The Math of the Multi-Manager: Fad or Better Mousetrap?

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A July 2022 Barclays report (1), surveying 290 hedge funds, revealed that multi-manager funds with “full pass-through” expense models delivered nearly double the net returns (11.8% vs 6.3%), more than twice the alpha (10.8% vs 4.1%), and over three times the net Sharpe Ratio (2.1 vs 0.6) compared to traditional 2/20 hedge fund structures despite higher fund expenses. A December 2022 Goldman Sachs report (2) showed that multi-manager fund assets grew at 18.8% per year, compared to 2.6% per year for the rest of the hedge fund industry from 2017 to 2022. However, multi-manager funds still account for only 8% of total industry assets.

One may wonder why these more expensive, full pass-through expense multi-manager funds outperformed other fund structures. Reasons often cited by investors include the ability to attract and compensate top portfolio management talent and the fund manager’s ability to quickly cut underperforming portfolio managers.

This paper emphasizes two other vital components for the success of multi-manager funds: 1) the assembly of a significant number of diverse investment strategies with low correlations to one another, and 2) the implementation of these strategies in a cash-efficient manner. These two elements of portfolio implementation greatly influence a fund’s ability to succeed, and any discussion of the multi-manager model would be incomplete without addressing both. In my opinion, the inherent edge in these types of funds is structural and driven by portfolio construction math – this is what makes these types of funds better mousetraps for delivering alpha. (3)

Portfolio Construction of a Multi-Strategy, Multi-Manager Fund

Table 1 - Hypothetical Hedge Fund Portfolio vs Multi-Manager Fund Example*

To comprehend the importance of cash efficiency in generating alpha for a multi-manager fund, let’s examine a series of hypothetical hedge fund scenarios and illustrate the math involved (Table 1).

Consider two hypothetical single strategy hedge funds: an Equity Hedge Fund (“Fund A”) and a Macro Hedge Fund (“Fund B”), respectively (Columns A and B). Each fund deploys $100 and achieves returns of 8% and 10%, respectively.

Column C represents a Hedge Fund Portfolio that allocates $50 each to the single strategy Funds A and B. This Hedge Fund Portfolio achieves the weighted average of the performance of the two single strategy funds (50%*8% + 50%*10% = 9%).

Column D, in stark contrast, represents how a multi-manager fund invests into the same two hedge fund strategies.

Rather than have to make a decision between investing $100 into either Fund A or Fund B or be forced to split the $100 between Funds A and B shown in the Hedge Fund Portfolio (C), Multi-Manager Fund (D) enters into the combination of the same positions that Fund A and B hold. By establishing the same positions as the combination of Fund A and Fund B (each of which normally would require $100 of capital) within one $100 fund, the Multi-Manager Fund is twice as cash efficient as the Hedge Fund Portfolio.

This cash efficient implementation is the main factor in driving the higher returns relative to the Hedge Fund Portfolio C (15% vs 9%).

You might think that if the Multi-Manager Fund were holding the combination of the positions of Fund A and Fund B then the return of the Multi-Manager Fund (15%) would be the sum of the returns generated by Funds A and B (8% + 10% = 18%). However, 18% isn’t the same as 15%, so what is driving that 3% return difference? The Multi-Manager Fund’s returns are the sum of the excess returns of Fund A and B plus the risk-free return. Excess return is the return earned above the risk-free return (generally considered to be the return of short-term treasury bills). Specifically, the excess returns are the returns earned from the trading P&L of the strategies within the fund. (4)

In the example shown in Table 1, we are using 3% as the interest earned on short-term treasury bills to represent the risk-free return. Fund A earns 5% excess returns (8% - 3% = 5%) and Fund B earns 7% excess returns (10% - 3% = 7%). The Multi-Manager Fund earns the sum of these two excess returns plus the risk-free interest rate, in other words, 15% (5% + 7% + 3% = 15%). Each fund earns interest only once. Just because the Multi-Manager Fund holds the sum of the positions of the two funds doesn’t mean it also gets to earn interest on its cash twice.

