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The ABC’s of the ARP: understanding alternative risk premium

Abstract

Alternative risk premium (ARP) has experienced significant growth as an investment category in recent years. While considerable educational efforts accompanied this growth, gaps and misunderstandings persist. This paper provides a detailed definition of and contextualization of ARP as well as a comprehensive review of its academic roots, explaining that ARP sits at the confluence of decades of research on empirical anomalies, hedge fund replication, multi-factor models and data snooping.

Introduction

In the wake of the global financial crisis (GFC), investors hurt by their equity market exposure, concerned about the prospective returns to traditional investments, or dissatisfied with their hedge fund experience increased their pursuit of strategies offering a combination of low correlation with traditional asset classes, an attractive expected Sharpe ratio and reasonable liquidity—all at a modest price. This quest certainly is not new, but the breadth of investment opportunities designed to satisfy this demand and the focus on alternative risk premium (ARP) as a solution both increased significantly in recent years. Two examples of these trends were the rise of diversified growth funds (DGF’s) in the U.K. and the willingness of some large quantitative hedge funds to offer “factor” portfolios carrying a lower fee, higher capacity, and better liquidity than their flagship strategies. The latter trend, specifically the emergence of ARP as an investment category, is the focus of this paper. Hundreds of billions of dollars have pursued dozens of asset manager products and a myriad of investment bank tradable indices. Despite the accompanying educational effort, ARP remains a source of questions and skepticism for many investors.

This paper is the first of a two-paper series. In this paper, we make a foundational contribution to the understanding of this nascent investment category. We provide a detailed definition of ARP, distinguishing it from other investments and clarifying the associated nomenclature. Practitioners uniformly emphasize the academic lineage of ARP, regularly citing seminal papers. However, a single, comprehensive review of the copious research underpinning the category does not exist. In the second paper, we organize and summarize decades of literature, positioning ARP as the nexus of work on empirical anomalies, hedge fund replication, multi-factor models, and data snooping.

The alternative risk premium

ARP is not a new concept but rather the byproduct of several lines of research—empirical anomalies, hedge fund risk attribution and replication, and factor-oriented asset allocation paradigms. What is new is the expanded access to these “factor” trades. These concepts no longer reside predominantly in academic papers or as part of hedge fund investment processes. For asset managers, ARP is an extension of decades of work in quantitative equity and systematic macro-portfolios. Supplementing these offerings, the abundance of tradable indices now available on swap from investment banks reflects a confluence of supply and demand dynamics following the GFC.

On the supply side, the 2010 Volcker Rule ceased proprietary trading at investment banks encouraging them to find a monetizable outlet for certain research resources and execution capabilities. The Dodd-Frank Act also limited the permissible size of bank balance sheets pushing them to increase their focus upon higher return-on-capital counterparty activities. Since that time, banks have increased their efforts to partner with investors in the area of ARP and have produced copious literature advocating allocations to the space.Footnote 1 As both counterparty and consultant in this evolving space of client solutions, investment banks now offer thousands of tradable index products seeking to deliver ARP to multi-asset managers, funds-of-hedge funds and sophisticated plan sponsors.

On the demand side, asset allocation groups at large money managers lacking the internal capability to manage such trades or seeking operational efficiency increasingly tapped these vehicles to expand their investment opportunity set. Funds-of-hedge funds (aggregators) introduced portfolios of tradable indices to leverage familiarity with hedge fund strategies and to counter disintermediation in their traditional offerings. The “Norwegian” model (Ang et al. 2009) provided a factor investing blue print for large institutions that required implementation options. But for operational, legal or conventional reasons most institutional investors still prefer an intermediary (multi-asset manager or aggregator) acting as a fiduciary to be the counterparty to the bank.

So, what constitutes an ARP? Establishing some context and terminology is necessary to answer this question. For the purpose of this research, ARP represents one of three publicly traded portfolio building blocks, beta and alpha being the other two, generating the preponderance of return in most institutional portfolios. Panel A of Fig. 1 illustrates how some combination of these three elements constitutes the core investments in most portfolios. Panel B of Fig. 1 acknowledges the privately traded universe that rounds out the investment opportunity set. This private universe offers a ubiquitous illiquidity premium and shares some risk factors with its publicly traded counterpart but is beyond the scope of this research.

Fig. 1
figure1

Fundamental Elements of Portfolio Construction. Panel A depicts the three foundational elements comprised of publicly traded positions (exchange traded or over the counter) that underpin most portfolio investments. The shading in the lower part of each circle indicates that there is a tradability or liquidity spectrum for each investment type. The circle size signifies the relative abundance of each investment type. Hedge funds can invest in private deals but most holdings across this universe are traded publicly. Panel B summarizes the privately traded positions that complete the investment opportunity set

Beta

Beta includes the traditional, long-only, basic benchmark investments commonly made through index funds, passively managed mutual funds, and exchange-traded funds (ETFs). The index methodologies here attempt to capture the entirety of a particular market so positions in individual securities are weighted on the basis of market capitalization (cap) or free float (equities), amount outstanding (bonds) and production value (commodities).

