A simple model of the effects of entity and activity constraints on alternative investment funds

Leo Fernandes, Harkeerit Kalsi, Nicholas Vause, Matthew Downer, Sarah Ek and Sebastian Maxted

Hedge funds and other alternative investment funds (AIFs) often take positions in financial markets that significantly exceed their investors’ capital by using debt or derivatives. However, such ‘leverage’ can pose risks to financial stability. Regulators seeking to reduce these risks may consider applying constraints to the fund entities or the activities in which they engage. In this post, we use a simple portfolio choice model to examine the effects of the two approaches on fund investments. Under the entity-based approach, we find that fund managers substitute from lower-risk to higher-risk investments, whereas an activity-based approach can avoid this unintended reallocation by targeting specific investments.

While traditional investment funds typically hold long positions in stocks and bonds, AIFs may take long and short positions in a wider range of assets, including illiquid assets like real estate or unlisted securities. In particular, hedge funds employ a diverse array of strategies that can be focused on a single asset class or span multiple classes, with large ‘multi-strategy’ funds simultaneously pursuing several strategies.

AIFs often leverage their investors’ capital by borrowing or using derivatives to increase their financial market exposures and amplify their investment returns. This requires funds to provide a portion of their capital as collateral – or ‘margin‘ – against their borrowings and derivatives. Despite internationally agreed margin standards putting an upper bound on leverage in many areas, funds are often able to increase their exposures to multiples of their investors’ capital. Some funds, such as those pursuing relative value strategies, employ significant leverage to take particularly large exposures to low-risk assets, while others use less leverage and take smaller positions in riskier or illiquid assets. AIFs and their managers are subject to regulatory reporting and oversight under the UK’s Alternative Investment Fund Managers Directive, which requires them to disclose information on their leverage use to investors but does not typically impose direct, entity-level leverage limits.

Such leverage can pose risks to financial stability. For instance, losses could spread from any defaulting funds to their counterparties, as with the failure of Archegos Capital Management. Losses could also spread from any funds selling assets in order to deleverage – perhaps because of a sudden increase in margin requirements or decline in their risk appetite – to holders of the same assets, due to downward pressure on prices arising from the sales, particularly for sales of more concentrated or illiquid positions, as with liability-driven investment funds in Autumn 2022.

Global regulators are considering ways to mitigate such risks. These include entity-level leverage limits and activity-level measures, such as enhanced margin requirements or collateral haircuts. Entity-level leverage limits typically constrain fund-level ratios of total exposures to net asset value (NAV), while enhanced margin requirements and collateral haircuts would raise the lower bound on the amount of capital required to finance a particular asset or set of assets.

In the remainder of this post, we apply a simple model of portfolio choice to AIFs to show how leverage limits and margin requirements would affect their investment decisions. A similar issue has been much studied in banking, both theoretically and empirically, as banks also face a leverage constraint (the leverage ratio) as well as risk-weighted capital charges against individual assets.

Portfolio choice model

We model funds with a given amount of investor capital. Each fund chooses a quantity of debt and the allocation of its portfolio between two strategies, where a ‘strategy’ is an investment in a particular asset or set of assets. We consider two types of fund: one invests in highly correlated strategies with similar expected returns and volatilities, such as a commercial real estate (CRE) fund investing in office blocks in different cities; and the other invests in less-correlated strategies with different expected returns and volatilities, such as a multi-strategy hedge fund operating a long-short equity strategy and a relative value strategy. The funds have a common risk aversion parameter, which governs the expected return they would give up in exchange for lower variance at the portfolio level. Given that risk-return trade-off, we can determine the optimal portfolios of the funds in the absence of both entity-level and activity-level constraints. Table A summarises the inputs – which were guided by research on returns and leverage – and outputs of this model.

Table A: Portfolio options and choices for two unconstrained funds

Note: Returns are ‘unlevered’ returns, ie returns on each £1 invested in a strategy. In principle, they should be excess returns over the risk-free interest rate, but we abstract from this issue by assuming the latter is zero. The risk-aversion parameter is 4.

In the absence of constraints, the CRE fund chooses 3.6x leverage (ie an assets-to-NAV ratio of 3.6) and invests equally in both strategies. In contrast, the multi-strategy hedge fund chooses substantially more leverage and tilts its portfolio heavily towards the low-risk relative value strategy.

We next impose fixed leverage limits and margin requirements and compare how these two types of constraints affect portfolio allocations between the strategies. The results are shown in Charts 1 and 2 for the CRE fund and multi-strategy hedge fund respectively. In each chart, the top row of charts shows optimal investments in the two strategies and the bottom row shows contributions of those investments to the portfolio variance. The left-hand column of charts shows how these variables change as the leverage limit is reduced to half of the leverage chosen by the unconstrained funds. The charts in the other columns show the effects of margin requirements being doubled – first for each individual strategy and then for both – from rates that do not constrain the funds.