Strategy Diversification Trumps “Rock Star” (5) Portfolio Managers

Interestingly, and perhaps counterintuitively, the success of these funds does not rely on having rock star portfolio managers. While it is crucial to have portfolio managers capable of generating profits, the presence of rock star managers is not as vital as commonly thought. High-performing managers are certainly beneficial; however, they cannot account for the intrinsic advantages of these fund structures that drive outperformance compared to other hedge fund structures. Rock star managers may not consistently perform well, yet multi-manager funds have historically outperformed through numerous iterations of portfolio manager cohorts.

“Prediction is very difficult, especially about the future.” – Niels Bohr, Nobel laureate

As you may have heard before, past performance does not future results. As Neils Bohr tells us, predicting whether a portfolio manager will perform well ahead of time is extremely difficult, and many would argue it’s impossible. The reality is that markets evolve and strategies which have worked historically can face difficult or different environments going forward.

Let’s explore the benefits of incorporating lowly correlated strategies into a portfolio.

Figure 1 - Hypothetical Relationship between number of Strategies and Net Sharpe Ratio

The success of the multi-manager model depends less on accurately forecasting individual portfolio managers’ performance and more on reaping the advantages of diversification by implementing numerous, mostly independent strategies simultaneously. Figure 1 illustrates the mathematical relationship between the number of strategies and Net Sharpe Ratio (6). For instance, a multi-manager fund comprising 20 lowly correlated strategies – each having a standalone Net Sharpe Ratio of 0.75 – would yield a multi-manager fund Sharpe Ratio of over 2.0.

It is not necessary for a multi-manager fund to have a single “rock star” portfolio manager for the fund overall to deliver a Net 2.0 Sharpe Ratio. However, for this to be mathematically true, it’s critical that the strategies are very lowly correlated to one another.

Running a multi-manager fund requires sophisticated risk management expertise and systems to ensure strategies are implemented in such a way as to maintain these low correlations in not only normal periods, but also (more importantly) in tail scenarios, often requiring adjustments to portfolio positioning and hedges to be implemented intra-month, whether at the strategy level or the fund level.

Correlation and Fund Volatility

Well-known strategies tend to be run by many market participants. ?The common holdings across hedge funds running these well-known strategies can drive up realized correlations in stressed market environments, such as during the Global Financial Crisis or March of 2020 (Covid19) (7). ?During these types of market-level events, when average strategy correlations rise, the expected Net Sharpe Ratio for a fund drops quickly and the expected volatility of a fund rises (Figure 2).

Figure 2 - Hypothetical Net Sharpe Ratio and Fund Volatility vs. Strategy Correlation

Figure 2 shows the mathematical impact of increasing average pairwise strategy correlations on both overall fund Net Sharpe Ratio and on Fund Volatility (7). ?As correlations between strategies increase, the fund’s expected volatility rises, at the same time that the fund’s expected consistency of performance – shown by it’s Net Sharpe Ratio declines.

A fund overall’s performance can be sensitive to seemingly modest changes in pairwise strategy correlations: the modeled Net Sharpe Ratio drops by approximately 40% (from 2.4 to 1.4) and expected Fund Volatility increases by approximately 70% (from 5.4% to 9.1%) when strategy correlations rise from 0.0 to just 0.1.

Importantly, the sensitivity to changes in correlations increases with the number of strategies in a fund. ?There is a balance between gaining additional diversification from adding more strategies and having too many strategies. ?The sensitivity of the fund’s performance characteristics to these correlations is higher for larger numbers of strategies. ?Similar numbers for a 100 strategy portfolio would imply an approximate 70% drop in Net Sharpe and a 230% rise in expected volatility from average correlations rising from 0.0 to 0.1 as a comparison.

While it’s great to have high Sharpe Ratio strategies like index rebalance arbitrage or bond basis trading, these strategies are also run by numerous portfolio management teams at multi-manager funds, within investment banks, and in multi-strategy hedge funds. ?

As a result, we believe these common hedge fund strategies have become more susceptible to increased correlations during market-wide deleveraging events like March of 2020. ?This phenomenon can happen when funds must reduce positions across all of their fund’s strategies as a means of managing risk and sustaining operations, which temporarily increases realized correlations across normally uncorrelated strategies.