In this research, beta includes global developed market large cap equities, global developed market small cap equities, emerging market equities, global developed market Treasury bonds, global developed market inflation-linked bonds, global investment-grade corporate bonds, global high-yield corporate bonds, emerging market bonds (dollar, local, corporate, linker) and commodities. Obviously, one could expand this list into sub-categories (regions, countries, sectors, etc.) or rearrange it according to objective (growth, real asset, alternative investment, and the like). One also could apply a risk factor lens in which case beta commonly represents a compound factor investment. For example, small cap stocks deliver equity beta (or growth sensitivity) but they also introduce liquidity and/or default exposures typically represented by the small cap premium. Inflation-linked bonds provide a combination of real interest rate, break-even inflation exposure, and an illiquidity component. Corporate bonds bundle nominal interest rate (real rate and inflation uncertainty), credit spread and liquidity risk. But the categorical classification in Fig. 1 focuses upon beta as the most fundamental portfolio building block implemented in a simple, long-only, theoretically oriented manner. As the principal source of non-diversifiable risk, beta drives the majority of portfolio return volatility.

Alternative risk premium

ARP is a nascent portfolio building block compared to the well-established notions of beta and alpha. Broadly speaking, the following three expectations underpin each ARP: (1) clear economic rationale supported by empirical research, (2) persistent risk-adjusted return distinct from that of traditional beta, and (3) liquid (scalable), rules-based, transparent, predominantly long-short trading profile

ARP captures systematic sources of return representing either compensation for bearing risk and/or behavioral biases among market participants. From an asset pricing perspective, a risk premium reflects compensation for non-diversifiable risk, for returns correlated with consumption growth (poor performance that hinders investor desire to smooth consumption), and for tail risk (insurance provision). Behavioral biases fall under the umbrella of market anomalies—persistent positive returns not explained by theory. Charoenrook and Conrad (2008) pursue an empirical distinction between the two types of returns, viewing risk premium as capturing systematic risk not represented by the market portfolio or changes over time in the investment opportunity. The authors contend that a risk premium should exhibit a positive relationship between its conditional mean return and variance, a mean excess return explained entirely by the variance, and a Sharpe ratio of plausible magnitude. Lempérière et al. (2014) classify risk premium as having an inverse relationship between Sharpe ratio and skewness (an equilibrium between expected return and large loss potential) and anomalies as representing the exceptions. Therefore, the use of “risk premium” in this paper is technically loose but reflects a practitioner grouping preference.

Another important asset pricing consideration is that departures from theoretical assumptions open the door to seemingly anomalous return opportunities. Pedersen (2015) compares neoclassical finance to efficiently inefficient markets to explain the gap between finance theory and empirical findings.Footnote 2 This exercise adds structure to the view that heterogeneous expectations, utility functions, information access, investment horizons and non-financial wealth among investors in addition to the presence of borrowing limitations, shorting restrictions, trading costs and information gathering frictions sow the seeds of ARP.

ARP refines the notion of alpha and beta by carving out space between the two. From the beta perspective, ARP expands the set of compensated risk factors or factor premiums beyond traditional beta. This is distinct from risk, non-priced or volatility factors offering an insignificant expected return so statistical significance will be an important consideration in this paper. Furthermore, ARP employs all the implementation techniques typically associated with hedge funds—leverage, short positions, and derivatives. This portfolio construction flexibility facilitates pure harvesting of risk premium, and the inclusion of short positions reduces the correlation with traditional beta. From the alpha perspective, ARP isolates performance previously attributed to alpha.

ARP essentially is a rules-based trading strategy (in contrast to passive, buy-and-hold beta) so overlap with traditional notions of both alpha and quantitative investing is to be expected. In fact, ARP reclassifies factors that have been the foundation of systematic investment processes for many years. Variation in the trading rules for a given ARP often results in meaningful tracking risk among the different specifications. Such specification noise introduces an idiosyncratic element. Some investors therefore break ARP into an ARP subset having basic trading rules and a systematic alpha subset relying upon more complicated rules; however, specification noise remains an issue for even the basic subset so such a sharp classification distinction can be challenging across the range of ARP.

