The Alternative Investment Management Association

Alternative Investment Management Association Representing the global hedge fund industry

Problems with 'extreme hedge fund returns'

Todd Brulhart and Peter Klein

KCS Fund Strategies Inc and Simon Fraser University, respectively

Q1 2005


This article is the winner of the 2005 AIMA Canada Research Award, which was sponsored by JCClark and RBC Capital Markets.

Hedge funds have existed since the 1960s but remained under the radar screen of the general public and most investors until 1998 when Long Term Capital Management lost 92% of investor capital. Since that time, sophisticated individual investors and institutions have continued to earn consistent and sometimes substantial returns from hedge funds, but the general perception among most investors is that hedge funds are very risky with a high potential for substantial losses. In recent years a number of researchers, including Brooks and Kat (2002), Lamm (2003), Getmansky, Lo and Makarov (2004), Agarwal and Naik (2004) and Malkiel and Saha (2004) have reported that while hedge funds look superior from a mean-variance perspective, the potential for large losses (or extreme event risk) is captured in the skew and kurtosis of hedge fund distributions.

In a recent working paper (2005) the authors of this article also looked at the extreme event risk of hedge funds and found that the skew and kurtosis in hedge fund returns do not necessarily imply that investors are exposed to undue risks. To make our argument, a good place to start is to look at pictures of hedge fund and traditional asset distributions. Figure 1 presents histograms for three common hedge fund indices and compares them with two well known equity indices. It is immediately apparent that none of the hedge fund indices has ever had monthly returns outside of 10% (either positive or negative) while both of the equity indices have. The Nasdaq has even had monthly returns exceeding 20% on both the positive and negative sides. It is also apparent that the hedge fund indices return 1% or 2% a month much more consistently than do the equity indices. Despite the concerns over extreme event risks in hedge funds, there does not appear to be any evidence of it in the distributions, at least relative to equity indices.

We also looked for evidence of extreme event risk in the maximum drawdowns for the indices. Table 1 shows the maximum drawdowns and recovery times for the same indices as shown in the histograms. The worst drawdown for any of the hedge fund indices was a 13.8% drawdown for the CSFB/Tremont Hedge Fund Index during the fall of 1998 at the time of the Long Term Capital meltdown. The drawdown lasted three months and the index took 13 months to recover the loss. Again this is minor in comparison to the two equity indices which still have not recovered from losses incurred since 1999 and which may take several more years to recover. Once again there is no evidence of substantial extreme event risk in the hedge fund indices.

Interpreting the data

Do skew and kurtosis provide a clue to some subtle risk that is not evident in other types of analysis or are skew and kurtosis problematic? Kaplansky (1945) in a brief article entitled “A Common Error Concerning Kurtosis”, written long before the first hedge fund existed, voiced concern about the way kurtosis is typically interpreted. Using examples, Kaplansky points out that the peakedness of different distributions does not match the common interpretations of kurtosis. Kaplansky focused on the peakedness of the distributions but his work can be extended to demonstrate the same inconsistencies when considering the tails, or extreme events, of distributions.

Scott and Horvath (1980) further developed the use of higher moments in return analysis when they demonstrated that each term in a Taylor series expansion of an investor’s utility function represented each subsequent statistical moment. They determined that investors prefer higher first and third moments but lower second and fourth moments. These preferences are now often applied to skew and kurtosis to claim that investors prefer higher skew and lower kurtosis. However, it should be noted that skew and kurtosis are not the same thing as the third and fourth statistical moments that Scott and Horvath worked with. Skew and kurtosis are ‘normalised’ by dividing the third and fourth statistical moment by the standard deviation raised to the third and fourth power respectively. Do Scott and Horvath’s conclusions also apply to skew and kurtosis or does the standard deviation in the denominator affect the interpretations?

Table 2 shows the standard deviation, skew and kurtosis, and third and fourth moments for the same indices as shown in the histograms. The table shows that the skew and kurtosis of the hedge funds are indeed inferior to those of the equities, as is often claimed. However the third and fourth statistical moments are substantially better for the hedge funds. This suggests that the lower standard deviation of hedge funds is hiding what are actually superior higher moments within the poorer skew and kurtosis measures.

