We introduce the simple arithmetic of portfolio construction where a strategy can be broken into a strategic allocation and a self-financing trading strategy.
For long/flat trend equity strategies, we introduce two potential decompositions.
The first implementation is similar to equity exposure with a put option overlay. The second is similar to a 50% equity / 50% cash allocation with a 50% overlay to a straddle.
By evaluating the return profile of the active trading strategy in both decompositions, we can gain a better understanding for how we expect the strategy to perform in different environments.
In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.
The Simple Arithmetic of Portfolio Construction
In our commentary A Trend Equity Primer, we introduced the concept of trend equity, a category of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following. In this brief follow-up piece, we aim to provide further transparency into the behavior of trend equity strategies by decomposing this category of strategies into component pieces.
First, what do we mean by “decompose”?
As it turns out, the arithmetic of portfolios is fairly straight forward. Consider this simple scenario: we currently hold a portfolio consisting entirely of asset A and want to hold a portfolio that is 50% A and 50% of some asset B. What do we do?
Figure 1
No, this is not a trick question. The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B. As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going short 50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2). Operationally, of course, these are very different things. Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.
The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.
Relative to our original portfolio, the long/short represents our active bets. A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay. It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero. This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.
In our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A. The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.
Decomposing Trend Equity
Trend equity strategies are those strategies that seek to combine structural exposure to equities with the potential benefits of an active trend-following trading strategy. A simple example of such a strategy is a “long/flat” strategy that invests in large-cap U.S. equities when the measured trend in large-cap U.S. equities is positive and otherwise invests in short-term U.S. Treasuries (or any other defensive asset class).
An obvious question with a potentially non-obvious answer is, “how do we benchmark such a strategy?” This is where we believe decomposition can be informative. Our goal should be to decompose the portfolio into two pieces: the strategic benchmark allocation and a dollar-neutral long/short trading strategy that captures the manager’s active bets.
For long/flat trend equity strategies, we believe there are two obvious decompositions, which we outline in Figure 4.
Figure 4
Strategic Position
Trend Strategy
Decomposition
Positive Trend
Negative Trend
Strategic + Flat/Short Trend Strategy
100% Equity
No Position
-100% Equity 100% ST US Treasuries
Strategic + 50% Long/Short Trend Strategy
50% Equity 50% ST US Treasuries
100% Equity -100% ST US Treasuries
-100% Equity +100% ST US Treasuries
Equity + Flat/Short
The first decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is allocated to U.S. equities. This is complemented by a trading strategy that goes short large-cap U.S. equities when the trend is negative, investing the available cash in short-term U.S. Treasuries, and does nothing otherwise.
The net effect is that when trends are positive, the strategy remains fully invested in large-cap U.S. equities. When trends are negative, the overlay nets out exposure to large-cap U.S. equities and leaves the portfolio exposed only to short-term U.S. Treasuries.
In Figures 5, we plot the return profile of a hypothetical flat/short large-cap U.S. equity strategy.
Figure 5: A Flat/Short U.S. Equity Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise. Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals. These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.
Our expectation for future returns, then, is a combination of the two underlying strategies:
100% Strategic Equity: We should expect to earn, over the long run, the equity risk premium at the risk of large losses due to economic shocks.
100% Flat/Short Equity: Empirical evidence suggests that we should expect a return profile similar to a put option, with negative returns in most environments and the potential for large, positive returns during periods where large-cap U.S. equities exhibit large losses. Historically, the premium for the trend-following “put option” has been significantly less than the premium for buying actual put options. As a result, hedging with trend-following has delivered higher risk-adjusted returns. Note, however, that trend-following is rarely helpful in protecting against sudden losses (e.g. October 1987) like an actual put option would be.
Taken together, our long-term return expectation should be the equity risk premium minus the whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset. In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.
Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
50% Equity/50% Cash + 50% Long/Short
The second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries. The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.
One difference in this approach is that to achieve the desired long/flat return profile, only 50% exposure to the long/short strategy is required. As before, the net effect is such that when trends are positive, the portfolio is invested entirely in large-cap U.S. equities (as the short-term U.S. Treasury positions cancel out), and when trends are negative, the portfolio is entirely invested in short-term U.S. Treasuries.