Beyond the evolution of the beta-alpha split, the increasing focus of the global investing community on ARP reflects two important drivers. First, the search by investors for strategies having a low correlation with traditional beta continues. Memories of the GFC remain relatively fresh. Developed stock markets are at or near historical highs, global sovereign yields remain low, and commodities price catalysts remain elusive fueling concern regarding return prospects for traditional beta. Unconventional monetary policy, anemic global growth, and uncharted waters for central banks (negative interest rates) only add to this trepidation. Second, the appetite continues to grow for liquid, “hedge fund light” alternatives offering transparency and modest fees. This trend reflects dissatisfaction with hedge fund investments stemming from disappointing performance, difficulty scaling an allocation to an impactful size, concerns regarding research and administrative burdens, a lack of conviction in the ability to source high-quality strategies, and fee pressure across the investment management industry. The existence of demand obviously does not legitimize ARP. But increasing educational requests and growing portfolio allocations do reinforce the importance of the topic to the investment management community. The fact that some large, established systematic hedge funds have begun offering ARP products only reinforces the significance of this development.

ARP taxonomy

Table 1 introduces our ARP taxonomy that can be used in ARP research. Table 2 shows the trades associated with each group have a distinct profile in terms of both objective and return characteristics and span the major asset classes: equities, interest rates, currencies, commodities, and credit spreads.

Table 1 ARP taxonomy: liquid ARP
Table 2 Short-form, execution-oriented classification for ARP

Taxonomy of liquid ARP

Four groups of liquid ARP exist: carry, trend, convergence, and risk anomaly. We describe each below.

Carry: Carry trades attempt to harvest some type of spread, be that the short-term rate difference between a low and high yielding currency market, the volatility risk premium from an equity index option market or the calendar spread between two futures contracts on a given commodities futures term structure. These trades target a combination of yield (bond coupon, dividend) and the roll down (or roll up) on yield curves and futures term structures due to the passage of time. One can view carry trades as status quo trades because a stable environment is conducive to such “income” accrual whereas a transitional regime will create a performance headwind. Time-series, market-level carry strategies can manifest persistent traditional beta characteristics, so uniqueness is an important consideration. Non-cross-sectional carry trades often have a short volatility profile meaning they can be vulnerable to a risk-off environment. (The negative skewness associated with the returns of some carry strategies has been characterized as “picking up pennies in front of a steamroller.”) But this is the risk for which the premium is compensation. The returns to carry generally represent compensation for bearing risk—be that for insurance provision or simply for the possibility that forward prices change. Behavioral biases generally play a lesser role. Therefore, maintaining resolve in the face of occasional steep losses, creating sufficient diversification to contain losing trades and managing the correlation with equity returns are the primary challenges in constructing a portfolio of carry strategies.

Trend: Conversely, cognitive biases as opposed to risk premium drive the returns to trend following (time-series momentum) and cross-sectional momentum strategies. For example, the representativeness heuristic can introduce an extrapolation bias or overconfidence in the information content of market action. The availability heuristic can lead to an excessive anchoring on recent price behavior. Other justifications for momentum include confirmation bias (reliance on recent market action to validate a portfolio position), horizon bias (short-termism), and bandwagon or herding bias (the fear of missing out on a seemingly consensus investment opportunity). Behavioral finance therefore offers plausible explanations for the existence of price trends and the recurrence of price patterns. Basically, the initial tendency of investors to underreact to news suggesting a reversal allows a trend to start slowly and provides an entry window for trend followers. The subsequent tendency of investors to overreact extends a trend and permits momentum traders to realize profits beyond those due solely to the price fully impounding the news. This dynamic also explains why some characterize trend following as positive feedback trading.

Determining the trend is at the heart of technical analysis. Ironically, this is inextricably linked with reversal as early trend identification is important in terms of both maximizing participation and avoiding crashes. For the technician, market action is all that matters—prices distill all relevant information, historical price patterns contain information, and Newton’s First Law of Motion applies to prices regardless of whether this runs counter to the weakest notion of market efficiency. As a result of this obedience to price, certain trend strategies are viewed as latent hedges due to their ability during a market downturn to hold short positions in markets representing the core allocations of most institutional portfolios. Often used interchangeably with trend, momentum technically relates to price changes as opposed to levels and appears in oscillator analysis, a complement to trend analysis. In the ARP context, however, momentum is part of the persistence trade family. Practitioners often associate momentum with a cross-sectional setting (e.g., long positions in stocks with positive returns over a certain trailing period funded by short positions in stocks with negative returns over that interval) and trend with a single asset, time-series setting (e.g., long position in an S&P 500 future due to positive price action).

The trend family in this taxonomy extends to indicator or fundamental momentum (e.g., a long position in a stock due to positive earnings revisions, which is correlated positively with the returns on that stock). This example obviously is a departure from technical analysis but fits best in this group of trades. The trend category also includes congestion trades, taking positions around calendar-based activity such as index rebalances that create short-term supply-demand imbalances, and seasonality trades. Lastly, trend is a liquidity-consuming strategy, blamed at times for exacerbating market sell-offs and inflating asset price bubbles. The portfolio construction challenge here involves managing the risk of sharp reversals (momentum crashes) and surviving extended periods of range-bound markets (“the chop”).