When evaluating multi-manager funds, it is essential to focus on the fund’s ability to find or develop truly uncorrelated and uncommon strategies and to allocate meaningful amounts of the portfolio’s risk to those strategies. ?Beyond assembling the right strategy ingredients, ensure that the multi-manager fund has the risk expertise and systems to monitor, adjust and hedge the various strategies to keep them independent of one another.

Summary

The multi-manager fund structure has several structural advantages over single strategy funds and traditional hedge fund portfolios. ?The ability to pay for portfolio managers, afford data and best-in class risk management enables these funds to remain competitive for talent and technology.

Yet we believe the special sauce in multi-manager fund portfolios is driven by the portfolio construction math - finding and allocating to enough lowly correlated strategies and implementing them in a cash efficient manner.

It’s critical that managers of these funds have significant experience in markets – in particular with respect to liquidity risk, risk modeling and hedging. ?These fund structures have delivered more alpha than other structures, and as a result, are likely here to stay.

Appendix – Leverage and Risk Management Considerations

While some of the advantage of multi-manager funds stems from the cash-efficient portfolio construction, investors are properly cautious about the use of leverage required to do so. ?Multi-manager funds are pursuing the same approach that’s been employed by private equity funds for decades. ?Among other activities, private equity funds identify companies which have a solid core operating franchise, but whose capital structure is not optimized to generate the highest returns on equity capital for shareholders. ?The private equity fund purchases those companies and adjusts their capital structure in order to increase ROI for shareholders. ?

Multi-manager funds are essentially doing the same thing. They identify viable strategies and enable their various investment teams to pursue those strategies within a capital efficient framework. ?The diversification that comes from having many strategies is comparable to a business with a variety of business lines. ?

This section aims to shine some light on how much risk this additional leverage can bring to these types of portfolios. ?Let’s start with some more detailed data on our original simple example from up top:

Table 2- Hypothetical Hedge Fund Portfolio vs Multi-Manager Fund

The first fund on the left is an example of an equity hedge fund. ?For every $100 dollars invested in this fund, the portfolio manager goes long $110 of equities and goes short $60 of equities. ?To support those $170 of positions, approximately $14 of margin would need to be deposited into the fund’s prime broker account. ?For a portfolio of highly liquid equities which you could normally sell within a day, setting aside enough cash to cover a 99th percentile, 5-day VaR expected loss is considered appropriate – this is also referred to as the Risk Capital Requirement.

For this portfolio, that’s about $2. ?Adding the $14 Margin Requirement and the $2 Risk Capital Requirement leaves $84 of cash available ($100 - $14 - $2 = $84). ?The Risk Coverage Ratio is the amount of times that the fund is able to cover its Risk Capital Requirement (its stress event), in this example, the Risk Coverage Ratio = 43x (($84 + $2) / 2 = 43x). ?The fund has enough cash to cover over forty-three times the amount of expected loss over a very bad 5-day P&L period without having to sell any positions.

The same math goes for the Macro Fund, the Hedge Fund Portfolio and the Multi-Manager Fund. ?You can see even though the Multi-Manager Fund has $600 in gross exposures, it still has enough cash to cover seventeen times the amount of expected loss over a very bad 5-day P&L period without having to sell any of its positions – still a very conservative posture. ?

Hopefully this exercise shows how these multi-manager funds operate at a higher level of capital efficiency while also offering some insight into how risk is managed within these funds. ?We do not cover here the many other areas which are important like counterparty risk, liquidity risk, margin optimization, or term financing agreements. ?Running these funds is a complex task and requires experienced professionals, particularly in the finance, risk, trading, treasury and portfolio management functions.

The Math of the Multi-Manager

For those readers who want a little more detail into how a multi-manager fund converts a number of relatively modest strategies into a fund which delivers consistent, market-neutral alpha, it’s helpful to understand the portfolio math. ?

The table below shows the key elements and math that are used by fund managers when designing these portfolios. (8)

Table 3 - Multi-Manager Math

The blue numbers are the input parameters, and the black numbers represent the output calculations.