Analysis tools

While Scott and Horvath used utility functions to get their results, a more general result relying on fewer assumptions can be seen in the work of Ingersoll (1987) who used leverage to equalize the mean or variance of two different investments and then used a stochastic dominance argument to show that investors would prefer one investment over the other. In our paper, we extend this approach to include the unscaled statistical third and fourth moments. We use leverage to equalize the fourth statistical moment and then use Scott and Horvath’s conclusions on investor preference, that investors prefer higher first and third moments and lower second and fourth moments, to see if one investment dominates another. Applying this approach to the hedge fund and equity indices show that the hedge fund indices dominate, as shown in Table 3. They tend to have higher returns, lower standard deviation, and higher third moments after the fourth moments have been equalised.

However, if leverage is used to equalise the second moments without regards for the higher moments as is often done by mean-variance analysis, hedge funds do not dominate. Table 4 shows that the hedge funds tend to have higher first and third moments but also higher fourth moments. Mean-variance analysis on hedge funds is exposing investors to increased risk in the fourth moment. This leads us to the conclusion that it is the analysis tools that investors are using which are causing exposure to higher risks and not the hedge funds themselves.


In conclusion, our results highlight several implications for investors. First, the large allocations that some investors have made to hedge funds have been justified. Based on the historical data, these investors have enjoyed higher returns without taking on undue risk. Second, the use of leverage on a portfolio of hedge funds, as is often applied by funds of hedge funds, may also be appropriate. The lower standard deviation and fourth statistical moments of hedge funds allows leverage to be applied without resulting in risk greater than that of equities.

However, investors should be careful with the tools they use in analysing hedge funds. Mean-variance tools can expose investors to risks in the higher moments that they are not aware of. Also, beware of using the standard measures of skew and kurtosis. The use of these tools is not consistent with academic theory and can lead to erroneous results.

Agarwal, V. and N.Y. Naik, (2004) “Risks and Portfolio Decisions Involving Hedge Funds”, Review of Financial Studies, 17, 63-98.

Brooks, C. and H. M. Kat, (2002) “The Statistical Properties of Hedge Fund Index Returns and Their Implications for Investors”, The Journal of Alternative Investments, 5, 26-44.

Getmansky, M., A. W. Lo and I. Makarov, (2004) “An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns”, Journal of Financial Economics 74, 529-609.

Ingersoll, J. E., (1987) Theory of financial decision making, Rowan and Littlefield: Savage, Maryland.

Kaplansky, I., (1945) “A Common Error Concerning Kurtosis”, American Statistical Association Journal, 40, 259.

Lamm Jr., R. M., (2003) “Asymmetric Returns and Optimal Hedge Fund Portfolios”, The Journal of Alternative Investments, 6, 9-21.

Malkiel, B. G. and A. Saha, (2004) “Hedge Funds: Risk and Return”, working paper.

Scott, R. C. and P. A. Horvath, (1980) “On the Direction of Preference for Moments of Higher Order Than the Variance”, Journal of Finance 35, 915-919.



