. If our extracted equilibrium expected returns for stocks is 5%, how certain are we it isn’t actually supposed to be 4.9% or 5.1%? This is where t comes back.  We use a small t (generally between 0.01 and 0.05) to scale S to create our uncertainty estimate around the expected return. (tS)-1, therefore, is our certainty, or confidence, in our prior equilibrium returns.
  • If O is the uncertainty in our view on that portfolio, O-1 can be thought of as our certainty, or confidence, in each view.
    Each row of P is the portfolio corresponding to our view. P’O-1P, therefore, can be thought of as the transformation that turns view uncertainty into asset class return certainty.
  • Using our prior intuition of (tS)-1, (tS)-1R can be thought of as certainty-scaled prior expected returns.
  • Q represents our views (a vector of returns). O-1Q, therefore, can be thought of as certainty-scaled P’O-1Q takes each certainty-scaled view and translates it into cumulative asset-class views, scaled for the certainty of each view.

With this interpretation, the second term – (tS)-1R + P’O-1Q – is a weighted average of our prior expected returns and our views.  The problem is that we need the sum of the weights to be equal to 1.  To achieve this, we need to normalize.

That’s where the first term comes in.  (tS)-1 + P’O-1P is the sum of our weights.  Multiplying the second term by ((tS)-1 + P’O-1P)-1 is effectively like dividing by the sum of weights, which normalizes our values.

Similar math has been derived for the posterior covariance matrix as well, but for the sake of brevity, we’re going to skip it.  A Step- by-Step Guide to Black-Litterman by Thomas Idzorek is an excellent resource for those looking for a deeper dive.

Black-Litterman as a Solution to Tactical Asset Allocation Problems

So how does Black-Litterman help us address problems #2-7 with tactical asset allocation?

Let’s consider a very simple example.  Let’s assume we want to build a long-only bond portfolio blending short-, intermediate-, and long-term bonds.

For convenience, we’re going to make a number of assumptions:

  1. Constant durations of 2, 5, and 10 for each of the bond portfolios.
  2. Use current yield-to-worst of SHY, IEI, and IEF ETFs as forward expected returns. Use prior 60 months of returns to construct the covariance matrix.

This gives us a prior expected return of:

E[R]
SHY1.38%
IEI1.85%
IEF2.26%

And a prior covariance matrix,

SHYIEIIEF
SHY0.000050.0001770.000297
IEI0.0001770.0007990.001448
IEF0.0002970.0014480.002795

In this example, we want to express a view that the curvature of the yield curve is going to change.  We define the curvature as:

Increasing curvature implies the 5-year rate will go up and/or the 2-year and 10-year rates will go down.  Decreasing curvature implies the opposite.

To implement this trade with bonds, however, we want to neutralize duration exposure to limit our exposure to changes in yield curve level and slope.  The portfolio we will use to implement our curvature views is the following:

We also need to note that bond returns have an inverse relationship with rate change.  Thus, to implement an increasing curvature trade, we would want to short the 5-year bond and go long the 2- and 10-year bonds.

Let’s now assume we have a view that the curvature of the yield curve is going to increase by 50bps over the next year.  We take no specific view as to how this curvature increase will unfold (i.e. the 5-year rate rising by 50bps, the 5-year rate rising by 25bps and each of the 2-year and 10-year rates falling by 25bps, etc.).  This implies that the curvature bond portfolio return has an expected return of negative 5%.

Implementing this trade in the Black-Litterman framework, and assuming a 50% certainty of our trade, we end up with a posterior distribution of:

E[R]
SHY1.34%
IEI1.68%
IEF1.97%

And a posterior ovariance matrix,

SHYIEIIEF
SHY0.0000490.0001820.000304
IEI0.0001820.0008190.001483
IEF0.0003040.0014830.002864

We can see that while the expected return for SHY did not change much, the expected return for IEF dropped by 0.29%.

The use of this model, then, is that we can explicitly use views about trades we might not be able to make (due to leverage or shorting constraints) to alter our capital market assumptions, and then use our capital market assumptions to build our portfolio.

For global tactical style premia – like value, momentum, carry, and trend – we need to explicitly implement the trades.  With Black-Litterman, we can implement them as views, create a posterior return distribution, and use that distribution to create a portfolio that still satisfies our policy constraints.

The Limitations of Black-Litterman

Black-Litterman is a hugely powerful tool.  It does, however, have a number of limitations.  Most glaringly,

  • Returns are assumed to be normally distributed.
  • Expressed views can only be on returns.

