Fund performance raises specific issues

Unlike the returns of common stocks and mutual funds, hedge fund returns are generally not normally distributed.1,i This has considerable consequences on a number of hedge fund risk measures, as presented in last month’s article, which was drawn from the EDHEC Hedge Fund Reporting Survey2 conducted with the support of Newedge Prime Brokerage.

Simple measures, such as the Sharpe ratio,3 which are based on the normality assumption, are then not valid for assessing the performance and riskiness of a hedge fund. The same applies to all value-at-risk (VaR) measures that assume normally distributed returns. Non-normality of hedge fund returns is seen easily with statistical tests for normality. The most well-known test is the Jarque-Bera test.4 Another popular one is the Lilliefors test,5 which is in fact an adaptation of the Kolmogorov-Smirnov test.

Many adjustments of standard risk measures have been proposed to account for the non-normality of hedge fund returns. For example, the Sortino ratio is a good improvement over the Sharpe ratio, and the Cornish-Fisher VaR a suitable extension of standard VaR measures. Hence, it is most important to be aware of a hedge fund’s non-normality – the suitable tools to analyse its returns are often straightforward.

Smoothed hedge fund returns
Another particularity of hedge fund returns is that they are smoother than the returns of mutual funds or common stocks – and, more important, smoother than they ought to be, given their risk exposure. How can this be? Essentially, there are two main reasons for these so-called smooth returns: investment in illiquid assets and deliberate cheating.
Since hedge funds often invest in illiquid assets, it is not always easy to determine the net asset value of the funds.

Sometimes there are no market prices for securities available, and the manager linearly extrapolates the price between two observable prices. Or there might be various quotes for thinly traded securities, so the manager is inclined to use smoothed broker-dealer quotes. The returns thus obtained will usually be much flatter than those of similarly risky but liquid investments. Returns may also be deliberately smoothed by hedge fund managers so their fund will appear less volatile than it is.

Smoothed hedge fund returns and smoothed return data have considerable consequences for the evaluation of hedge funds. Most of all, the fund’s volatility does not reflect its true riskiness; it is biased downwards.6 As a direct consequence, risk-adjusted performance measures are no longer accurate and might even be meaningless. In fact, there is empirical evidence that hedge fund returns are too smooth. Getmansky et al.7 proposed an econometric model of the illiquidity exposure of hedge funds and showed that illiquidity is the major reason for the smoothing of hedge fund returns.

In contrast, Bollen and Pool8 developed a model that makes it possible to detect deliberate cheating in hedge fund returns. They found that for some funds the most likely reason for return smoothing is simply fraud – i.e. the managers misreport return figures to reduce the volatility of the fund’s returns, thereby achieving higher Sharpe ratios.

Return smoothing, deliberate or not, can be detected by serial correlation in hedge fund returns. A simple test is the test of autocorrelation by Ljung and Box.9 In principle, it is also possible to construct risk measures that overcome this problem. Getmansky et al.,7 for example, propose adjustments to the standard Sharpe ratio that correct for the bias caused by illiquid assets in hedge fund portfolios.

Holdings-based reporting
All the risk measures discussed in last month’s article share a reliance, in one way or another, on past return data. Risk-adjusted performance measures relate past returns to past risk exposure; factor analysis explains the sources of past returns by some common risk factors. In contrast to this so-called return-based risk reporting, holdings-based reporting takes a completely different approach.

Holdings-based reporting is in fact a bottom-up approach. It consists of disclosing the exact portfolio composition of a fund, which then allows investors to analyse each of the securities that make up the whole portfolio. The individual risks are then aggregated over the entire fund to obtain the fund’s overall risk exposure.

Holdings-based reporting thus has many advantages. First, by definition, it allows a much more detailed analysis of all the risks involved. Second, as a direct consequence, it thereby avoids the estimation errors inherent to return-based reporting. Holdings-based reporting enables investors to choose their own technique for aggregating the risk of different asset or security classes and thus to reflect individual risk preferences.

Finally, holdings-based reporting reduces the problems related to the lack of transparency of hedge funds: since the investor is informed of the exact portfolio composition, the scope for unexpected or even fraudulent behaviour by the hedge fund manager is very limited. Full portfolio disclosure, however, is counterproductive to good hedge fund performance, since other market participants can easily make use of this information to trade against a hedge fund’s strategy. For this reason, holdings-based reporting for hedge funds cannot be too detailed; instead of individual securities, only the holdings of the security classes are made public. In addition, hedge funds publish their portfolio composition with a time-lag, such that the risk profile reflects only earlier positions taken by the fund.

Holdings-based reporting also requires substantial data processing, and the investor must have the time and ability to analyse it, as risk analysis is left to the investor. Hence, risk analysis using portfolio holdings requires not only current and past portfolio holdings, but also the exact risk characteristics and risk classification of each of the holdings involved. If not done accurately, it is easy to draw mistaken conclusions.

