This post is available as a PDF download here.

Summary­­

• Traditionally, investors have used a balance between stocks and bonds to govern their asset allocation. Expanding this palette to include other asset classes can allow them to potentially both enhance return and reduce risk, benefiting from diversification.
• Modern portfolio theory tells us, however, that the truly optimal choice is to apply leverage to the most risk-efficient portfolio.
• In a low expected return environment, we believe that capital efficiency is of the utmost importance, allowing investors to better capture the returns they are already earning.
• We believe that the select application of leverage can allow investors to both benefit from enhanced diversification and capital efficiency, in a concept we are calling portable beta.

Diversification has been the cornerstone of investing for thousands of years as evidenced by timeless proverbs like “don’t put all your eggs in one basket.” The magic behind diversification – and one of the reasons it is considered the only “free lunch” available in investing – is that a portfolio of assets will always have a risk level less-than-or-equal-to the riskiest asset within the portfolio.

Yet it was not until Dr. Harry Markowitz published his seminal article “Portfolio Selection” in 1952 that investors had a mathematical formulation for the concept. His work, which ultimately coalesced into Modern Portfolio Theory (MPT), not only provided practitioners a means to measure risk and diversification, but it also allowed them to quantify the marginal benefit of adding new exposures to a portfolio and to derive optimal investment portfolios. For his work, Dr. Markowitz was awarded a Nobel prize in 1990.

What became apparent through this work is that the risk and expected reward trade-off is not necessarily linear.  For example, in shifting a portfolio’s allocations from 100% bonds to 100% stocks, risk may actually initially decrease and expected return may increase due to diversification benefits.  For example, in the hypothetical image below, we can see that the 60/40 stock-bond blend offers a nearly identical risk level to the 100% bond portfolio with significantly higher expected return.

Of course, these benefits are not limited solely to stock/bond mixes.  Indeed, many investors focus on how they can expand their investment palette beyond traditional asset classes to include exposures that can expand the efficient frontier: the set of portfolios that represents the maximum expected return for each given risk level.

In the example graph below we can see this expectation labeled as the diversification benefit.

The true spirit of MPT suggests something different, however.  MPT argues that in an efficient market, all investors would hold an identically allocated portfolio, which turns out to be the market portfolio. Holding any other portfolio would be sub-optimal.  The argument goes that rational investors would all seek to maximize their expected risk-adjusted return and then simply introduce cash or leverage to meet their desired risk preference.  This notion is laid out below.

In practice, however, while many investors are willing to expand their investment palette beyond just stocks and bonds, few ultimately take this last step of adding leverage.  Conservative investors rarely barbell a riskier portfolio with cash, instead opting to be fully invested in fixed income centric portfolios.  Aggressive investors rarely apply leverage, instead increasing their allocation to risky assets.  Some argue that this leverage aversion actually gives rise to the low volatility / betting-against-beta anomaly.

This is unfortunate, as the prudent use of leverage can potentially enhance returns without necessarily increasing risk.  For example, below we plot the hypothetical growth of a dollar invested in the S&P 500, a 60/40 portfolio, and a 60/40 portfolio levered to target the volatility level of the S&P 500.

Source: CSI.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees except for underlying ETF expense ratios.  The S&P 500 represented by SPDR S&P 500 ETF (”SPY”).  60/40 Portfolio is a 60% SPDR S&P 500 ETF (“SPY”) and 40% iShares 7-10 Year U.S. Treasury ETF (“IEF”) mix, rebalanced annually.  Levered 60/40 applies 182% leverage to the 60/40 Portfolio by shorting an 82% position in the iShares 1-3 Year U.S. Treasury ETF (“SHY”).  The leverage amount was selected so that the Levered 60/40 Portfolio would match the annualized volatility level of the S&P 500.

We can see that the Levered 60/40 portfolio trounces the S&P 500, despite sharing nearly identical risk levels.  The answer as to why is two-fold.

First is the diversification benefits we gain from introducing a negatively correlated asset to a 100% equity portfolio.  We can see this by comparing the annualized return and volatility of the S&P 500 versus the standard 60/40 portfolio.  While the S&P 500 outperformed by 120 bps per year, it required bearing 640 bps of excess volatility (14.9% vs. 7.7%) and a realized drawdown that was of 2540 bps deeper (55.2% vs. 29.8%).  Introducing the diversifying asset made the portfolio more risk-efficient.  Unfortunately, in doing so, we were forced to allocate to an asset with a lower expected return (from equities to bonds), causing us to realize a lower return.

This lower return but higher risk-adjusted return is the thinking behind the common saying that “investors can’t eat risk-adjusted returns.”

