April 2023 - Flirting with Models

Several years ago, I started using the phrase, “It’s long/short portfolios all the way down.” I think it’s clever. Spoiler: it has not caught on.

The point I was trying to make is that the distance between any two portfolios can be measured as a long/short strategy. This simple point, in my opinion, is a very powerful and flexible mental model for understanding portfolios.

If that sounds like gibberish, consider this practical example: you are a value investor who benchmarks to the S&P 500. To implement your strategy, you buy the iShares MSCI USA Value ETF (“VLUE”). If we subtract the weights of holdings in VLUE from the S&P 500, we can identify how much VLUE is over- or underweight any given position.

Figure 1. Relative Weight Differences Between VLUE and S&P 500 for the Top 20 Stocks in the S&P 500 by Weight
Source: SSGA; iShares. Calculations by Newfound Research.

Functionally, this is equivalent to saying, “VLUE is equal to the S&P 500 plus a long/short portfolio” where the longs are the overweights and the shorts are the underweights.

This is important for two reasons. First, it helps us identify our implicit hurdle rate for alpha required to overcome the fee.

If we continue the exercise above for all the holdings of the S&P 500 and VLUE, we find that the longs and shorts both sum up to 86.2%¹. If we normalize the portfolio such that the longs and shorts both add up to 100%, we can say:

VLUE = 100% x S&P 500 + 86.2% x Long/Short

The positions in the long/short capture our active bets while the 86.2% here is our active share. You may recall articles of years past about whether active share is predictive of alpha. I believe it is clear, through this decomposition, that it is the active bets that control whether any alpha is generated. Active share is key, however, in determining whether the strategy can overcome its fee.

For example, the current expense ratio for VLUE is 0.15% and the current expense ratio for the iShares Core S&P 500 ETF (“IVV”) is 0.03%. Using the formula above, we can say:

0.15% = 0.03% + 86.2% x Fee of Long/Short

Doing some simple arithmetic, we find that the implicit fee of the long/short strategy is 0.139%. This is the hurdle rate that the long/short portfolio must clear before it adds any excess return.

What if the active share was just 10% (i.e., the fund was a closet benchmarker)? In that case, the hurdle rate would jump to 1.2%! While active bets are responsible for generating alpha, the combination of a high fee and a low active share can lead to an unclearable hurdle rate.

The second reason I believe this concept is important is because it demystifies the idea of portfolio overlays. Through the lens of long/short portfolios all the way down, everything is an overlay. Buying value stocks? Equity long/short overlay on broad equity market. Rebalancing your portfolio? Multi-asset long/short overlay on top of your prior asset allocation.

Consider the figure below, where I plot the equity curves of two strategies. In the first, I buy the broad US equity market and overlay a 70% position in the classic Fama-French long/short value factor.² In the second strategy is simply buying large-cap value stocks.

Figure 2. Equity Market plus Long/Short Value Overlay versus Value Stocks

Source: Kenneth French Data Library. Calculations by Newfound Research. Market is the Fama-French Market Factor. Value Long/Short is the Fama-French HML Factor. Value Stocks is the Fama-French BIG HiBM. Performance is backtested and hypothetical. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise. Performance assumes the reinvestment of all dividends. Past performance is not indicative of future results. See Appendix A for index definitions.

We can see how similar these two approaches are. Buying value stocks is, effectively, buying the market and adding a big overlay of the long/short value factor.

There are some subtle, and important, differences. For example, in tilting towards value stocks, the implicit short in any given stock is limited to that stock’s weight in the index (as the weight cannot go below zero). In tilting towards value stocks, the size of the long/short overlay will also vary over time.³

Nevertheless, over the long run, on a log scale, drawn with a large enough crayon, and if we squint, we see a very similar picture.

This is all well and good on paper, but for many leverage-constrained investors, making room for an interesting equity long/short strategy means having to sell some existing exposure, giving the resulting cash to an alternative manager who holds onto it while implementing their strategy. In the figure below, I plot two equity lines. In the first, we hold 80% in broad U.S. equities, 20% in cash⁴, and 20% in the classic Fama-French long/short value factor. In the second, we buy large-cap value stocks.

Figure 3. Selling Stocks to Buy Alternatives Leads to a Beta Drag

The terminal wealth results are not even close for two reasons. First, as we saw in Figure 2, the appropriate overlay level is closer to 70%, not 20%. Second, to make room for the long/short portfolio, we had to sell broad equity beta. Which means the portfolio can really be thought of as:

100% U.S. Equity + 20% Long Cash / Short U.S. Equity + 20% Value Long/Short

Once again, it’s long/short portfolios all the way down. That “long cash / short U.S. equity” component is a big drag over a 100-year period and captures what I like to call the “funding problem.” As attractive as that value long/short may be, can it overcome the hurdle rate of what we had to sell to make room?

Part of the takeaway here is, “implicit leverage is good and may be hard to beat.” The other takeaway, however, is, “there may be interesting things to invest in that may become more interesting if we can solve the funding problem.”