In short, holdings-based reporting is essentially a very good concept. However, for many investors the convenient and rather easy to understand return-based reporting might be more appropriate.
Liquidity risk indicators

Investment in illiquid assets not only causes return smoothing, but is also a source of risk on its own. Liquidity problems can quickly increase the risk of fund failure. Since illiquid positions are very common in hedge funds, liquidity risk is much more of a problem for hedge funds than for mutual funds. Liquidity and liquidity risk are, unfortunately, not clearly defined. In what follows, we describe the two main versions of liquidity risk and liquidity risk measures: asset liquidity risk and funding liquidity risk.

Asset liquidity risk is a fund’s risk of being unable to sell positions in the portfolio. Funding liquidity risk is the risk of being unable to meet financial obligations when they fall due. Although the two kinds of risk are closely related, the distinction is important. Whereas asset liquidity is much more of an asset management task, funding liquidity has more to do with cash management.ii

Asset liquidity risk measures attempt to indicate the liquidity of the assets in the portfolio. The Ljung-Box test9 of auto-correlation of hedge fund returns is a practical test for evaluating to what extent the fund contains illiquid assets. Since illiquid assets tend to exhibit relatively constant prices, the returns of a portfolio containing illiquid assets are more likely to be auto-correlated.6 The percentage of hard-to-value (non-marketable or illiquid) assets is another convenient asset liquidity risk indicator.

Average liquidation periods for a specified part of the portfolio are also a good measure of the liquidity risk of a portfolio, although the estimation of such liquidation periods is not straightforward. Hedge funds can also provide estimated impact costs (i.e. the differences between market and realised prices) when unwinding large investments. Finally, similar to extreme performance risks, stress tests can help to analyse the impact of critical market situations on a portfolio’s liquidity.

Funding liquidity risk indicators try to capture the provision of cash to meet obligations. Liquidity ratios, such as cash-to-equity or VaR-to-cash ratios, are a simple class of funding liquidity risk measures. Asset-liability match analysis attempts to examine the timing of portfolio transactions. By relating future payments and redemptions to each other, this analysis helps to detect possible mismatches and thus liquidity constraints well in advance. Similarly to asset liquidity, hedge funds can simulate funding liquidity stress tests to evaluate the impact of adverse market conditions on the cash situation of the fund.

Leverage risk indicators
Unlike mutual funds, hedge funds can make use of financial leverage by borrowing large amounts of capital. Although leverage is not a source of risk on its own, it usually amplifies all other risks. Especially great is the impact of leverage on liquidity risk. It is important to note that leverage is not bad in itself, as it is a convenient means of shifting a portfolio towards the desired risk-return profile. But there is no universal leverage risk indicator, since the usefulness of the indicator depends very much on the hedge fund strategy. A good overview of leverage indicators is found in Rahl.10

Leverage risk indicators can be classified into two main groups: accounting and risk-based leverage measures. Accounting-based leverage indicators are usually simple ratios of information found in a hedge fund’s financial statement. These measures, such as gross assets-to-equity, debt-to-equity, or their inverses, allow an initial assessment of a fund’s leverage. The problem with these ratios is that they do not capture off-balance sheet leverage. For example, futures can imply high leverage but may not appear in the financial statements. Neglecting this exposure can be misleading. For this reason, Breuer11 suggested incorporating off-balance sheet leverage exposure in the ratios (such as that represented by futures) by calculating their balance sheet equivalent.

Risk-based measures are another possible means of capturing off-balance sheet leverage. The aim of these measures is to capture the leverage of a fund by relating its risk exposure to a balance sheet component, again usually net asset value of equity. Some of the prominent ratios are VaR-to-equity, volatility-to-equity, or stress loss-to-equity. Here, off-balance sheet leverage risk is automatically included via the risk component in the numerator. McGuire et al.12 proposed another risk-based leverage measure using hedge fund style analysis.

They observed that the coefficients of the factors in style analysis should add up to 1 if no leverage is used. This observation led the authors to the conclusion that the sum of the coefficients is a very useful leverage indicator, since any deviation from 1 is a clear sign of using leverage, both on and off balance sheet. For example, a sum of beta coefficients of 2 indicates a portfolio risk exposure twice as large as the investors’ capital, and hence leverage of 100%.

Operational risk disclosure
Although often neglected as an independent source of risk, operational risk is perhaps the greatest risk for hedge fund investors. As Giraud13 showed, half of all hedge fund failures are caused by operational risk problems, such as misrepresentation of a fund’s net asset value, fraud, or trading activities outside of the fund’s mandate.

That this risk is the cause of so many failures underscores the need for disclosure. It is clear that no investor can expect to be fully insured against fraud by hedge fund management, but detailed operational risk disclosure can reduce its impact significantly. We describe below the basic ingredients of operational risk disclosure. Since risk related to a fund’s valuation framework accounts for the lion’s share of operational risk disclosure, it is presented in a separate paragraph.