In Figures 7, we plot the return profile of a hypothetical long/short large-cap U.S. equity strategy.
Figure 7: A Long/Short Equity Trend-Following Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
We can see the traditional “smile” associated with long/short trend-following strategies. With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments. The premium paid to buy these options causes the strategy to lose money in more normal environments. We see a similar result with the long/short trend-following approach.
As before, our expectation for future returns is a combination of the two underlying strategies:
50% Equity / 50% Cash: We should expect to earn, over the long run, about half the equity risk premium, but only expect to suffer about half the losses associated with equities.
50% Long/Short Equity: The “smile” payoff associated with trend following should increase exposure to equities in the positive tail and help offset losses in the negative tail, at the cost of whipsaw during periods of trend reversals.
Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments. We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.
In Figure 8, we plot the return combined return profile of the two component pieces. Note that it is identical to Figure 6.
Figure 8
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
Conclusion
In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.
In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative. In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.
For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate. It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses. While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.
In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy. If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.
This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation. The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.
In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.
In this sense, trend equity strategies help investors achieve capital efficiency. Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio. Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.
Few investors hold explicit shorts in their portfolio, but all active investors hold them
We (re-)introduce the simple framework of thinking about an active portfolio as a combination of a passive benchmark plus a long/short portfolio.
This decomposition provides greater clarity into the often confusing role of terms like active bets, active share, and active risk.
We see that while active share defines the quantity of our active exposure, the active bets themselves define the quality.
Ask the average investor if they employ shorting in their portfolios and “no” is likely the answer.
Examine the average portfolio, however, and shorts abound. Perhaps not explicitly, but certainly implicitly. But what in the world is an implicit short?
As investors, if we held no particular views about the market, our default position would be a market-capitalization weighted portfolio. Any deviation from market-capitalization weighted, then, expresses some sort of view (intentional or not).
For example, if we hold a portfolio of 40 blue-chip stocks instead of a total equity market index, we have expressed a view. That view is in part determined by what we hold, but equally important is what we do not.
In fact, we can capture this view – our active bets – by looking at the difference between what we hold in our portfolio and the market-capitalization weighted index. And we quite literally mean the difference. If we take the weights of our portfolio and subtract the weights of the index, we will be left with a dollar-neutral long/short portfolio. The long side will express those positions that we are overweight relative to the index, and the short side will express those positions we are underweight.
Below is a simple example of this idea.
Portfolio
Benchmark
Implied Long/Short
Stock A
25%
50%
-25%
Stock B
75%
50%
25%
“Dollar-neutral” simply means that the long and short legs will be of notional equal size (e.g. in the above example they are both 25%).
While our portfolio may appear to be long only, in reality it expresses a view that is captured by a long/short portfolio. As it turns out, our portfolio has an implicit short.
This framework is important because it allows us to go beyond evaluating what we hold and instead evaluate both the bets we are taking and the scale of those bets. Generically speaking, we can say:
Portfolio = Benchmark + b x Long/Short
Here, the legs of the Long/Short portfolio are assumed to have 100% notional exposure. Using the example above, this would mean that the long/short is 100% long Stock B, 100% short Stock A, and b is equal to 25%.
This step is important because it allows us to disentangle quantity from quality. A portfolio that is very overweight AAPL and a portfolio that is slightly overweight AAPL are expressing the same bet: it is simply the magnitude of that bet that is different.
So while the Long/Short portfolio captures our active bets, b measures our active share. In the context of this framework, it is easy to see that all active share determines is how exposed our portfolio is to our active bets.
We often hear a good deal of confusion about active share. Is more active share a good thing? A bad thing? Should we pay up for active share? Is active share correlated with alpha? This framework helps illuminate the answers.
Let’s slightly re-write our equation to more explicitly highlight the difference between our portfolio and the benchmark.
Portfolio – Benchmark = b x Long/Short
This means that the difference in returns between the portfolio and the benchmark will be entirely due to the return generated by the Long/Short portfolio of our active bets and how exposed we are to the active bets.