Convergence: Sometimes referred to as “negative feedback trading,” the convergence group of strategies is the antithesis of the trend category. The primary focus here is the reversal of a perceived mispricing or disequilibrium. The basis for the returns is a combination of risk premium (e.g., default risk) and cognitive biases such as those mentioned above (e.g., overreaction and extrapolation). Convergence trades include a variety of arbitrage strategies characterized by pair trading and limited directionality (but not riskless profit, so arbitrage is a bit of a misnomer). Yield curve arbitrage takes long and short positions along the term structure betting that actual yields will return to fair value estimates. Volatility arbitrage sells options with relatively expensive implied volatility and purchases options with relatively cheap implied volatility. Statistical arbitrage identifies short-term, numerical divergences and then bets on these closing. Convergence also includes relative value trades. This often involves a cross section of stocks or markets (e.g., buying relatively cheap assets and shorting relatively expensive ones). Practitioners often use relative value or, simply, value interchangeably with convergence but this study favors the broader inclusivity of the latter term.

In this taxonomy shown in Table 1, the convergence group extends to indicator convergence (e.g. short position in an S&P 500 future due to an increase in implied volatility and/or inflation expectations, both of which may be correlated negatively with equity returns). Finally, the convergence category includes technical reversal trades (e.g., daily-weekly mean reversion trade) and contrarian sentiment trades (e.g., positioning against large speculative buildups in the CFTC Commitments of Traders (COT) reports). The primary portfolio construction challenge with convergence trading is staying power—avoiding forced unwinds due to establishing a position too early. Diversification across assets and investment horizon is important for each ARP and this is particularly true here. Deviations from fair value can persist and become increasingly extreme for extended periods of time. Being early in initiating a contrarian position is referred to as “catching a falling knife” given the performance pain one can experience. If concentrated, such losses could exacerbate drawdowns in the core holdings of most institutional portfolios so managing this risk though a variety of convergence positions is important.

Risk anomaly: Risk anomaly trades represent the fourth ARP category. The objective here is to find situations in which incremental risk does not appear adequately compensated. These trades target a realized return difference between a high- and low-risk subset of a given market that is inconsistent with the volatility or risk difference. Specifically, the trade consists of a long position in the low-risk group offering the superior Sharpe ratio and a short position in the high-risk group. The prototypical implementation of this trade combines a long basket of low beta or low volatility stocks with a short basket of high beta or high volatility stocks. The inconsistency with the classic theoretical assumption that systematic risk should be compensated is the reason this group carries an anomaly moniker. Another example is a steepener trade in fixed income—a duration-neutral long position in short maturity Treasuries or high-quality corporate bonds combined with a short position in long maturity Treasuries or low-quality corporate bonds. Such opportunities may arise because many investors face constraints with respect to leverage or short positions. Behavioral factors also may be at work (e.g., lottery preference or overconfidence). The primary portfolio construction challenge for the risk anomaly category is managing the eventuality of what is loosely termed a “junk rally”—a sharp relative run-up in the lower quality or higher risk portion of an investment universe often occurring in the wake of a significant market correction or potentially late in the cycle. (The timing is a bit different for the long-short bond maturity trade given the impact of Fed policy on the short-end of the yield curve.)Footnote 3

Execution-oriented classification

Table 2 presents a secondary, execution-oriented classification of ARP also having four broad groups: equity style, event driven, macro, and volatility. This approach also resembles a hedge fund style grouping. Given the long and extensive history of cross-sectional equity research and the relative familiarity of the marketplace with quantitative equity managers and the associated terminology, the first premium group is equity style which encompasses the primary factor tilts present in the large, long-short hedge fund category. Note that this group does not list a pair of stock strategies offered by some ARP providers—high dividend and growth. These two strategies generally do not command a sufficiently distinct, significant and persistent premium for inclusion in the table. High dividend can have a quality or value linkage while growth is essentially a risk factor, although certain specifications may appear as part of a composite momentum factor.

Size does appear in the catalog due to common practice but not without issue. The literature is not compelling on the post-publication (post-1980) significance of an institutionally tradable (non-micro-cap) size premium. Figure 2 provides an analysis of the small cap premium, highlighting the non-existent premium since 1980 and suggesting that either institutionalization of small stock buying has eliminated the premium or a very long holding period is required to earn a relatively slim long-term premium. Furthermore, the modest significance of the 90-year average premium would not survive the data snooping adjustments discussed later in this paper. Size has a long research pedigree, appears attractive at certain points in the business cycle (early expansion), and offers positive skewness suggestive of some long optionality. However, nagging questions regarding the magnitude of the average small cap premium counter these justifications and the likelihood that illiquidity drives most of the size premium argues for its exclusion from the liquid ARP taxonomy.