Chart 1: CRE fund portfolio allocations and their contributions to portfolio variance under entity-level leverage and activity-level margin constraints

Note: Moving from left to right on the x-axes, the charts show how tighter leverage (first column) or margin (other columns) requirements affect the fund’s portfolio allocation (top row) and the variance of its portfolio return (bottom row).

Chart 2: Multi-strategy hedge fund portfolio allocations and their contributions to portfolio variance under entity-level leverage and activity-level margin constraints

Entity-level constraints

The fixed leverage limit is effective in constraining both the total assets and portfolio risk of the CRE fund (Chart 1, first column). But this result is driven by the similarity of its investment options. In contrast, the multi-strategy hedge fund responds to the leverage limit by substituting some of its large positions in the low-risk (relative value) strategy for smaller ones in the high-risk (long-short equity) strategy (Chart 2, top-left chart). This substitution limits the decline in the fund’s overall portfolio risk (Chart 2, bottom-left chart).

If extrapolated across multiple funds, such reallocation between strategies could have two unintended consequences. First, the focused reduction in capital allocated to the low-risk strategy could undermine certain economic benefits arising from these investments. For example, relative-value trades help to keep the prices of related assets in line with one another, which promotes the efficient allocation of investment. Second, the concentration of portfolios into the high-risk strategy makes funds more vulnerable to idiosyncratic shocks to those investments, which could prompt more-severe spirals of deleveraging and asset price falls due to more funds having larger positions in common strategies (ie ‘crowded trades’).

Conceivably, a dynamic entity-level constraint that took into account not only the size of investments but also their riskiness could contain such reallocations. However, value-at-risk (VaR) is the only such risk metric that is currently applied widely across asset classes and strategies, but its estimation bias and other limitations have been well documented.

Activity-level constraints

Activity-level constraints could give regulators the flexibility to reduce risk from investment activities that are difficult to contain with entity-level limits. For example, whereas the entity-level leverage limit had no constraining effect on the multi-strategy hedge fund’s exposure to the long-short equity strategy (Chart 2, first column), tightening a margin requirement would directly reduce those investments (Chart 2, second column).

Constraining only one activity, however, prompts funds to substitute into the other activity (Charts 1 and 2, second and third columns). This risk is especially pronounced for funds with similar investment options, as they would more readily allow their portfolio risk to become dominated by an investment substitute (compare bottom-middle charts in Charts 1 and 2) and, in so doing, retain a level of portfolio risk that is not much reduced.

To disincentive substitution into other activities, regulators could apply multiple activity-level constraints. In our model, this reduces the riskiness of fund portfolios without inducing shifts in their composition for both the CRE fund (Chart 1, final column) and the multi-strategy hedge fund (Chart 2, final column). This is achieved by setting margin requirements proportional to the riskiness of the strategies, eg relatively high values for the long-short equity strategy and relatively low values for the relative value strategy. Moreover, when margin requirements are universally applied, the fund effectively becomes subject to an entity-level limit that adjusts to the portfolio of strategies that it employs at any time.

As it happens, risk-sensitive margin requirements are already widespread as a result of existing regulatory frameworks (such as those for cleared and non-cleared derivatives) and prudent counterparty risk management. That said, gaps in coverage remain (eg bilateral government bond repo haircuts are often zero) and in some cases their current calibration may fail to adequately cover the financial stability risks (eg if hedge funds have crowded into particular strategies).

Conclusion

Our model demonstrates that applying fixed leverage limits at the entity level can be effective for simpler funds with highly similar assets or strategies. But applying them to more complex funds may have the unintended consequence of increasing portfolio concentration risk or crowding funds into certain strategies, while reducing liquidity in others. Alternatively, activity-level measures can target different assets and strategies with risk-sensitive constraints that do not generate an unintended impact on capital allocation, such as a shift towards riskier assets with less leverage. In effect, fixed leverage limits set an average price for leverage across a portfolio of assets, whereas margin requirements set marginal prices on individual assets, making the latter more universally effective in limiting the build-up of risk from leverage. These results demonstrate the benefits of policies which address leverage risks from more-complex funds in a risk-sensitive way, for example, by enhancing activity-level measures.

Leo Fernandes, Harkeerit Kalsi and Nicholas Vause work in the Bank’s Market-Based Finance Division; Matthew Downer is a technical specialist at the Financial Conduct Authority; Sarah Ek is a senior associate at the Financial Conduct Authority; and Sebastian Maxted is an associate at the Financial Conduct Authority.

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