Practical analysis for investment professionals
30 June 2015

# An Easier Way to Understand Hedge Fund Leverage

Absolute return goals are widely used in the hedge fund industry and are achieved through leverage and alpha relative to various market betas. As a result, it is possible to create a valuation-based “rule of thumb” computation for the implied leverage that hedge fund strategies need given market valuations.

Traditional metrics, such as notional, nominal, and net leverage, can be confusing or annoying for investors to interpret given their composition and spectrum of values. Candidly, using these traditional metrics does not seem the most efficient way to communicate leverage to the average investment committee member, who may have trouble understanding all the underlying calculations. Clearly, we need a simpler solution that better reflects the implied leverage clients are asking their managers to take.

Because leverage is a direct function of valuations, which are a result of the absolute return goals set by managers and their clients, a leverage metric can be derived from basic algebra and a couple of easy assumptions.

We call this computation the Implied Hedge Fund Leverage Ratio. It is simple to use and gives a pragmatic understanding of the leverage associated with any hedge fund strategy based on prevailing market valuations.

Why Does This Concept Matter Now?

This issue is relevant now because we are in a low-return, challenging alpha environment as a result of monetary stimulus compressing valuations and the cross-volatility of asset returns. These issues are succinctly illustrated with a few charts that show the cross-volatility of developed market equity returns (proxy for pricing opportunities) and implied returns for major asset classes before, during, and after the last bear market.

Russell Equity Cross Volatility Index

Earnings and Dividend Yields (Implied Returns)

Yields to Maturity

What Is the Implied Hedge Fund Leverage Ratio Equation?

The first part of the Implied Hedge Fund Leverage Ratio is based on the assumption that the manager’s gross returns must meet the client’s expected return goal net of management and incentive fees.

This value is derived as

• Rg = Rc/(1 – I) + F,

where

• Rg = Gross needed return
• Rc = Client return hurdle/expectation for investing
• I = Incentive fees as a percent of profits
• F = Fees

Furthermore, once a client’s return hurdle is known, implied portfolio leverage can be calculated by using an appropriate beta for the strategy and the client’s alpha expectations.

This value is derived as

• LRg/(B + A),

where

• L = Implied leverage to market beta
• Rg = Gross needed hedge return
• B = Market beta associated with strategy
• A = Alpha expected by client

How Are Betas Selected for Various Strategies?

Hedge fund managers generally dislike being associated with market betas because their strategies are usually complex and involve securities far more complicated than, say, the S&P 500 Index. However, derivatives are derived from market betas and are, therefore, driven by them. The following are examples of how betas can be selected for a few common strategies.

Long–Short Equity Managers

• For this strategy, we use the S&P 500 because these managers’ returns follow the index very closely over time.

Credit Managers

• For a credit manager, beta is a direct function of the manager’s level of credit risk (or the yield to maturity).

Arbitrage Managers

• These managers calculate potential profits relative to their cost of capital, which is the centerpiece of any arbitrage calculation. Any investment must exceed the cost of capital to be undertaken, making this the baseline for pre-leverage returns, a relationship that can be seen in aggregate performance over time for these strategies. Therefore, for arbitrage managers, we select the cost of capital as the beta.

Commodity Trading Strategies

• Selecting this beta is more theoretical in nature but rather simple to derive because the return expectation for most natural resources over time is the cost of capital, making this the baseline return for holding commodities.

Examples of the Equation

Before calculating examples of the Implied Hedge Fund Leverage Ratio, we need to make a few basic assumptions:

1. The client’s return goal is 10% net of fees. This assumption is based on long-term public market returns, expected manager alpha, a small illiquidity premium, and common hedge fund manager return goals.
2. Expected alpha in March 2009 is 6% given tremendous opportunities resulting from the credit crisis.
3. Expected alpha for March 2007 and March 2015 is reduced to 2% given the challenging alpha environment.
4. Management fees are 1% and incentive fees are 20% of profits

Example 1: Long–Short Equity Manager

Implied Leverage Ratios for Long/Short Equity Managers

Implied equity returns for the Russell 1000 Index are used as the beta in the above leverage calculations and happen to show a tremendous difference among these dates.

Example 2: Credit Manager

Implied Leverage Ratios for Credit-Based Hedge Fund Strategies

This example uses the Barclays US High Yield Index as the beta for a credit-based hedge fund strategy operating in the middle range of the credit spectrum. Again, we can see how market valuations affect potential leverage and that implied leverage is higher now than before the last bear market.

Example 3: Arbitrage Manager

Implied Leverage Ratios for Arbitrage Strategies

For this example, we use the Barclays US Credit Index as the beta, or the cost of capital, and baseline return expectation that must be exceeded for any investment to be made pre-leverage. We can clearly see the effects of low interest rates on implied leverage ratios given March 2015 values.

Example 4: Commodity Manager

Implied Leverage Ratios for Commodity Managers

As mentioned earlier, the long-term cost of capital is the baseline return expectation for most natural resources. Consequently, we use the Barclays US Long Credit Index as the beta for this calculation.

These examples are interesting and would likely draw criticism from the hedge fund industry regarding their efficacy. Nonetheless, the theories are sound from a big picture perspective and tell us conclusively that capital market conditions are very conducive to high levels of leverage.

Increasing Leverage during a Low-Return Environment Is a Bad Idea

Seeing implied leverage ratios similar to those prior to the last bear market is not the best thing from a risk management perspective. The examples given clearly show how robust equity valuations, low fixed-income yields, and lowered alpha opportunities strongly encourage managers to take on additional leverage to meet clients’ return goals.

Leveraging low-returning/highly valued assets always presents the possibility for significant downside during a sudden market correction. Recall the low-return environment of 2007 and that hedge funds generally lost around 20% the following year. Furthermore, the last thing you want to do is leverage expensive assets prior to a reversion in valuations, which is inevitable when monetary policy eventually gets unwound.

The good news for the hedge fund industry is that if this happens slowly, hedge funds will likely do fine. If it does not happen slowly, returns could look a lot more like those in 2008. Either way, now may be a good time to dimension leverage in your hedge fund portfolio.

We don’t need complex calculations to discern how valuations affect hedge funds. The equation is just simple math, and that’s the beauty of it.

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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.

Image credit: ©iStockphoto.com/FrankRamspott

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About the Author(s)
##### Eric Petroff, CFA

Eric Petroff, CFA, is the founder of Petroff Institutional. He has more than a decade of institutional consulting experience across virtually all client types, having served as a senior consultant and shareholder at Hammond Associates and as a director of research and chief strategist at Wurts & Associates. In addition to his CFA, Eric holds the Financial Risk Manager (FRM) and Chartered Alternative Investment Analyst (CAIA) designations, and has an MBA with an emphasis in finance from Webster University.

## 1 thought on “An Easier Way to Understand Hedge Fund Leverage”

1. Vastie Joseph says:

This is a very interesting way to look at leverage. But I was just wondering why divided by the sum of Beta & alpha?

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