RPortfolio – RBenchmark = b x RLong/Short
Our expected excess return is then quite easy to think about: it is quite simply the expected return of our active bets (the Long/Short portfolio) scaled by how exposed we are to them (i.e. our active share):
E[RPortfolio – RBenchmark] = b x E[RLong/Short]
Active risk (also known as “tracking error”) also becomes quite easy to conceptualize. Active risk is simply the standard deviation of differences in returns between our Portfolio and the Benchmark. Or, as our framework shows us, it is just the volatility of our active bets scaled by how exposed we are to them.
s[RPortfolio – RBenchmark] = b x s[RLong/Short]
We can see that in all of these cases, both our active bets as well as our active share play a critical role. A higher active share means that the fee we are paying provides us more access to the active bets. It does not mean, however, that those active bets are necessarily any good. More is not always better.
Active share simply defines the quantity. The active bets, expressed in the long/short portfolio, will determine the quality. That quality is often captured by the Information Ratio, which is the expected excess return of our portfolio versus the benchmark divided by how much tracking error we have to take to generate that return.
IR = E[RPortfolio – RBenchmark] / s[RPortfolio – RBenchmark]
Re-writing these terms, we have:
IR = E[RLong/Short] / s[RLong/Short]
Note that the active share component cancels out. The information ratio provides us a pure measure of the quality of our active bets and ignores how much exposure our portfolio actually has to those bets.
Both quantity and quality are ultimately important in determining whether the portfolio will be able to overcome the hurdle rate set by the portfolio’s fee.
b x E[RLong/Short] > FeePortfolio – FeeBenchmark
The lower our active share, the higher our expectation for our active bets needs to be to overcome the fee spread. For example, if the spread in fee between our portfolio and the benchmark is 1% and our active share is just 25%, then we have to believe that our active bets can generate a return in excess of 4% to justify paying the fee spread. If, however, our active share is 75%, then the return needed falls to 1.33%.
Through this equation we can also understand the implications of fee pressure. If the cost of the active portfolio and the cost of the benchmark are equivalent, there is zero hurdle rate to overcome. We would choose active so long as we expect a positive return from our active bets.[1]
However, through its organizational structure and growth, Vanguard has been able to continually lower the fee of the passive benchmark over the last several decades. All else held equal, this means that the hurdle rate for active managers goes up.
Thus as the cost of passive goes down, active managers must lower their fee in a commensurate manner or boost the quality of their active bets.
Conclusion
For long-only “smart beta” and factor portfolios, we often see a focus on what the portfolio holds. While this is important, it is only a piece of the overall picture. Just as important in determining performance relative to a benchmark is what the portfolio does not hold.
In this piece, we explicitly calculate active bets as the difference between the active portfolio and its benchmark. This framework helps illuminate that our active return will be a function both of the quality of our active bets as well as the quantity of our exposure to them.
Finally, we can see that if our aim is to outperform the benchmark, we must first overcome the fee we are paying. The ability to overcome that fee will be a function of both quality and quantity. By scaling the fee by the portfolio’s active share, we can identify the hurdle rate that our active bets must overcome.
[1] More technically, theory tells us we would need a positive marginal expected utility from the investment in the context of our overall portfolio.
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.
Decomposing Trend Equity
By Corey Hoffstein
On September 24, 2018
In Risk & Style Premia, Risk Management, Trend, Weekly Commentary
This post is available as a PDF download here.
Summary
The Simple Arithmetic of Portfolio Construction
In our commentary A Trend Equity Primer, we introduced the concept of trend equity, a category of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following. In this brief follow-up piece, we aim to provide further transparency into the behavior of trend equity strategies by decomposing this category of strategies into component pieces.
First, what do we mean by “decompose”?
As it turns out, the arithmetic of portfolios is fairly straight forward. Consider this simple scenario: we currently hold a portfolio consisting entirely of asset A and want to hold a portfolio that is 50% A and 50% of some asset B. What do we do?
Figure 1
No, this is not a trick question. The straightforward answer is that we sell 50% of our exposure in A and buy 50% of our exposure in B. As it turns out, however, this is entirely equivalent to holding our portfolio constant and simply going short 50% exposure in A and using the proceeds to purchase 50% notional portfolio exposure in B (see Figure 2). Operationally, of course, these are very different things. Thinking about the portfolio in this way, however, can be constructive to truly understanding the implications of the trade.
