March The Relationship Between Leverage and Risk

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1 The Relationship Between Leverage and Risk Abstract There is a popular misconception that leverage equates to risk and that a levered fund is automatically riskier than an unlevered fund. We argue that the quantity of leverage must not be judged in isolation. Leverage simply amplifies any risks or imbalances that exist in an unlevered portfolio. Therefore, any incremental risks from leverage depend largely on the risk profile of the underlying assets and return stream. Leverage is not appropriate for all strategies, especially those with high basis risk (i.e. imbalances between longs and shorts). Leveraging alpha, as opposed to systematic premia-based returns, presents fewer problems. When discussing an investment strategy, the word leverage carries heavy baggage. It conjures up negative associations with Long Term Capital Management (LTCM), subprime mortgagelinked structured credit products, and other spectacular liability-induced blow-ups during periods of market turbulence. Such historical artifacts have led many to believe that leverage equates directly to risk and that a levered portfolio is inherently riskier than a portfolio that uses no leverage. In reality, however, leverage only amplifies pre-existing risks in an unlevered asset base. What matters then is not leverage, per se, but the underlying risks in the portfolio that is being levered - these should be the focus of an investor s attention. If the risks of the unlevered return profile are reasonable, then the increase in return from leverage may outweigh the amplification in risks. Leverage can be measured and expressed in a variety of ways, but the most common metric is gross leverage. The gross leverage of a portfolio is equal to the total market value of its assets (both long and short positions) divided by its net asset value (NAV). In Figure 1, Portfolios A and B both have NAVs (equity) of $100, and with $200 in margin debt, control $300 in total assets. Note that actual portfolio balance sheets can vary in appearance (i.e. short positions can appear as liabilities). The ultimate objective is to compare the investments held with the means of financing them. In this case, gross leverage for both portfolios is 3x (or 300%), even though the composition of assets held demonstrates they pursue markedly different strategies. Portfolio A appears to be market neutral while Portfolio B simply levers its long positions. With only this very high-level information, we can already determine that the two portfolios will have very different risk profiles, despite having the same level of gross leverage. Portfolios with the same level of gross leverage can have very different risk profiles. Figure 1. Illustrative balance sheets of two equally levered portfolios Portfolio A Portfolio B Assets Liabilities Assets Liabilities Long Positions $150 Margin Debt $200 Long Positions $300 Margin Debt $200 Short Positions $150 Equity Equity Total Assets $300 Net Asset Value $100 Total Assets $300 Net Asset Value $100 * We are grateful to Professor Robert Stambaugh of the Wharton School of the University of Pennsylvania and the National Bureau of Economic Research for his review and helpful comments.

2 Which part of the balance sheet poses the greatest risk for the investor? In theory, leverage risks can arise from any of the three components, but the primary risks generally stem from the assets. Concerns about the stability of the equity capital base (withdrawals) and/or terms of financing (margin calls) generally only arise when the value of the assets falls quickly, thus this analysis will focus on the assets. Total risk from the asset side of a portfolio s balance sheet is driven by the characteristics and return properties of the individual securities held, as well as how the securities interact with each other. These properties and the ensuing risks exist even in the absence of leverage. The relative risk profiles of Portfolios A and B, for instance, would likely be very similar to their respective unlevered equivalents. Analyzing the risks inherent in the unlevered asset will also reveal whether it is appropriate to add any leverage to the portfolio. Before investigating the key contributors to risk, however, it is helpful to review some of the investment metrics that change with the addition of leverage. Some investment metrics change with leverage while others do not. Figure 2. Selected investment metrics that change or do not change with leverage Do change with Leverage Do NOT Change with Leverage* Return Correlation to Equity Market Volatility Skewness Beta to Equity Market Batting Average Upside / Downside Capture Time in Drawdown** Drawdowns** Drawdown (as % of volatility)** Value at Risk (VaR) Return / Volatility Note: See last page for definitions of certain terms. * Assumes no financing costs. ** Assumes no deleveraging during drawdown. Evident from the lists in Figure 2, though returns increase, a variety of risk measurements will also scale up proportionately with leverage. The extent of deterioration in volatility, beta, downside capture, drawdowns, and Value at Risk (VaR) 1 depends on their levels on an unlevered basis. To illustrate this point, we examine changes in the return profiles of the MSCI World Index and HFRI Market Neutral Index with the addition of leverage. The unlevered (1x gross leverage) risk statistics in Figure 3 represent the actual values for the 10 years ended December 2014, and then higher-leverage portfolios are simulated using the unlevered baseline. 1 Value at Risk (VaR) is defined as the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval. The final chart in Figure 3 assumes a 99% confidence interval and monthly time periods. 2