That is where the benefits from leverage come into play.  Leverage creates capital efficiency.  In this example, we were able to treat each $1 invested as if it were $1.82.  This allowed us to match the risk level of equities and benefit from the enhanced risk-efficiency of the diversified portfolio.

Efficiency Over Alpha

In a recent Barron’s roundtable[1], we were asked our thoughts on the future of ETFs.  We receive this question fairly often when speaking on panels.  The easy, obvious answers are, “more niche products,” or “an ETF for every asset class,” or even “smarter beta” (as if somehow beta has gone from high school to college and is now matriculating to graduate school).

In truth, none of these answers seem particularly innovative or even satisfactory when we consider that they will likely do little to help investors actually achieve their financial goals.  This is especially true in a low expected return environment, where finding the balance between growth and safety is akin to sailing between Scylla and Charybdis[2]: too much exposure to risky assets can increase sequence risk and too little can increase longevity risk.  Edging too close to either can spell certain financial doom.

With this in mind, our answer as of late has deviated from tradition and instead has focused on greater efficiency.  Instead of trying to pursue excess returns, our answer is to maximize the returns investors are, largely, getting already.  Here are a few examples of how this can be achieved:

• Lower Costs. As expected excess returns go down, the proportion taken by fees goes up.  The market may bear a 1% fee when expected excess returns are abundant, but that same fee may be the difference between retirement success and failure in a low return environment.  Therefore, the most obvious way to increase efficiency for investors is to lower costs: both explicit (fees) and implicit (trading costs and taxes).  Vanguard has led the charge in this arena for decades, and active managers are now scrambling to keep up.  While simply lowering fees is the most obvious solution, more creative fee arrangements (e.g. flexible fees) may also be part of the solution.
  
• Increased Exposure to Active Views. In a recent commentary, It’s Long/Short Portfolios All the Way Down[3], we explored the idea that an active investment strategy is simply a benchmark plus a dollar-neutral long/short portfolio layered on top.  This framework implies that if the cost of accessing beta goes down, the implied cost for active necessarily goes up, creating a higher hurdle rate for active managers to clear.  In our perspective, the way to clear this hurdle is for active managers to offer portfolios with greater exposure to their active views, with the most obvious example being be a high active share / active risk, concentrated equity portfolio.  Such an approach increases the efficiency of exposure to active strategies.
• Risk Management. Traditional risk management focuses exclusively on the use of capital diversification.  Traditionally allocated portfolios, however, are often significantly dominated by equity volatility and can therefore carry around a disproportionate amount of fixed income exposure to hedge against rare tail events.  We believe that diversifying your diversifiers – e.g. the incorporation of trend-following approaches – can potentially allow investors to increase their allocation to asset classes with higher expected returns without significantly increasing their risk profile.
• Leverage.  As we saw in our example above, leverage may allow us to invest in more risk-efficient, diversified portfolios without necessarily sacrificing return.  In fact, in certain circumstances, it can even increase return.  So long as we can manage the risk, increasing notional exposure to $1.50 for every $1 invested in a low return environment is effectively like increasing our returns by 1.5x (less the cost of leverage).  For active strategies, a subtler example may be the return to a 130/30 style investment strategy (130% long / 30% short), which can allow investors enhanced access to a manager’s active views without necessarily taking on more beta risk.  We expect that institutional investors may begin to re-acquaint themselves with ideas like portable alpha, where traditional portfolio exposures may be used as collateral for market-neutral, alpha-seeking exposures.[4]

Portable Beta Theory

We see lower costs as inevitable: Vanguard has made sure of that.  We see increased exposure to active views as the only way for traditional active management (i.e. long-only stock pickers) to survive.  A number of alternative diversifiers have already made their way to market, including defensive factor tilts, long/flat trend-following, options strategies, and managed futures.  Leverage is where we really think new innovation can happen, because it allows investors to re-use­ capital to invest where they might not otherwise do so because it would have reduced their risk profile.

For example, for young investors the advice today is largely to invest predominately in equities and manage risk through their extended investment horizon.  This has worked historically in the United States, but there are plenty of examples where such a plan would have failed in other markets around the globe.  In truth, in almost no circumstance is 100% equities a prudent plan when leverage is available.[5]

As a simple example, let us constrain ourselves to only investing in stocks and bonds.  Using J.P. Morgan’s 2018 capital market assumption outlook[6], we can create a stock-bond efficient frontier.  In these assumptions, U.S. large-cap equities have an expected excess return of 4.4% with a volatility of 14.0%, while U.S. aggregate bonds have an expected excess return of 1.3% with a volatility of 3.8%.  The correlation between the two asset classes is zero.