The difference in performance between our new portfolio and our old portfolio will be entirely captured by the performance of this long/short overlay. This tells us, for example, that the new portfolio will outperform the old portfolio when asset B outperforms asset A, since the long/short portfolio effectively captures the spread in performance between asset B and asset A.
Figure 2: Portfolio Arithmetic – Long/Short Overlay
Relative to our original portfolio, the long/short represents our active bets. A slightly more nuanced view of this arithmetic requires scaling our active bets such that each leg is equal to 100%, and then only implementing a portion of that overlay. It is important to note that the overlay is “dollar-neutral”: in other words, the dollars allocated to the short leg and the long leg add up to zero. This is also called “self-funding” because it is presumed that we would enter the short position and then use the cash generated to purchase our long exposure, allowing us to enter the trade without utilizing any capital.
Figure 3: Portfolio Arithmetic – Scaled Long/Short Overlay
In our prior example, a portfolio that is 50% long B and 50% short A is equivalent to 50% exposure to a portfolio that is 100% long B and 100% short A. The benefit of taking this extra step is that it allows us to decompose our trade into two pieces: the active bets we are making and the sizing of these bets.
Decomposing Trend Equity
Trend equity strategies are those strategies that seek to combine structural exposure to equities with the potential benefits of an active trend-following trading strategy. A simple example of such a strategy is a “long/flat” strategy that invests in large-cap U.S. equities when the measured trend in large-cap U.S. equities is positive and otherwise invests in short-term U.S. Treasuries (or any other defensive asset class).
An obvious question with a potentially non-obvious answer is, “how do we benchmark such a strategy?” This is where we believe decomposition can be informative. Our goal should be to decompose the portfolio into two pieces: the strategic benchmark allocation and a dollar-neutral long/short trading strategy that captures the manager’s active bets.
For long/flat trend equity strategies, we believe there are two obvious decompositions, which we outline in Figure 4.
Figure 4
Strategic Position
Trend Strategy
Positive Trend
Negative Trend
Flat/Short Trend Strategy
100% Equity
-100% Equity
100% ST US Treasuries
50% Equity
50% ST US Treasuries
-100% ST US Treasuries
-100% Equity
+100% ST US Treasuries
Equity + Flat/Short
The first decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is allocated to U.S. equities. This is complemented by a trading strategy that goes short large-cap U.S. equities when the trend is negative, investing the available cash in short-term U.S. Treasuries, and does nothing otherwise.
The net effect is that when trends are positive, the strategy remains fully invested in large-cap U.S. equities. When trends are negative, the overlay nets out exposure to large-cap U.S. equities and leaves the portfolio exposed only to short-term U.S. Treasuries.
In Figures 5, we plot the return profile of a hypothetical flat/short large-cap U.S. equity strategy.
Figure 5: A Flat/Short U.S. Equity Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
The flat/short strategy has historically achieved a payoff structure that looks very much like a put option: positive returns during significantly negative return regimes, and (on average) slight losses otherwise. Of course, unlike a put option where the premium paid is known upfront, the flat/short trading strategy pays its premium in the form of “whipsaw” resulting from trend reversals. These head-fakes cause the strategy to “short low” and “cover high,” creating realized losses.
Our expectation for future returns, then, is a combination of the two underlying strategies:
Taken together, our long-term return expectation should be the equity risk premium minus the whipsaw costs of the flat/short strategy. The drag in return, however, is payment for the expectation that significant left-tail events will be meaningfully offset. In many ways, this decomposition lends itself nicely to thinking of trend equity as a “defensive equity” allocation.
Figure 6: Combination of U.S. Large-Cap Equities and a Flat/Short Trend-Following Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Flat/Short Equity shorts U.S. Large-Cap Equity when the prior month has a negative 12-1 month total return, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Flat/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
50% Equity/50% Cash + 50% Long/Short
The second decomposition achieves the long/flat strategy profile by assuming a strategic allocation that is 50% large-cap U.S. equities and 50% short-term U.S. Treasuries. The overlaid trend strategy now goes both long and short U.S. equities depending upon the underlying trend signal, going short and long large-cap U.S. Treasuries to keep the dollar-neutral profile of the overlay.