3 Maximum Drawdown Annualized Volatility Beta to MSCI World Index March 2015 Measures of risk scale with the addition of leverage, but levels depend on the starting point. Figure 3. Common measurements of risk (beta, volatility, maximum drawdown, and 1% Value at Risk (VaR)) as leverage is added to the MSCI World Index and the HFRI Market Neutral Index MSCI World Index HFRI Market Neutral Index % 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% -10% -20% -30% -40% -50% -60% -70% -80% -90% -100% x 1.50x 2.00x 2.50x 3.00x 3.50x 4.00x 4.50x 5.00x Gross Leverage 16.0% 2.8% 48.0% 8.4% 80.0% 14.0% 1.00x 1.50x 2.00x 2.50x 3.00x 3.50x 4.00x 4.50x 5.00x Gross Leverage -9.2% -53.7% -25.5% -93.5% -39.4% -99.9% 1.00x 1.50x 2.00x 2.50x 3.00x 3.50x 4.00x 4.50x 5.00x Gross Leverage 3

4 1% Value at Risk (VaR) March % -10% -20% -30% -1.7% -10.1% -5.0% -30.3% -8.3% -40% -50% -50.5% -60% 1.00x 1.50x 2.00x 2.50x 3.00x 3.50x 4.00x 4.50x 5.00x Gross Leverage Note: Unlevered risk statistics calculated using monthly returns from January 2005 to December Addition of leverage assumes no financing costs and monthly rebalance back to target leverage. See last page for important disclosures. Source: MSCI, FactSet, HFRI. As the charts in Figure 3 illustrate, investments with greater risk on an unlevered basis (i.e. 1x gross leverage) will become proportionately riskier with the addition of leverage. The MSCI World Index, for example, starts with 100% market risk (by definition), and utilizing leverage elevates these to extreme levels. Coupling leverage with an all-beta investment such as this would have destroyed most, if not all, of an investor s capital during its maximum drawdown of 2008/2009. This scenario highlights the path dependency of extreme drawdowns: an investor simply cannot recover from a significant loss of capital. The HFRI Market Neutral Index, on the other hand, exhibits much lower risk characteristics on an unlevered basis. These metrics still deteriorate, but nowhere near the levels of the MSCI World Index. In fact, the risk levels of the 5x levered HFRI Market Neutral Index shown in Figure 3 are still all below the respective risk levels of the unlevered MSCI World Index. The fact that a 5x-levered portfolio can be less risky than an unlevered portfolio prompts the question: Which underlying risks are most dangerous to lever? Figure 4 lists a variety of common risks at the position level, long and short side level, and the combined portfolio level. Many managers only consider the risks associated with positions individually. However, as these individual positions aggregate to the portfolios and overall strategy, other risks may arise based on how the components interact and covary with each other. Ultimately, strategies with fewer risks on an unlevered basis are better candidates for leverage. When considering long/short or market-neutral funds specifically, the most important source of risk, and one that is responsible for many hedge fund casualties, is basis risk referring to imbalances created by incomplete or imperfect hedging between the long and short sides of the portfolio. The most obvious source of basis risk is net market exposure, which will be reflected in the overall beta of the net portfolio. This risk is apparent in the charts of Figure 3. While beta in the HFRI Market Neutral Index rises from 0.10 to 0.50 as leverage is added, the beta in the MSCI World Index rises from 1 to 5. In this case, levering beta creates high basis risk, driving risk measurements to extreme levels. 4