Fig. 2
figure2

Size premium. The figure presents the US small cap premium between January 1928 and December 2019. This premium is the difference between the excess return on the Ibbotson Associates Small Cap Stock Index and the beta-adjusted excess return on the S&P 500. The Ibbotson index concatenates three sets of returns: Banz NYSE fifth quintile returns (1926–1981), DFA US Small Company 9–10th decile Portfolio (1982–2001), and DFA US Micro Cap 20th ventile Portfolio (2001–2017). The portfolio returns are net of trading costs and fund expenses. The beta is a two-year rolling monthly estimate with betas below 1.1 averaged with a prior of 1.1 to manage estimation risk. The yellow line highlights that the average annual post-1980 small cap premium is essentially zero. The summary table breaks the 90-year history into four economic regimes, splitting periods of recession and expansion in half (The exhibit is a conditional mean summary, highlighting that only one economic state produces a mean significantly different than zero and is the driver of the marginally significant 90-year small cap premium. (No state delivers a significant mean post 1980.) This is effectively an indicator variable regression, and not an overly dynamic one given the focus on the economic cycle. As such, it does not explain the monthly variation in the small cap premium. The adjusted R2 is approximately zero and the F-statistic insignificant. However, the objective here is not variance explanation but mean decomposition.). The bulk of the small cap premium accrues during early expansions, emphasized by the shading which indicates a premium significant at the 1% level (one-tailed test for a positive value). The premium for the entire period is significant at the 5% level. The beta adjustment methodology used here produces an average 2.6% small cap premium and 0.2 Sharpe ratio for the entire period, equivalent to that generated by the Fama-French SMB factor (Kenneth French data library, three-factor model), and it results in a correlation between the small cap premium and large cap excess returns that is consistently zero across economic regimes. The correlation between the small cap factor presented here and the SMB factor is 0.83 with SMB having a lower volatility but a positive correlation with S&P 500 excess returns. Finally, note the positive skew of the small cap premium, particularly during early expansions

The second premium group in Table 2 includes strategies commonly employed by event driven managers. IPO trading does not appear because it does not meet the liquidity threshold. Capital structure arbitrage also does not appear given the challenges associated with a rules-driven approach but could be considered an extension of convertible bond arbitrage. The third group encompasses trades typically associated with tactical asset allocators, commodity trading advisors (CTA’s) and global macro-hedge funds. The macro-group encompasses both directional and relative value market-level (as opposed to security level) trades. The final volatility group covers higher moment trading, predominantly short volatility positions but also including volatility arbitrage.

Distinguishing ARP from smart beta

The ARP terminology and portfolio application continue to evolve among both academics and practitioners. For example, the marketplace associates a jumble of terms with ARP—exotic beta, smart beta, scientific beta, strategic beta, advanced beta, alternative beta, engineered beta, hedge fund beta, and systematic alpha. Even hedge fund replication gets tossed into the muddle. As the following digressions on smart beta and hedge fund replication illustrate, these labels are not interchangeable and therefore can be a source of confusion.

Smart beta, or more appropriately enhanced beta since there is nothing smart per se about it, often is confused with ARP. Enhanced beta is custom indexation, embedding factor tilts and portfolio construction preferences in traditional benchmarks. While custom index design has increased across all asset classes, the bulk of the investment has occurred in equity, with high dividend, equally weighted and low volatility ETFs being the largest beneficiaries. Enhanced beta may combine elements of ARP with beta so the confusion is understandable. Although such enhancement can introduce significant tracking risk versus beta, the latter still explains the majority of enhanced beta volatility and this is the reason for the distinction. The influence from the ARP in this long-position-only setting is relatively small and tethered to the dominant underlying beta so enhanced beta is a closer cousin to beta than to ARP. The situation is analogous to the currency exposure that accompanies the stock positions in a global equity index—equity beta is the principal driver of risk while currency is a marginal contributor so the MSCI World Index will not be confused with the US Dollar Index.

Figure 3 uses commodity indices to illustrate this dynamic. The Goldman Sachs Commodity Index (GSCI) represents the beta—commodities are weighted by production value and positions are in the front-month contracts of the underlying commodities. The other eleven indices listed in the bottom of Fig. 3 represent enhanced betas that change the GSCI rules governing commodity weighting scheme, contract selection, contract rolls and commodity inclusion. Some of these methodological changes bear traces of ARP while others reflect different characterizations of the commodities market. The annual variation in return among the indices is substantial. The median difference between the best and worst performing index is 22%. In only seven of 24 years has the GSCI return been above the median. Despite the high 11% median tracking risk of the 11 enhanced indices versus the GSCI, the GSCI still explains 80% of the return variation of these indices. Enhanced beta is first and foremost an extension of beta. The relatively modest, typically constrained and often indirect exposure to ARP available through enhanced beta is a poor substitute for a proper investment in ARP.