One difference in this approach is that to achieve the desired long/flat return profile, only 50% exposure to the long/short strategy is required. As before, the net effect is such that when trends are positive, the portfolio is invested entirely in large-cap U.S. equities (as the short-term U.S. Treasury positions cancel out), and when trends are negative, the portfolio is entirely invested in short-term U.S. Treasuries.
In Figures 7, we plot the return profile of a hypothetical long/short large-cap U.S. equity strategy.
Figure 7: A Long/Short Equity Trend-Following Strategy
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
We can see the traditional “smile” associated with long/short trend-following strategies. With options, this payoff profile is reminiscent of a straddle, a strategy that combines a position in a put and a call option to profit in both extremely positive and negative environments. The premium paid to buy these options causes the strategy to lose money in more normal environments. We see a similar result with the long/short trend-following approach.
As before, our expectation for future returns is a combination of the two underlying strategies:
Taken together, we should expect equity up-capture exceeding 50% in strongly trending years, a down-capture less than 50% in strongly negatively trending years, and a slight drag in more normal environments. We believe that this form of decomposition is most useful when investors are planning to fund their trend equity from both stocks and bonds, effectively using it as a risk pivot within their portfolio.
In Figure 8, we plot the return combined return profile of the two component pieces. Note that it is identical to Figure 6.
Figure 8
Source: Newfound Research. Return data relies on hypothetical indices and is exclusive of all fees and expenses. Returns assume the reinvestment of all dividends. Long/Short Equity goes long U.S. Large-Cap Equity when the prior month has a positive 12-1 month total return, shorting an equivalent amount in 3-month U.S. Treasury Bills. When the prior month has a negative 12-1 month total return, the strategy goes short U.S. Large-Cap Equity, investing available capital in 3-month U.S. Treasury Bills. The strategy assumes zero cost of shorting. The Long/Short Equity strategy does not reflect any strategy offered or managed by Newfound Research and was constructed exclusively for the purposes of this commentary. It is not possible to invest in an index. Past performance does not guarantee future results.
Conclusion
In this commentary, we continued our exploration of trend equity strategies. To gain a better sense of how we should expect trend equity strategies to perform, we introduce the basic arithmetic of portfolio construction that we later use to decompose trend equity into a strategic allocation plus a self-funded trading strategy.
In the first decomposition, we break trend equity into a strategic, passive allocation in large-cap U.S. equities plus a self-funding flat/short trading strategy. The flat/short strategy sits in cash when trends in large-cap U.S. equities are positive and goes short large-cap U.S. equities when trends are negative. In isolating the flat/short trading strategy, we see a return profile that is reminiscent of the payoff of a put option, exhibiting negative returns in positive market environments and large gains during negative market environments.
For investors planning on utilizing trend equity as a form of defensive equity, this decomposition is appropriate. It clearly demonstrates that we should expect returns that are less than passive equity during almost all market environments, with the exception being extreme negative tail events, where the trading strategy aims to hedge against significant losses. While we would expect to be able to measure manager skill by the amount of drag created to equities during positive markets (i.e. the “cost of the hedge”), we can see from the hypothetical example inn Figure 5 that there is considerable variation year-to-year, making short-term analysis difficult.
In our second decomposition, we break trend equity into a strategic portfolio that is 50% large-cap U.S. equity / 50% short-term U.S. Treasury plus a self-funding long/short trading strategy. If the flat/short trading strategy was similar to a put option, the long/short trading strategy is similar to a straddle, exhibiting profit in the wings of the return distribution and losses near the middle.
This particular decomposition is most relevant to investors who plan on funding their trend equity exposure from both stocks and bonds, allowing the position to serve as a risk pivot within their overall allocation. The strategic contribution provides partial exposure to the equity risk premium, but the trading strategy aims to add value in both tails, demonstrating that trend equity can potentially increase returns in both strongly positive and strongly negative environments.
In both cases, we can see that trend equity can be thought of as a strategic allocation to equities – seeking to benefit from the equity risk premium – plus an alternative strategy that seeks to harvest benefits from the trend premium.
In this sense, trend equity strategies help investors achieve capital efficiency. Allocations to the alternative return premia, in this case trend, does not require allocating away from the strategic, long-only portfolio. Rather, exposure to both the strategic holdings and the trend-following alternative strategy can be gained in the same package.