5 Basis risk, especially in the form of market beta, is one of the more dangerous risks to lever. Figure 4. Selected list of underlying long/short strategy risks (regardless of leverage) Position Long Side / Short Side Combined Portfolio Balance Sheet Earnings Quality Valuation Liquidity Volatility Duration / Growth Others Concentration Correlations Others Basis Risk Market / Beta Sector Geographies Style Others Basis risk can extend beyond simple market risk to any unhedged exposure to diversifiable risk factors. Risk management has evolved extensively since the development of the Capital Asset Pricing Model (CAPM), when the only risk factor was assumed to be exposure to the equity market. But current risk management strategies still run the spectrum, from managers who approach risk on a position-by-position basis to certain quantitative managers who have proprietary risk models to capture portfolio risk in virtually any form. Risk modeling can include a broad range of potential factors including styles, countries, sectors, currencies, and commodities, among others. Of course, some risk factors cannot be modeled ex-ante, and basis risk is not static. More subtle forms of basis risk may not be evident or may change over time. The more developed the definition of risk, the more likely an investor will be able to balance or neutralize hidden, unintended risks. The smaller the basis risk in a portfolio (in all its forms), the higher the leverage level the portfolio can support, especially during periods of market turbulence. Quantitative long/short funds, for instance, tend to use higher leverage than fundamental long/short funds because they generally have much more sophisticated risk models. 2 But limits to risk modeling imply limits to leverage. And no matter how minor the underlying risks, 30x leverage (as was standard for LTCM, for example 3 ) can destroy the entire equity base during even a minor market downturn. Perversely, leveraging basis risk is more ingrained in our everyday lives than most people realize. The largest asset on the balance sheet of most Americans is a home. Most banks require a down payment of 20%, and the rest is mortgaged. Borrowing 80% against 20% equity translates to 5x gross leverage. A down payment less than 20% further increases this statistic. And most homeowners do nothing to hedge out their risk to the housing market. Traditional banks are equally vulnerable to shocks since they lend out a substantial portion of their capital: 2 Frank Barbarino, Leverage, Hedge Funds, and Risk, NEPC (Summer 2009), accessed May 2014 < 3 Roger Lowenstein, When Genius Failed: The Rise and Fall of Long-Term Capital Management (New York: Random House, 2001)

6 The average leverage of the entire U.S. financial sector is 9.4x. 4 risk became readily apparent to all during the financial crisis. The dangers of leveraging basis Beyond basis risk, another key source of risk that will deteriorate with leverage is position concentration. The smaller the number of portfolio positions, the more likely that idiosyncratic risk will contribute significantly to portfolio volatility. This may be acceptable if a manager has extremely high conviction, but it can nevertheless cause concern if those few concentrated portfolio holdings experience unforeseen problems. Additionally, some residual basis risk may be unavoidable since hedging out all systematic risks may be impossible with a small number of positions. Leverage is less appropriate for more concentrated portfolios due to this high degree of idiosyncratic risk. However, most quantitative managers in particular will seek to minimize idiosyncratic risk with a large number of positions, so concentration is generally not a concern. Although leverage risk generally originates from the asset side of the balance sheet, there are a few caveats. Capital withdrawals have the potential to impact asset valuations in the case of relatively less liquid portfolio holdings. According to a common adage, you never know the true price of liquidity until you need it. If a manager is forced to sell illiquid assets quickly, the resulting steep discounts will further worsen mark-to-market leverage ratios. For this reason, it is imperative that managers match the liquidity/duration of their assets to the liquidity of their equity. This explains why long/short mutual funds only invest in highly liquid securities while private equity firms lock up their investor capital to match the duration of their investments. Mismatches in liquidity or duration are recipes for disaster with the addition of leverage. Even if assets are liquid, however, herd behavior can periodically cause abrupt dislocations in market prices, particularly in highly crowded trades. The sudden failure of Fund ABC, for instance, and subsequent forced liquidation will impact Fund XYZ if it employs a similar strategy and holds many of the same positions. Managers of Fund XYZ may see a rapid fall in those asset prices as a reason to reduce their own exposure, which will further pressure market prices. These types of occasional shocks are virtually impossible to model ex-ante and thus further highlight the prudence in eschewing extreme levels of leverage. Highly differentiated strategies, especially those in which long and short portfolios are managed using separate investment processes and distinct selection factors, are more likely to avoid such crowded trades. In summary, leverage amplifies existing risks in an unlevered portfolio. To the extent those risks are few and minor, the return benefits of leverage may exceed the amplification of risk. In these cases, one can simply adjust gross leverage to maximize total return given a specific level of risk tolerance (or expected volatility). However, certain strategies, especially those with high basis risk, begin with such elevated measures of risk that adding leverage is generally not advisable. And there are limits to leverage with any strategy. Even relatively insignificant risks will balloon to extreme levels if enough leverage is added. 4 Andrew Ang, Sergiy Gorovyy, and Gregory B. van Inwegen, Hedge Fund Leverage, National Bureau of Economic Research (2011): Working Paper 16801, accessed May 2014 < 6