Plotting the efficient frontier, we can also solve for the portfolio that maximizes the risk-adjusted expected excess return (“Sharpe optimal”).  We find that this mixture is almost exactly a 20% stock / 80% bond portfolio: a highly conservative mixture.  However, this mix has an expected excess return of just 1.92%.

Source: J.P. Morgan.  Calculations by Newfound Research.

However, if we are willing to apply 3.4-times leverage to this portfolio, so as to match the volatility profile of equities, the story changes.  A levered maximum Sharpe ratio portfolio – 278% bonds and 66% stocks – would now offer an expected excess return of 6.6%: a full 2.2% higher than a 100% stock portfolio (again ignoring the spread charged above the risk-free rate in real world for accessing leverage).

What if an investor already has a 100% equity portfolio with significant capital gains?  One answer would be to overlay the existing position with the exposure required to move the portfolio from its currently sub-optimal position to the optimal allocation.  In this case, we could sell-short a 34% notional position in the S&P 500, use the proceeds to buy 34% in a core U.S. bond position, and then borrow to buy the remaining 244%.  We would consider the -34% equity and +278% position in bonds our “portable beta.”

Portable Beta in Practice: Risk Cannot Be Destroyed, Only Transformed

In theory, the optimal decision is to lever a 20/80 stock/bond mix by 340%.  In practice, however, volatility is not an all-encompassing risk metric.  We know that moving from a portfolio dominated by equities to one dominated by bonds introduces significant sensitivity to interest rates.  Furthermore, the introduction of leverage introduces borrowing costs and operational risks that are not insignificant.

Risk parity proponents would argue that this is actually a beneficial shift, creating a more diversified profile to different risk factors.  In our example above, however, we can compare the results of a 100% stock portfolio to a 66% bond / 278% stock portfolio during the 1970s, when not only did interest rates climb precipitously, but the yield curve inverted (and remained inverted) on several occasions.

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities and a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index.  The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously.

While $1 invested on 12/31/1969 U.S. equities was worth $2.29 on 12/31/1981, the same dollar was worth only $0.87 in the levered portfolio.  Of course, the outlook for stocks and bonds (including expected excess return, volatility, and correlation) was likely sufficiently different in 1969 that the Sharpe optimal portfolio may not have been a 20/80.  Regardless, this highlights the significant gap between theory and practice.  In modern portfolio theory, capital market assumptions are assumed to be known ex-ante and asset returns are assumed to be normally distributed, allowing correlation to fully capture the relationship between asset classes.  In practice, capital market assumptions are a guess at best and empirical asset class returns exhibit fat-tails and non-linear relationships.

In this case in particular, an inverted yield curve can lead to negative expected excess returns for U.S. fixed income, correlation changes can lead to dramatic jumps in portfolio volatility, and the introduction of duration can lead to losses in a rising rate environment.  Thus, a large, concentrated, and static portable beta position may not be prudent.

Traditional portfolio theory tells us that an asset should only be added to a portfolio (though, the quantity not specified) if its Sharpe ratio exceeds the Sharpe ratio of the existing portfolio times the correlation of that asset and the portfolio.  We can use this rule to try to introduce a simple timing system to help manage risk.

When the trigger says to include bonds, we will invest in the Levered 20/80 portfolio; when the trigger says that bonds will be reductive, we will simply hold U.S. equities (labeled “Dynamic Levered 20/80” below).  We can see the results below:

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Levered 20/80 portfolio is comprised of a 66% position in U.S. equities, a 278% position in a 10-year constant maturity U.S. Treasury index and a -244% position in a constant maturity 1-year U.S. Treasury index.  The period of 12/31/1969 to 12/31/1981 was used to capture an example period where interest rates rose precipitously. 

Tactical timing, of course, introduces its own risks (including estimation risk, model risk, whipsaw risk, trading cost risk, reduced diversification risk, et cetera).  Regardless, empirical evidence suggests that styles like value, momentum, and carry may have power in forecasting the level and slope of the yield curve.[7]  That said, expanding the portable beta palette to include more asset classes (through explicit borrowing or derivatives contracts) may reduce the need for timing in preference of structural diversification.  Again, risk parity argues for exactly this.

In practice, few investors may be comfortable with notional leverage exceeding hundreds of percentage points.  Nevertheless, even introducing a modest amount of portable beta may have significant benefits, particularly for investors lacking in diversification.