Fig. 3
figure3

Commodity indices—enhanced beta versus GSCI. The box plot summarizes the return distribution for the 12 commodity indices listed below the chart. The vertical axis shows the calendar year total return based upon data from January 1996 to December 2019. In the box plot, the red line indicates the median return, the blue box captures the interquartile range, and the black whiskers extend to the minimum and maximum return. The median interquartile range is 7%. The yellow dot denotes the return for the GSCI, an early benchmark standard. The median annualized tracking risk of the 11 indices versus the GSCI is 11% with a median R2 of 80%

Unlike beta, the objective of enhanced beta is not simple market representation but rather establishing a set of rules for an index containing only long positions to capture a certain security profile (or array of factor tilts) and to impose a portfolio construction methodology. Specifically, enhanced beta design follows three steps.

  • Step 1: Define the universe of eligible securities and specify (in multiple ways) the desired attributes.

    • value, size, momentum, volatility, quality, liquidity, yield, 13F holdings, geography

  • Step 2: Select a security weighting scheme (including a constraint set and rebalancing frequency).

    • characteristic-based (market capitalization, free float, equal—by security or group, square root of capitalization or diversity, fundamental variables, factor exposure, macro-variables)

    • engineered (minimum variance, maximum diversification, risk contribution)

  • Step 3: Refine the payout profile.

    • target volatility, leveraged, covered call writing, collared (long put, short call)

Of course, this process also requires careful consideration of transaction costs, the risk of incidental tilts offsetting target exposures, capacity and crowding, index transparency, the shift in accountability (from portfolio managers to plan sponsor), and the relative impact of rebalancing versus security effects.

Four factors have propelled the interest in enhanced beta.

  • Concentrated positions A simple, theoretical index methodology does not absolve investors of responsibility for a risk insensitive benchmark. Figure 4 provides three examples of concentration in traditional notions of beta. By December 1988, near the height of the Nikkei bubble, Japanese stocks represented 65% of the MSCI Europe, Asia, Far East (EAFE) index. Over the next 10 years that weight plummeted to 20%. Returning to commodities, energy accounted for 80% of the GSCI in August 2005, a particularly significant concentration given the relatively high volatility of energy sector returns. Even the S&P 500 index is not immune to concentration, with two percent of the companies at times accounting for more than a quarter of the index weight.

  • Persistent anomalies An increasing volume of the literature highlights, for example, the Sharpe ratio benefit of emphasizing low volatility, positive momentum or high gross profitability stocks in an equity benchmark. The desire to leverage this research to improve portfolio efficiency is not surprising. This pursuit of anomalies is the motivation that creates the link to (and confusion with) ARP.

  • Philosophical misgivings Leaning into winners via a market value weighting scheme eventually introduces bubble risk. A fixed income index weighting individual bonds on the basis of amount outstanding emphasizes the most prolific issuers of debt, an unappealing attribute.

  • Preferences Investors can create a particular return profile via an index rule base at little or no fee. This may be an “active management light” approach to improve returns or a portfolio construction tool such as a completion portfolio. The rapid growth in recent years of products from index companies, money managers, investment banks and ETF providers has enabled investors to implement preferences to an extent not previously possible (Fig. 4).

Fig. 4
figure4

Beta concentration extremes. The top left panel shows Japan accounting for two-thirds of MSCI Europe, Asia, Far East (EAFE) market capitalization at the height of the Nikkei bubble in December 1988. The top right panel shows energy accounting for 80% of the production value of the Goldman Sachs Commodity Index (GSCI) in August 2005. The bottom panel show dates at which 10 companies accounted for more than 25% of the weight in the S&P 500. None of the panels paints a picture of diversification

Distinguishing ARP from hedge fund replication

Hedge fund clones or trackers hold positions in liquid assets (ETFs, futures, options, swaps), attempting to replicate the risk-return profile of hedge fund indices. The objective is to capture the traditional beta, ARP and some market timing in hedge funds while necessarily foregoing the alpha. Managers of these portfolios choose among three implementation methodologies.

  1. 1.

    Factor-Based a top-down, econometric (often linear regression) approach focused upon identifying key drivers of hedge fund returns and then estimating the loadings on these exposures. Challenges include nonlinearities and non-normality in hedge fund returns, time-varying factor exposures, illiquidity, and spurious dependencies.

  2. 2.

    Distribution-Based a top-down, statistical approach focused upon creating and dynamically trading a reserve asset to replicate not the time-series of hedge fund returns but the distributional characteristics (volatility, skewness, correlation, etc.). Challenges include the opacity and complexity of the process as well as performance evaluation when distributional parameters (not replication per se) are the objective.

  3. 3.

    Trade-Based a bottom-up, rules-driven approach focused upon capturing the essence of hedge fund trading strategies. Challenges include time-varying factor exposures, developing an appropriate trade weighting methodology, and resource intensity (many trading rules to replicate a broad hedge fund index). Note that these trades can be factors so the distinction between 1 and 3 need not be black and white.