7 Conclusion In the wake of the financial crisis, the popular belief is that all leverage is dangerous. However, leverage does no more than amplify risks already present in the absence of leverage. Investors will benefit from analyzing basis risk and unlevered return characteristics in order to determine appropriateness of leverage. While many strategies should not be levered, all-alpha products that pay special attention to basis risk are prime candidates for leverage since they begin with relatively fewer risks. Sources Cited Ang, Andrew, Sergiy Gorovyy, and Gregory B. van Inwegen. Hedge Fund Leverage. National Bureau of Economic Research (2011): Working Paper 16801, accessed May 2014 < Barbarino, Frank. Leverage, Hedge Funds, and Risk. NEPC (Summer 2009), accessed May 2014 < Lowenstein, Roger. When Genius Failed: The Rise and Fall of Long-Term Capital Management. New York: Random House,

8 Solely for the use of institutional investors and professional advisers. This presentation expresses the authors views as of March 3, 2015 and should not be relied on as research or investment advice regarding any investment. These views and any portfolio characteristics are subject to change. There is no guarantee that any forecasts made will come to pass. The MSCI World Index is a free float-adjusted market capitalization index, designed to measure developed market equity performance, consisting of 23 developed country indices, including the U.S. The Index is gross of withholding taxes, assumes reinvestment of dividends and capital gains, and assumes no management, custody, transaction or other expenses. MSCI has not approved, reviewed or produced this report, makes no express or implied warranties or representations and is not liable whatsoever for any data in the report. You may not redistribute the MSCI data or use it as a basis for other indices or investment products. The HFRI Monthly Indices ("HFRI") are a series of benchmarks designed to reflect hedge fund industry performance by constructing equally-weighted composites of constituent funds, as reported by the hedge fund managers listed within the HFR Database. Equity Market Neutral strategies employ sophisticated quantitative techniques of analyzing price data to ascertain information about future price movement and relationships between securities, select securities for purchase and sale. These can include both Factor-based and Statistical Arbitrage/Trading strategies. Factor-based investment strategies include strategies in which the investment thesis is predicated on the systematic analysis of common relationships between securities. In many but not all cases, portfolios are constructed to be neutral to one or multiple variables, such as broader equity markets in dollar or beta terms, and leverage is frequently employed to enhance the return profile of the positions identified. Statistical Arbitrage/Trading strategies consist of strategies in which the investment thesis is predicated on exploiting pricing anomalies which may occur as a function of expected mean reversion inherent in security prices; high frequency techniques may be employed and trading strategies may also be employed on the basis on technical analysis or opportunistically to exploit new information the investment manager believes has not been fully, completely or accurately discounted into current security prices. Equity Market Neutral Strategies typically maintain characteristic net equity market exposure no greater than 10% long or short. It is not possible to invest directly in an index. Alpha is a measurement of performance return in excess of a benchmark index. Batting Average is the percentage of months in which a portfolio produces a positive (>0%) return. Beta is a measurement of sensitivity to the benchmark index. A beta of 1 indicates that a portfolio s value will move in line with the index. A beta of less than 1 means that the portfolio will be less volatile than the index; a beta of greater than 1 indicates that the security's price will be more volatile than the index. Maximum Drawdown is the peak-to-trough decline in value of an investment during a specific period. Skewness describes asymmetry from the normal distribution in a set of statistical data. Skewness can come in the form of "negative skewness" or "positive skewness", depending on whether data points are skewed to the left (negative skew) or to the right (positive skew) of the data average. Upside/Downside Capture are statistical measures of an investment manager's overall performance in up/down markets. The upside capture ratio is used to evaluate how well an investment manager performed relative to an index during periods when that index has risen, and the downside capture ratio measures performance when that index has fallen. These ratios are calculated by dividing the manager's returns by the returns of the index during up-market (down-market) months, and multiplying that factor by 100. Value at Risk (VaR) is the potential loss in value of a risky asset or portfolio over a defined period for a given confidence interval. Volatility is the standard deviation of returns. 8