What are some of those things? Ideally, we are adding things to a portfolio that have positive expected returns⁵ and also diversifying our existing holdings. For most allocators, that means a portfolio of stocks and bonds. An easy starting point, then, is to consider when stocks and bonds perform poorly and try to identify things that do well in those environments.

Following the methodology of Ilmanen, Maloney, and Ross (2017)⁶, we identify growth and inflation regimes using a composite of economic growth, inflation, and surprise factors. Growth and inflation regimes are then combined to create four combined regimes: Growth Up / Inflation Down, Growth Up / Inflation Up, Growth Down / Inflation Down, and Growth Down / Inflation Up.

By design, each of these combined regimes occurs approximately 25% of the time throughout history. We find that any given decade, however, can exhibit significant variation from the average. For example, the 2000s were characterized by the Growth Down environment, whereas the 2010s were characterized by an Inflation Down environment.

Figure 4: Regime Classifications

Source: St. Louis Federal Reserve Economic Data; Federal Reserve of Philadelphia Survey of Professional Forecasters. See Appendix B for regime definitions.

Using these regimes, we can evaluate how different asset classes, equity factors, and trading strategies have historically performed. In Figures 5, 6, 7, and 8 we do precisely this, plotting the regime-conditional Sharpe ratios of various potential investments.

Note that due to data availability, each figure may cover a different time period. The 60/40 portfolio is included in each graph as a reference point for that sub-period.

Figure 5: Sharpe Ratio of Equities, Bonds, and a 60/40 Portfolio in Different Economic Regimes (March 1962 to March 2023)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg. Performance is backtested and hypothetical. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise. Performance assumes the reinvestment of all dividends. Past performance is not indicative of future results. See Appendix A for index definitions. See Appendix B for economic regime definitions.

Figure 6: Sharpe Ratios of Equity Long/Shorts in Different Economic Regimes (March 1962 to December 2022)

Figure 7: Sharpe Ratios of Hedge Fund Categories in Different Economic Regimes (March 1998 to December 2022)

Source: Kenneth French Data Library; Tiingo; FRED; AQR; Bloomberg; HFRX. Performance is backtested and hypothetical. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise. Performance assumes the reinvestment of all dividends. Past performance is not indicative of future results. See Appendix A for index definitions. See Appendix B for economic regime definitions.

Figure 8: Sharpe Ratios of Commodities and Managed Futures in Different Economic Regimes (March 1985 – December 2022)

There are two standout takeaways:

Stocks and bonds don’t do well during Growth Down / Inflation Up periods.⁷
Other stuff does.

Specifically, we can see that Quality long/short and Managed Futures have historically been robust across regimes and have provided diversification during Growth Down / Inflation Up regimes. Unfortunately, while the Quality long/short – or, at least, a proxy for it – can be achieved by tilting our long-only equity exposure, the same cannot be said for Managed Futures.

One question we might pose to ourselves is, “given the possible canvas of tilts and overlays, if we wanted to maximize the Sharpe ratio of our portfolio for a given active risk budget, what would we do?” We can, at the very least, try to answer this question with the benefit of hindsight.

We’ll make a few assumptions:

Our strategic portfolio is 60% stocks and 40% bonds.
Our equity tilts can only be up to 60% of the portfolio (i.e., replace long-only equity one-for-one).
Our overlays can fill up the rest of the portfolio (i.e., we can replace any remaining long-only stock or bond exposure with capital efficient instruments – like futures or swaps – and allocate the available cash to fund the overlay strategy).

Using these rules, we can run an optimization⁸ maximizing the realized Sharpe ratio subject to a tracking error constraint. The results are illustrated in Figure 9. As the active risk budget increases, so does the allocation to tilts and overlays. To understand the relative proportional exposure to each, normalized weights are presented in Figure 10.

Without emphasizing the specific allocations, the blue band represents the tilts while the orange, grey, green, purple bands represent the different overlay categories (long/short equity, hedge fund strategies, commodities, and managed futures, respectively).

This whole process uses the benefit of hindsight to measure both returns and covariances, so is by no means a prescriptive endeavor. Nevertheless, I believe the results point in at least one clear direction: at all levels of active risk, the solution calls for a mix of tilts and overlays.

Figure 9: Maximizing the Realized Sharpe Ratio of a 60/40 Portfolio for a Given Active Risk Budget

Source: AQR Data Library; Kenneth French Data Library; HFRX. Calculations by Newfound Research. Performance is backtested and hypothetical. Performance is gross of all costs (including, but not limited to, advisor fees, manager fees, taxes, and transaction costs) unless explicitly stated otherwise. Performance assumes the reinvestment of all dividends. Past performance is not indicative of future results. See Appendix A for index definitions.