Hedge fund trackers and bank-sponsored indices appeared in the mid-2000’s, primarily during 2007. After some initial investor interest, redemptions followed as the GFC unfolded. Despite some renewed traction in recent years, hedge fund replication remains a nascent investment category. For example, Chronert and Odette (2016) list almost two dozen ETFs, all with post-GFC inception dates, currently tracking various hedge fund styles ranging from merger arbitrage to shadowing the holdings of top hedge fund investors via quarterly SEC 13F filings. But these funds in aggregate manage only a couple billion dollars with IQ Hedge Multi-Strategy Tracker representing half of this total.

No single reason explains either the redemptions or the plodding adoption rate of this conceptually appealing category. Significant performance variability exists among these products so weak comparative returns likely are a factor in certain instances. For other products, net returns underperform either upwardly biased hedge fund indices or absolute return objectives established by the managers. The redemptions also may reflect investors using these products as a liquidity source during periods of market turmoil. Importantly, investors may be uncomfortable with the downside correlation between trackers and traditional assets even if this mirrors hedge fund behavior. Perhaps investors view these products as rear-view mirror strategies, unable to deliver the market timing of hedge funds and overexposed to traditional assets already well-represented in most portfolios. Maybe the leverage, derivatives and short positions in these products give investors pause. Whatever the reason, investors have not embraced hedge fund replication products as an important part of their alternative investment structures.

The following exercise provides the motivation behind the hedge fund replication effort using a simple, factor-based approach. Specifically, this regression-based model attempts to capture the returns of the major hedge fund index sub-components listed in Fig. 5 (Equity Hedge, Event Driven, Macro and Relative Value) using traditional beta sources. An investor then could aggregate these four pieces using the strategy weights in a broad index like the Hedge Fund Research HFRX Global Hedge Fund Index. Figure 6 summarizes the extent to which traditional beta drives ex post hedge fund index returns. The focus on index returns is important as individual hedge funds typically deliver significant idiosyncratic risk, but this variability diversifies away in an index leaving material common factor risk. Figure 6 reveals significant levels of equity beta in Equity Hedge, Event Driven, and more recently Relative Value funds. This analysis also shows that ten risk factors explain a substantial proportion of hedge fund index return variability. The median rolling R2 value is approximately 60% for Macro and almost 90% for the other three hedge fund strategies. Therefore, blending long and short positions in traditional market indices appears to offer a path to hedge fund-like returns. Of course, such an effort hinges on the persistence and explanatory power of the factor exposures and, to a lesser extent, the ability of these regression betas to subsume the constant term (i.e., capturing hedge fund market timing activity, ARP investments and any aggregate manager alpha).

Fig. 5
figure5

taken from Hedge Fund Research, Inc. (HFR). The bullets list the typical underlying approaches. (Note that these are not the HFR sub-strategy descriptions.)

Hedge fund classification. No universal classification system exists for hedge funds. The four primary strategy descriptions in this figure are

Fig. 6
figure6

Hedge fund strategy risk attribution. Using monthly returns between July 2004 and December 2019, the four charts provide an in-sample, 24-month rolling attribution of the excess return volatility of four Hedge Fund Research investable strategy indices (HFRX Equity Hedge, Macro, Event Driven and Relative Value) to ten orthogonalized traditional beta sources—MSCI World (Equity), FTSE World Government Bond Hedged (Rates), MSCI Emerging Markets (EM Eq), MSCI World Small Cap (Sm Eq), Barclays Global Inflation-Linked Hedged (Infl Link), Barclays Global Aggregate Credit (IG Cr), Barclays Global High Yield ((HY Cr), JP Morgan Emerging Markets Bond (EM Cr), Bank of America Merrill Lynch All Convertible Bonds (Convert), and S&P Goldman Sachs Commodity (Commod). Returns for Equity and Rates are the anchors to a hierarchical orthogonalization process. Beginning with the third set of returns in the preceding list (EM Eq), index returns are orthogonalized to the preceding factors (Equity and Rates) using an OLS regression. The residual returns become the EM Eq factor. This process continues sequentially through the index list with an expanding set of orthogonal regressors. Such an approach provides a more refined picture of incremental risk among correlated betas. Regressing the hedge fund index returns on the ten factor returns yields the loadings for the contribution to risk calculation. The yellow area is the percent of volatility unexplained by the ten risk factors. The total contribution to risk from the ten factors highlights the explanatory power of the regression. The table below the charts uses average Newey–West (1987) p value per p value quartile for the four hedge fund strategy regressions to indicate the significance persistence for each risk factor. The shading highlights 5, 10 and 20% significance levels (orange, green and red, respectively)

Some investors view ARP as inextricably linked with hedge fund replication; however, hedge fund replication is not the raison d’etre for ARP. Critically, ARP is a return source, a factor, a building block. As such, ARP does share hedge fund risk attribution research lineage with the replication space, hence the confusion. But replicating the returns of a hedge fund index is an entirely different matter than identifying return sources having attributes that make hedge funds appealing. Robust hedge fund replication should incorporate ARP (trade-based and hybridized factor-based approaches), but this represents a very specific portfolio construction application. After all, investors typically do not seek hedge funds to deliver the significant amount of equity beta indicated in Fig. 6. The quest is for a hedge fund return profile as opposed to hedge fund index returns, suggesting some objective alignment with the distribution-based approach. ARP is the basis for constructing a portfolio with characteristics distinct from those provided by the beta portion of the portfolio and consistent with investor directionality and downside preferences. Equating ARP with hedge fund replication fundamentally confuses inputs with outputs.