First, each hedge fund should issue a private placement memorandum (PPM) that provides an overview of the hedge fund’s strategy, including its investment style, the asset classes it uses and its geographic exposure, and the planned use of leverage. It also includes a detailed description of the organisation of the fund: the legal framework, information on proxy voting, redemption rights or fee structure of the fund should be stated clearly.

Next, the fund should provide as much information as possible on the fund management itself – e.g. the vitae of the managers and the possible conflicts of interests of the management team. In addition to the problems relating to fee incentives, such internal conflicts can arise when managers run different hedge funds, so they could be inclined to manage the fund’s allocation to optimise their joint fee income.

Conflicts of interest can also occur between hedge fund investors, such as those induced by side letters and parallel-managed accounts for some specific investors. Hence, any fund should disclose the existence of such arrangements.

Another source of operational risk is the involvement of third parties. The hedge fund team should consequently disclose the main counterparties of the hedge fund and provide a short analysis of the risks involved in outsourcing activities to partners. Finally, hedge funds should arrange for special event reporting – i.e. an irregular disclosure of important information on the occasion of significant market or strategy changes.

Valuation framework
By far the most important part of operational risk disclosure is the valuation framework. Since hedge funds invest in many different and complex financial products, some of which are not regularly traded, the calculation of its net asset value is not simple. Often there are many ways to calculate the current value of a specific asset, and all yield different results. Moreover, it is not always obvious which valuation technique – and thus which valuation – is most appropriate. For this reason, a clear statement of a fund’s valuation principles is indispensable. The main valuation principles used by hedge funds are summarised below.

For liquid assets, market prices are in general the best source of an asset’s value. However, prices can be either ask, bid or mid-prices, and they can be calculated as an average over a certain time period. Obtaining a value for illiquid assets is much more difficult. One possibility is to use pricing models: derivatives are best priced with stochastic pricing models. Loans or private equity investments might be valued with the help of discounted cash flow models. If related financial instruments are traded in the market, arbitrage pricing models are useful. Finally, counterpart quotes or estimates are another source of an asset’s value. It is sometimes possible to assign the valuation of difficult and complex assets to third parties.

It is also important to have clear control mechanisms to ensure that the valuation principles are respected at all times. An initial mechanism is to assign the determination of the fund’s net asset value to a third-party valuation service provider or administrator. If the valuation is done in-house, it is possible to ensure compliance with the valuation framework by strictly separating the duties of the manager and administrator who is in charge of the valuation. Finally, hedge fund managers might opt to do the valuation themselves but have the valuation policy validated by an external auditor.

This article is based on an EDHEC Risk and Asset Management Research Centre programme on hedge funds which is supported by Newedge Prime Brokerage.

By David Schröder, business analyst, and Felix Goltz, head of applied research, EDHEC Risk and Asset Management Research Centre

References

1   Lhabitant FS. Hedge Funds – Quantitative Insights. Chichester: John Wiley & Sons, 2004.
2   Goltz F & Schröder D.EDHEC Hedge Fund Reporting Survey. Nice: EDHEC, 2008.
3   Sharpe WF. Mutual fund performance. Journal of Business 39(1), 119–138.
4   Jarque CM & Bera AK. Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters 6(3), 255–259.
5   Lilliefors H. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association 62, 399–402.
6   Asness CS, Krail RJ & Liew JM. Do hedge funds hedge? Journal of Portfolio Management 28(1), 6–19.
7   Getmansky M, Lo AW & Makarov I. An econometric model of serial correlation and illiquidity in hedge fund returns. Journal of Financial Economics 74(3), 529–609.
8    Bollen NPB & Pool VK. A Screen for Fraudulent Return Smoothing in the Hedge Fund Industry. Owen Graduate School of Management, working paper, 2006.
9    Ljung GM & Box GEP. On a measure of lack of fit in time series models. Biometrica 65(2), 297–303.
10   Rahl L. Hedge Fund Risk Transparency. London: Risk Books, 2003.
11   Breuer P. Measuring Off-Balance-Sheet Leverage. IMF, working paper WP/00/202, 2000.
12   McGuire P, Remolona E & Tsatsaronis K. Time-varying exposures and leverage in hedge funds. Bank for International Settlement Quarterly Review (March 2005), 59–72.
13   Giraud J-R. Mitigating Hedge Funds’ Operational Risks. Nice: EDHEC, 2008.

NOTES
i    Strictly speaking, hedge funds are not log-normally distributed – i.e. their log returns are not normally distributed. However, often this distinction is not made. It is also important to mention that the returns of stocks and mutual funds are not normally distributed either, but the normality assumption is less violated compared to hedge fund returns.
ii    Note that both kinds of liquidity risk refer to risks in hedge funds. In addition to these risks, investors usually face an additional liquidity risk due to the lock-up periods.