This example shows a 20-strategy portfolio, in which the strategies are equally weighted. ?The Average Net Strategy Excess Return is achieved by taking the Average Strategy Net Sharpe Ratio of 0.75 and multiplying that by the Average Strategy Volatility of 10% to arrive at 7.5% Net return. ?The Portfolio Net Volatility is calculated assuming an Average Pairwise Strategy Correlation of 0.03. ?The last step is applying the 3x Leverage figure to that portfolio, raising the Portfolio Excess Returns to 22.5% (7.5% * 3x) and total gross returns to 25.5% (22.5%+3.0%). ?

Platform Fixed Costs of five percent and a twenty percent overall Platform Performance Fee are deducted to arrive at a 16.4% Total Net Return for the fund.

Disclosures

This document is strictly confidential and intended exclusively for the use of the person to whom it was delivered by ClearAlpha. This presentation may not be reproduced or redistributed in whole or in part. ClearAlpha disclaims any obligation to update this document to reflect subsequent developments. All information provided herein is current as of the date distributed.

Except as otherwise noted, the figures and examples in this paper are for illustrative purposes only and do not reflect the returns or other characteristics of any fund. Additionally, as noted throughout, certain of the information in this paper is based on assumptions that we believe to be reasonable as of the date of this document; however, there is no guarantee that our assumptions are correct or that developments after the date of this paper could warrant using different assumptions. Different assumptions could lead to materially different outcomes from those described above.

Investors should not construe the contents of this document as legal, tax, investment or other advice, or a recommendation to purchase or sell any particular security. Accordingly, prospective investors should consult their own legal, tax and financial advisors as to the consequences of any investment. Investors should have the financial capacity and willingness to accept the risk of loss, and other risks associated with an investment including the loss of some or all of their investment.

Certain information contained in this presentation constitutes “forward-looking statements,” which can be identified by the use of forward-looking terminology such as “may,” “will,” “should,” “expect,” “anticipate,” “target,” “project,” “estimate,” “intend,” “continue” or “believe,” or the negatives thereof or other variations thereon or comparable terminology. Any such estimates or projections are based upon forecasts and reflects prevailing conditions, assumptions, and our best judgment as of the date of this document. There is no guarantee that any of these estimates, assumptions or projections will materialize or be achieved, and as a result thereof, actual results may vary from the estimates or projections. Furthermore, any such variations may be material. Nothing contained herein is, or shall be relied upon as, a promise or representation as to the past or future.

(1) Source: Performance by Fee Type and Level, Barclays Prime Services Capital Solutions, July 2022.

(2) Source: The Multiplier Effect, report on Multi-Manager Hedge Funds, Goldman Sachs Global Markets Division, December 5, 2022. ?

(3) Other reasons for the multi-manager fund structure’s success are detailed in our whitepaper entitled “The Evolution of Alpha,” which is available upon request.

(4) For the purpose of this table in this paper, we define excess returns as the trading P&L minus the commissions and financing costs in the case where all trading strategies that are within a fund are fully funded (ie. incur the costs of financing the positions the strategies hold).

(5) “Rock star” can be defined as a portfolio manager who consistently delivers a Net Sharpe Ratio 2.0 or more.

(6) Figure 1 shows the relationship between Net Sharpe Ratio and number of strategies. ?For this calculation, we assume an average strategy Net Sharpe Ratio of 0.75, average strategy volatility of 10% annualized, fixed fund expenses of 5% per year, a 20% incentive allocation for the fund, and 3x leverage. ?Regardless of the assumptions used, this relationship (i.e. Net Sharpe Ratio increases as a function of number of strategies) holds as long as the strategies aren’t perfectly correlated to one another. ?The spreadsheet model is available upon request.

(7) This graph shows the results of the mathematical calculations for a hypothetical fund which has 20 strategies which each have a net Sharpe Ratio of 0.75, a strategy volatility of 10% annualized, while the fund has fixed expenses of 5% per year and a 20% incentive allocation. ?Regardless of the assumptions used, this relationship (i.e. Net Sharpe Ratio decreases and Fund Volatility increases as a function of average strategy correlation) holds. ?The spreadsheet model is available upon request.

(8) There are many more nuances to be considered in modelling an actual multi-manager fund. ?This is intentionally simplified to convey the high-level concepts to be considered. The Microsoft Excel model is available upon request. ?Please email [email protected] for a copy.