To highlight the latter limitation, consider a momentum portfolio that ranks asset classes based on prior returns.  The expectation with such a strategy is that each asset class will outperform the asset class ranked below it.  A rank view, however, is inexpressible in a Black-Litterman framework.

Enter Flexible Views with Entropy Pooling

While a massive step forward for those looking to incorporate a variety of views, the Black-Litterman approach remains limited.

In a paper titled Fully Flexible Views: Theory and Practice[5], Attilio Meucci introduced the idea of leveraging entropy pooling to incorporate almost any view a practitioner could imagine.  Some examples include,

  • A prior that need not be normally distributed – or even be returns at all.
  • Non-linear functions and factors.
  • Views on the return distribution, expected returns, median returns, return ranks, volatilities, correlations, and even tail behavior.

Sounds great!  How does it work?

The basic concept is to use the prior distribution to create a large number of simulations.  By definition, each of these simulations occurs with equal probability.

The probability of each scenario is then adjusted such that all views are satisfied.  As there may be a number of such solutions, the optimal solution is the one that minimizes the relative entropy between the new distribution and the prior distribution.

How is this helpful?  Consider the rank problem we discussed in the last section.  To implement this with Meucci’s entropy pooling, we merely need to adjust the probabilities until the following view is satisfied:

Again, our views need not be returns based.  For example, we could say that we believe the volatility of asset A will be higher than asset B.  We would then just adjust the probabilities of the simulations until that is the case.

Of course, the accuracy of our solution will depend on whether we have enough simulations to accurately capture the distribution.  A naïve numerical implementation that seeks to optimize over the probabilities would be intractable.  Fortunately, Meucci shows that the problem can be re-written such that the number of variables is equal to the number of views.[6]

A Simple Entropy Pooling Example

To see entropy-pooling in play, let’s consider a simple example.  We’re going to use J.P. Morgan’s 2017 capital market assumptions as our inputs.

In this toy example, we’re going to have the following view: we expect high yield bonds to outperform US small-caps, US small-caps to outperform intermediate-term US Treasuries, intermediate-term US Treasuries will outperform REITs, and REITs will outperform gold.  Exactly how much we expect them to outperform by is unknown.  So, this is a rank view.

We will also assume that we are 100% confident in our view.

The prior, and resulting posterior expected returns are plotted below.

We can see that our rank views were respected in the posterior.  That said, since the optimizer seeks a posterior that is as “close” as possible to the prior, we find that the expected returns of intermediate-term US Treasuries, REITs, and gold are all equal at 3%.

Nevertheless, we can see how our views altered the structure of other expected returns.  For example, our view on US small-caps significantly altered the expected returns of other equity exposures.  Furthermore, for high yield to outperform US small-caps, asset class expectations were lowered across the board.

Conclusion

Tactical views in multi-asset portfolios can be difficult to implement for a variety of reasons.  In this commentary, we show how methods like Black-Litterman and Entropy Pooling can be utilized by asset allocators to express a variety of views and incorporate these views in a cohesive manner.

Once the views have been translated back into capital market assumptions, these assumptions can be leveraged to construct a variety of portfolios based upon policy constraints.  In this manner, the same tactical views can be embedded consistently across a variety of portfolios while still acknowledging the unique objectives of each portfolio constructed.


[1] https://blog.thinknewfound.com/2017/07/four-important-details-tactical-asset-allocation/

[2] For clarity, we’re using “addressed” here in the loose sense of the word.  As in, “this is one potential solution to the problem.”  As is frequently the case, the solution comes with its own set of assumptions and embedded problems.  As always, there is no holy grail.

[3] By risk premia, we mean things like the Equity Risk Premium, the Bond Risk Premium (i.e. the Term Premium), the Credit Risk Premium, the Liquidity Risk Premium, et cetera.  Active Premia – like relative value – confuse this notion a bit, so we’re going to conveniently ignore them for this discussion.

[4] For example, see: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2352932

[5] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1213325

[6] Those looking to implement can find Meucci’s MatLab code (https://www.mathworks.com/matlabcentral/fileexchange/21307-fully-flexible-views-and-stress-testing) and public R code (https://r-forge.r-project.org/scm/viewvc.php/pkg/Meucci/R/EntropyProg.R?view=markup&root=returnanalytics) available.  We have a Python version we can likely open-source if there is enough interest.

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