Figure 10: Normalized Portfolio Weights

For leverage-constrained allocators (e.g. many financial advisors), overlays have historically remained out of reach. More flexible institutions were able to implement it through a process that became known as “portable alpha,” originally pioneered by PIMCO in the 1970s. The implementation, on paper, is fairly simple:

Replace passive beta exposure with a capital efficient derivative (e.g. futures or swaps) to free up capital.
Allocate freed up capital to the desired alpha source.

Figure 11: Portable Alpha Example

The net portfolio construction, in effect, retains the beta and “ports” the alpha on as an overlay.

Historically, this required investors to manage a book of derivatives or hire a separate account manager. Today, mutual funds and ETFs exist that provide pre-packaged capital efficiency.

Figure 12 demonstrates one such example where a 60/40 allocation is packaged into a capital efficient “90/60” fund, allowing an investor to utilize just 2/3^rds of their capital to capture the same exposure. Figure 13 demonstrates that when this freed up capital is allocated, it effectively “stacks” the exposure⁹ on top of the original 60/40 portfolio. We have taken to calling this approach Return Stacking^TM.

Figure 12: Capital Efficient Funds

For illustrative purposes only.

Figure 13: Return Stacking^TM

For illustrative purposes only.

The other in figure 13 is where we can implement our alternative investment, effectively creating an overlay. Ideally this is something that has positive expected returns and low correlation to both stocks and bonds. We’re partial to managed futures for a variety of reasons, but allocators can pick their own adventure here.

Tilts and overlays are not mutually exclusive: it’s long/short portfolios all the way down. While overlays remained out of reach for many leverage-constrained investors, new capital efficient mutual funds and ETFs enable their implementation.

Appendix A: Index Definitions

U.S. Stocks – U.S. total equity market return data from Kenneth French Library until 5/24/2001 when total returns returns from the Vanguard Total Stock Market ETF (VTI) are used. Returns after 5/24/2021 are net of VTI’s underlying expense ratio. Data for VTI provided by Tiingo.

10-Year U.S. Treasuries – The 10-Year U.S. Treasury index is a constant maturity index calculated by assuming that a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index, and unmanaged index returns do not reflect any fees, expenses or sales charges. The referenced index is shown for general market comparisons and is not meant to represent any Newfound index or strategy. Data for 10-year U.S. Treasury yields come from the Federal Reserve of St. Louis economic database (“FRED”).

Value Tilt – BIG HiBM Returns for U.S. Equities (Kenneth French Data Library)

Size Tilt – ME LO 30 Returns for U.S. Equities (Kenneth French Data Library)

Momentum Tilt – BIG HiPRIOR Returns for U.S. Equities (Kenneth French Data Library)

Quality Tilt – 50% BIG LoINV + 50% BIG HiOP Returns for U.S. Equities (Kenneth French Data Library)

Low Beta Tilt – BIG LoBETA Returns for U.S. Equities (Kenneth French Data Library)

Value Long/Short – HML Devil Factor Returns for U.S. Equities (AQR Data Library)

Size Long/Short – SMB Factor Returns for U.S. Equities (Kenneth French Data Library)

Momentum Long/Short – UMD Factor Returns for U.S. Equities (Kenneth French Data Library)

Quality Long/Short – QMJ Factor Returns for U.S. Equities (AQR Data Library)

Anti-Beta Long/Short – BAB Factor Returns for U.S. Equities (AQR Data Library)

HFRX Equity Long/Short –HFRX Equity Hedge Index (Hedge Fund Research, Inc.)

HFRX Event Driven – HFRX Event Driven Index (Hedge Fund Research, Inc.)

HFRX Macro/CTA – HFRX Macro/CTA Index (Hedge Fund Research, Inc.)

HFRX Relative Value – HFRX Relative Value Arbitrage Index (Hedge Fund Research, Inc.)

Managed Futures – Time Series Momentum Factor (AQR Data Library). From inception to 2003, a 2% annual management fee and 3% annual estimated transaction cost are applied. From 2003 to 2013, a 1.5% annual estimated transaction cost is applied. From inception to 2013, a 20% annual performance fee is applied at the end of each year, so long as the end-of-year NAV exceeds the prior high-water mark. From 2013 onward a 1.5% annual fee and 0.6% annual estimated transaction cost is applied.

Equal-Weight Commodities – Excess Return of Equal Weight Commodities Portfolio (AQR Data Library)

Appendix B: Regime Classifications

Growth and Inflation are each defined as a composite of two series, which are first normalized to z-scores by subtracting the full-sample historical mean and dividing by the full-sample historical volatility.

“Up” and “Down” regimes are defined as those times when measures are above or below their full sample median.

Growth:

Chicago Fed National Activity Index
Realized Industrial Production minus prior year Industrial Production forecast from the Survey of Professional Forecasters.

Inflation:

Year-over-year CPI change
Realized year-over-year CPI minus prior year NGDP forecast from the Survey of Professional Forecasters.

The Research Library of Newfound Research

Month: April 2023

Portfolio Tilts versus Overlays: It’s Long/Short Portfolios All the Way Down