Problems with Extreme Hedge Fund Returns - Figure 1

Problems with Extreme Hedge Fund Returns - Figure 2

Problems with Extreme Hedge Fund Returns - Figure 3

Problems with Extreme Hedge Fund Returns - Figure 4

Problems with Extreme Hedge Fund Returns - Figure 5


Back to Listing

Main Menu

  1. Home
  2. About
    1. Our Core Objectives
    2. AIMA's Policy Principles
    3. Meet the team
    4. AIMA Council
    5. Global Network
    6. Sponsoring Partners
    7. Opportunities at AIMA
    8. AIMA’s 25th anniversary in 2015
  3. Join AIMA
    1. Benefits of Membership
    2. Membership Fees
    3. Application form
  4. Members
    1. AIMA DDQs
    2. AIMA Annual Reports
    3. AIMA Governance
    4. AIMA Logo
      1. Policy note
    5. AIMA Members' List
    6. AIMA Review of the Year
    7. Committees and Working Groups
    8. Weekly News
    9. Update Profile
  5. Investors
    1. AIMA Investor Services
    2. AIMA Members' List
    3. Investor Steering Committee
  6. Regulation
    1. Asset Management Regulation
      1. EU Asset Management Regulation
        1. AIFMD
        2. European Capital Markets Regulation
        3. MiFID / MiFIR
        4. UCITS
        5. European Venture Capital Directive
        6. Shareholder Rights Directive
        7. European Long Term Investment Fund Regulation
        8. Loan Origination Funds
        9. Capital Raising
        10. AIFMD-Related Events
      2. US Hedge Fund Adviser Regulations
        1. Registration and Reporting
        2. Incentive-Based Compensation
        3. JOBS Act
      3. Asia Pacific Asset Management regulation
      4. Other Jurisdictions’ Asset Management Regulation
      5. Private Placement Regime
        1. Canada
        2. Dubai
        3. Finland
        4. Germany
        5. Hong Kong
        6. Japan
        7. Saudi Arabia
        8. Sweden
        9. United Arab Emirates
      6. Systemically Important Financial Institutions ('SIFIs')
      7. Remuneration
        1. UK
        2. United States
        3. CRD IV and CRR
        4. AIFMD
        5. MiFID
      8. Shadow Banking
      9. Volcker Rule
      10. Other
      11. Systemic Risk Reporting
      12. Dealing Commission
      13. Corporate Governance
      14. Securitisation
    2. Markets Regulation
      1. Bank/Capital Regulation
        1. Capital Requirements Directive
        2. EU Bank Structural Reforms
      2. Capital Markets Union
      3. Derivatives/Clearing
        1. EMIR
        2. MiFID II / MiFIR - Derivatives
        3. MAD / MAR
        4. Dodd-Frank Act Title VII
        5. Hong Kong
        6. IOSCO
        7. Singapore
      4. High Frequency Trading
        1. EU automated trading
          1. ESMA Guidelines
          2. Germany
          3. MiFID II / MiFIR - HFT
        2. US automated trading
          1. SEC Regulation SCI
          2. CFTC Automated Trading
        3. IOSCO
        4. Flash Crash
      5. Insurance Regulation
        1. Solvency II
      6. Market Abuse
        1. MAD / MAR
        2. Indices as Benchmarks
      7. Position Limits
        1. MiFID II - Commodities
        2. CFTC Position Limits
      8. Resolution of Financial Institutions
        1. Europe
          1. EU Bank Recovery and Resolution Directive
          2. EU Non-Bank Recovery and Resolution
        2. CPSS-IOSCO
        3. Financial Stability Board
        4. UK
        5. USA
      9. Shadow Banking
        1. International Shadow Banking
        2. EU Shadow Banking - SFT reporting & transparency
      10. Short Selling
        1. EU Short Selling Regulation
        2. Hong Kong Short Selling Regulation
        3. US Short Selling Regulation
      11. Trading
        1. Dodd-Frank Act
        2. MiFID Portal
        3. REMIT
        4. Securities Settlement
    3. Tax Affairs
      1. Automatic Exchange of Information (AEOI)
        1. FATCA
        2. EU - AEFI
        3. OECD - Global Standard on AEFI
      2. Australia - Investment Manager Regime (IMR)
      3. Base Erosion - Profit Shifting (BEPS)
      4. FIN 48 and IAS 12
      5. Financial Transaction Tax (FTT)
      6. UK Investment Management Exemption (IME)
      7. UK Offshore Funds Regime
      8. Other
    4. AIMA's Policy Principles
    5. Search
    6. Resources
      1. Guidance Notes
      2. Jurisdictional Guides
      3. Noticeboard
        1. AEOI: FATCA and other regimes
        2. AIFMD
        3. Bank/Capital Regulation (including NSFR)
        4. BEPS
        5. CFTC Registration and Exemptions
        6. Corporate Governance
        7. Dealing Commission
        8. Derivatives
        9. FTT
        10. High Frequency Trading
        11. MiFID / MiFIR
        12. Other Hot Asset Management Topics
        13. Other Hot Markets Topics
        14. Other Hot Tax Topics
        15. Position Limits
        16. Trading
        17. UCITS
        18. UK Partnership Tax Review
        19. US State and Local Taxes
        20. Volcker Rule
      4. Hedge Fund Manager Training
      5. Quarterly Regulatory Update
      6. Webinar Programme
      7. Regulatory Compliance Association
        1. About the Regulatory Compliance Association
        2. RCA Curricula and initiatives for alternative investment firms
        3. Meet the regulators and Sr. Fellows
  7. Education
    1. Research
      1. AIMA Research
      2. Industry research
      3. Search research documents
    2. "The Case for Hedge Funds"
      1. Global Hedge Fund Industry Paper: The value of our industry
      2. The Value of the Hedge Fund Industry to Investors, Markets and the Broader Economy: Research commissioned by AIMA and KPMG
      3. The Evolution of an Industry: KPMG/AIMA Global Hedge Fund Survey
      4. Contributing to Communities: A global review of charitable and philanthropic activities by the hedge fund industry
      5. Beyond 60-40: The evolving role of hedge funds in institutional investor portfolios
      6. The Cost of Compliance: Global hedge fund survey by AIMA, MFA and KPMG
      7. Capital Markets and Economic Growth: Long-term trends and policy challenges
      8. Apples and Apples: How to better understand hedge fund performance
      9. The Extra Mile: Partnerships between hedge funds and investors
      10. Key articles by AIMA on the case for hedge funds
    3. AIMA Journal
      1. Recent issues
      2. Search AIMA Journal articles
      3. AIMA Journal Archive
    4. AIMA Guides to Sound Practices
    5. AIMA guides for institutional investors
    6. CAIA Association pages
      1. Fundamentals of Alternative Investments
    7. Regulatory Compliance Association pages
      1. About the Regulatory Compliance Association
      2. RCA Curricula and initiatives for alternative investment firms
      3. Meet the regulators and Sr. Fellows
    8. Certified Investment Fund Director programme
    9. Services to Start-up Managers
    10. Glossary
  8. Events
    1. AIMA Events
      1. AIMA Annual Conference
        1. AIMA 25th Anniversary AGM & Annual Conference
      2. AIMA's Global Policy and Regulatory Forum
        1. 2015 Forum - Review
        2. 2015 Forum - Photos
        3. 2015 Forum - Agenda
        4. 2015 Forum - Sponsors and Supporting Organisations
    2. AIMA webinars
    3. Industry events
  9. Media
    1. Press Releases & Statements
    2. AIMA's blog
    3. Media Coverage
      1. Articles by AIMA
        1. Archive
      2. AIMA in the news
      3. Video interviews
      4. Industry news
    4. Media Contacts
    5. Press Materials