Alpha

Alpha represents the third and final portfolio building block. For the purposes of this analysis, alpha represents the portion of a portfolio return not attributable to beta and ARP (or more generally the average return in excess of a proper benchmark). Zero-sum by nature, alpha therefore retains its traditional role as the residual, active, abnormal, or unexplained return generated via security selection or factor/market rotation/timing. Alpha (generated fundamentally or quantitatively) obviously is the scarcest of the portfolio building block triad, vulnerable to diminution by competition, dependent upon unique talent and often illusory due to statistical noise.

Note that this definition acknowledges the existence of quantitatively sourced alpha. To contend that, the systematic nature of ARP spans the entire realm of quantitative investing would be overreaching given the unique work being done in areas such as big data, computational linguistics, machine learning, and evolving traditional factor-based approaches.

Carhart (1997) and Barras et al. (2010), Fama and French (2010), and Ferson and Chen (2015) document the paucity of (after-cost) alpha among mutual fund managers. Ibbotson et al. (2011) report the generation of alpha by hedge funds although adjustments for survivorship and backfill return biases and estimation of appropriate ‘benchmarks’ create methodology-related variation in alpha that is unique to the hedge fund manager universe. Nevertheless, the operating (and long-debated) assumption among consultants, fund-of-fund managers and many asset allocators is that they possess sufficient skill to identify investors having a positive information ratio (i.e., a positive ratio of alpha to tracking risk). While manager identification represents the primary portfolio construction challenge, two additional issues warrant mention—expected return forecasting and risk contribution materiality. The former clearly is extremely difficult for an idiosyncratic return source while the latter is due to the highly diversifying nature of alpha making it difficult to increase its risk allocation relative to that of ARP and particularly beta.

Summary

An emerging investment category that has been an increasing focus of institutional investors since the GFC, ARP occupies a distinct niche between beta and alpha. Not to be confused with smart beta or hedge fund replication, ARP provides investors with liquid access to carry, trend, convergence and risk anomaly strategies offering potential diversification and return enhancement.

Notes

  1. 1.

    Rennison and Staal (2010), Tien et al. (2010), Mesomeris et al. (2012), Little and King 2012, Turc et al. (2013, 2016), Jenkins et al. (2013), Kolanovic and Wei (2013, 2014, 2015) to list but a few.

  2. 2.

    These friction-related dynamics that may explain the gap between finance theory and empirical findings are summarized in Table I.1 in Pedersen (2015): Modigliani-Miller irrelevance of capital structure vs. capital structure matters; two fund separation where all investors invest in the market portfolio and cash vs investor select different portfolios depending on their individual funding constraints; capital asset pricing model versus the influence of liquidity risk and funding constraints on expected returns; law of one price and Black-Scholes framework for pricing derivatives vs arbitrage opportunities impact derivatives pricing; Merton’s rule on exercising a call option vs optimal early and conversion; real business cycles and Ricardian equivalence regarding the irrelevance of macroeconomic policy on finance vs credit cycles and liquidity spirals that drive the interaction of macroeconomic policy, asset pricing, and funding constraints; and Taylor’s rule regarding monetary authorities impact on interest rates vs two monetary tools impact on interest rates and collateral polity.

  3. 3.

    Note that a few of the constituents in Table 1 arguably could reside in a different column—primarily the event driven strategies. Convertible bond arbitrage is one example. Because the strategy typically assumes some mispricing in the convertible bond, this table classifies convertible arbitrage as convergence. But there are many possible convertible arbitrage trades involving various hedges of delta, rho, vega, gamma, and credit, some of which might support slotting the trade under carry instead of convergence. Share buyback is another example having attributes of quality (balance sheet integrity) and relative value (long positions in negative net issuance companies coupled with negative positions in diluting companies). With few exceptions, however, strategy placement (Table 1) is intuitive.

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Gorman, S.A., Fabozzi, F.J. The ABC’s of the ARP: understanding alternative risk premium. J Asset Manag 22, 391–404 (2021). https://doi.org/10.1057/s41260-021-00231-3

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Keywords

  • Alternative risk premium
  • Alpha
  • Beta
  • Hedge fund style
  • Smart beta