For example, equity heavy investors may add little risk by introducing modest amounts of exposure to U.S. Treasuries.  Doing so may allow them to harvest the term premium over time and potentially even benefit from flight-to-safety characteristics that may offset equity losses in a crisis.  On a forward-looking basis (again, using J.P. Morgan’s 2018 capital market assumptions), we can see that using leverage to exposure to intermediate-term U.S. Treasuries is expected to both enhance return and reduce risk relative to a 100% equity portfolio.

Source: J.P. Morgan.  Calculations by Newfound Research.

How would this more moderate approach have fared historically? Below we plot the returns of U.S. equities, a constant 100/50 portfolio (a 100% equity / 50% bond portfolio achieved using leverage), a dynamic 100/50 portfolio (100% equity portfolio that selectively adds a levered 50% bond position using the same timing rules discussed above).

Source: Federal Reserve of St. Louis and Robert Shiller.  Calculations by Newfound Research.  Results are hypothetical and backtested.  Past performance is not an indicator of future results.  Returns assume the reinvestment of all dividends and income and are gross of all fees.  The Constant 100/50 portfolio is comprised of a 100% position in U.S. equities and a 50% position in a 10-year constant maturity U.S. Treasury index funded by a -50% position in a constant maturity 1-year U.S. Treasury index.  The Dynamic 100/50 portfolio invests in either the U.S. Equity portfolio or the Constant 150/50 portfolio depending on the dynamic trade signal (see above).  The period of 2/1962 to 10/2017 represents the full set of available data.

We can see that the Dynamic 100/50 strategy is able to add 110 bps in annualized return with only an added 10 bps in increased volatility, while reducing the maximum realized drawdown by 390 bps.  Even naïve constant exposure to the Treasury position proved additive over the period.  Indeed, by limiting exposure, the Constant 100/50 portfolio achieved a positive 95.7% total return during the 1969-1981 period versus the -13% return we saw earlier.  While this still underperformed the 129.7% and 136.6% total returns achieved by U.S. equities and the Dynamic 100/50 portfolio respectively, it was able to add value compared to U.S. equities alone in 67% of years between 1981 and 2017.  For comparison, the Dynamic 100/50 strategy only achieved a 60% hit rate.

Conclusion

We will be the first to admit that these ideas are neither novel nor unique.  Indeed, the idea of portable beta is simply to take the theoretically inefficient exposure most investors hold and move it in the direction of a more theoretically optimal allocation through the prudent use of leverage.  Of course, the gap between theory and practice is quite large, and defining exactly what the optimal target portfolio actually is can be quite complicated.

While the explicit concept of portable beta may be more palatable for institutions, we believe the concepts can, and should, find their way into packaged format.  We believe investors can benefit from building blocks that enable the use of leverage and therefore allow for the construction of more risk- and capital-efficient portfolios.  Indeed, some of these ideas already exist in the market today.  For example:

• Risk parity portfolios.
• An alpha-generating fixed-income portfolio overlaid with equity futures.
• The S&P 500 overlaid with a position in gold futures.
• A strategic 60/40 allocation overlaid with a managed futures strategy.

We should consider, at the very least, how packed leverage applied to our traditional asset class exposures may allow us to free up capital to invest in other diversifying or alpha-seeking opportunities.  The 100/50 portfolio discussed before is, effectively, a 66/34 portfolio levered 1.5 times.  Thus, putting 2/3^rds of our capital in the 100/50 portfolio gives us nearly the same notional exposure as a 60/40, effectively freeing up 1/3^rd of our capital for other opportunities.  (Indeed, with some mental accounting gymnastics, we can actually consider it to be the same as holding a 66/34 portfolio with 100% of our capital and using leverage to invest elsewhere.)

While “no derivatives, leverage, or shorting” may have been the post-2008 mantra for many firms, we believe the re-introduction of these concepts may allow investors to achieve much more risk-efficient investment portfolios.

[1] https://www.barrons.com/articles/whats-next-for-etfs-1510976833

[2] Scylla and Charybdis were monsters in Greek mythology.  In The Odyssey, Odysseus was forced to sail through the Strait of Messina, where the two monsters presided on either side, posing an inescapable threat.  To cross, one had to be confronted.  The equivalent English seafaring phrase is, “Between a rock and a hard place.”

[3] https://blog.thinknewfound.com/2017/11/longshort-portfolios-all-the-way-down/

[4] https://en.wikipedia.org/wiki/Portable_alpha

[5] https://www.aqr.com/library/journal-articles/why-not–equities

[6] https://am.jpmorgan.com/us/institutional/our-thinking/2018-long-term-capital-market-assumptions

[7] See Duration Timing with Style Premia (Newfound 2017) and Yield Curve Premia (Brooks and Moskowitz 2017)