Sub Menu

  1. Education
    1. AIMA Journal
    2. Bibliography
    3. CAIA Designation
    4. Research
    5. Roadmap to Hedge Funds
    6. AIMA's Investor Steering Committee Paper
    7. Glossary
  2. Regulatory, Tax, Policy & Government Affairs
    1. AIMA Position Papers
    2. AIMA Responses
      1. Australian Tax Office
      2. Authority for the Financial Markets
      3. Committee of European Banking Supervisors
      4. Committee of European Securities Regulators
      5. Commodity Futures Trading Commission
      6. Dubai Financial Services Authority
      7. European Commission
      8. European Securities and Markets Authority
      9. Swiss Financial Market Supervisory Authority
      10. Financial Services Authority (UK)
      11. Financial Services and the Treasury Bureau
      12. Guernsey Financial Services Commission
      13. HM Revenue & Customs
      14. HM Treasury
      15. Independent Commission on Banking
      16. IOSCO
      17. Monetary Authority of Singapore
      18. Securities and Exchange Board of India
      19. Securities and Exchange Commission (USA)
      20. Securities and Futures Commission
      21. Singapore Exchange
      22. The Takeover Panel
      23. US House of Representatives / Senate
      24. Federal Deposit Insurance Corporation
      25. Financial Stability Oversight Council
      26. Financial Stability Board
      27. US Treasury
      28. Internal Revenue Service
      29. US Federal Reserve
      30. Financial Industry Regulatory Authority (FINRA)
      31. Council of European Union
      32. Hong Kong Exchanges and Clearing
      33. House of Lords
    3. AIMA Summaries
      1. CESR
      2. European Commission
      3. Financial Services Authority (UK)
      4. HM Revenue & Customs
      5. HM Treasury
      6. IOSCO
      7. Securities and Exchanges Commission
      8. FSOC
      9. CFTC
    4. Guidance Notes
    5. Jurisdictional Resource
    6. AIMA Noticeboard
      1. EU Directive on Alternative Investment Fund Managers
      2. FSA Remuneration Code
      3. Short Selling
      4. US Dodd-Frank Wall Street Reform and Consumer Protection Act
      5. UK Stewardship Code
      6. Securities Law Directive
      7. EU Directive on Alternative Investment Fund Managers - Level II
      8. EU Directive on Markets in Financial Instruments (MiFID)
      9. International Financial Centres
      10. Bribery Act
      11. Market Abuse Directive
      12. MF Global
      13. FATCA
      14. FTT
      15. Other Tax Issues
    7. AIMA Regulatory Update
  3. Sound Practices
    1. Due Diligence Questionnaires
    2. Guides to Sound Practices
  4. Start-Up Service Providers
  5. Useful Websites