IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1501.03768.html
   My bibliography  Save this paper

On the martingale-fair index of return for investment funds

Author

Listed:
  • Leslaw Gajek
  • Marek Kaluszka

Abstract

A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven to be martingale-fair, i.e. be a martingale provided the prices of assets on the financial market form a vector martingale. The problem of merger of the funds is treated in detail.

Suggested Citation

  • Leslaw Gajek & Marek Kaluszka, 2015. "On the martingale-fair index of return for investment funds," Papers 1501.03768, arXiv.org.
    • Handle: RePEc:arx:papers:1501.03768
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1501.03768
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mehta, S.J.B., 1998. "Pension Fund Excellence: Creating Value for Stakeholders. By Keith Ambachtsheer and Don Ezra (Wiley, 1998)," British Actuarial Journal, Cambridge University Press, vol. 4(5), pages 1081-1081, December.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. Fisher, Franklin M. & Shell, Karl, 1972. "The Economic Theory of Price Indices," Elsevier Monographs, Elsevier, edition 1, number 9780122577505 edited by Shell, Karl.
    4. Diewert, W Erwin, 1978. "Superlative Index Numbers and Consistency in Aggregation," Econometrica, Econometric Society, vol. 46(4), pages 883-900, July.
    5. Ogwang, Tomson, 1995. "The stochastic approach to price index numbers: An expository note," Economics Letters, Elsevier, vol. 49(4), pages 373-379, October.
    6. Fisher,Franklin M. & Shell,Karl, 1998. "Economic Analysis of Production Price Indexes," Cambridge Books, Cambridge University Press, number 9780521556231, June.
    7. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    8. Dumagan, Jesus C., 2002. "Comparing the superlative Tornqvist and Fisher ideal indexes," Economics Letters, Elsevier, vol. 76(2), pages 251-258, July.
    9. Brad Barber & Reuven Lehavy & Maureen McNichols & Brett Trueman, 2001. "Can Investors Profit from the Prophets? Security Analyst Recommendations and Stock Returns," Journal of Finance, American Finance Association, vol. 56(2), pages 531-563, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jacek Białek, 2011. "Remarks about the generalizations of the Fisher index," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 12(1), pages 139-156, August.
    2. Leonard I. Nakamura, 2010. "Intangible Assets And National Income Accounting," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(s1), pages 135-155, June.
    3. Jesus C. Dumagan, 2009. "Comparing GDP in Constant and in Chained Prices : Some New Results," Macroeconomics Working Papers 22633, East Asian Bureau of Economic Research.
    4. J. C. Dumagan & V. E. Ball, 2009. "Decomposing growth in revenues and costs into price, quantity and total factor productivity contributions," Applied Economics, Taylor & Francis Journals, vol. 41(23), pages 2943-2953.
    5. Jesus C. Dumagan, 2008. "Avoiding Anomalies of GDP in Constant Prices by Conversion to Chained Prices," Macroeconomics Working Papers 22632, East Asian Bureau of Economic Research.
    6. Sutirtha Bandyopadhyay & Bharat Ramaswami, 2022. "The representative agent bias in cost of living indices," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 155-178, January.
    7. William A. Barnett, 2003. "Aggregation-Theoretic Monetary Aggregation over the Euro Area, when Countries are Heterogeneous," Macroeconomics 0309018, University Library of Munich, Germany.
    8. W. Erwin Diewert, 1995. "Price and Volume Measures in the System of National Accounts," NBER Working Papers 5103, National Bureau of Economic Research, Inc.
    9. Jesus C. Dumagan, 2008. "Implementing US GDP in Chained Prices for Cross-country GDP Growth and Sectoral Comparisons : Application to Selected ASEAN Countries," Macroeconomics Working Papers 22631, East Asian Bureau of Economic Research.
    10. Keinsley, Andrew, 2025. "Measuring the monetary services of US treasury securities," Economic Modelling, Elsevier, vol. 143(C).
    11. Marshall Reinsdorf & Jack E. Triplett, 2009. "A Review of Reviews: Ninety Years of Professional Thinking About the Consumer Price Index," NBER Chapters, in: Price Index Concepts and Measurement, pages 17-83, National Bureau of Economic Research, Inc.
    12. Andreas Benedictow & Pål Boug, 2017. "Calculating the real return on a sovereign wealth fund," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(2), pages 571-594, May.
    13. Dumagan, Jesus C., 2011. "Implementing Weights for Additivity of Chained Volume Measures in the National Accounts," Discussion Papers DP 2011-09, Philippine Institute for Development Studies.
    14. Leonard I. Nakamura, 2009. "Intangible assets and national income accounting: measuring a scientific revolution," Working Papers 09-11, Federal Reserve Bank of Philadelphia.
    15. Managi, Shunsuke & Opaluch, James J. & Jin, Di & Grigalunas, Thomas A., 2006. "Stochastic frontier analysis of total factor productivity in the offshore oil and gas industry," Ecological Economics, Elsevier, vol. 60(1), pages 204-215, November.
    16. Dariusz Cezary Kotlewski, 2023. "The soundness of returning to manufacturing through the lens of productivity accounting," Ekonomista, Polskie Towarzystwo Ekonomiczne, issue 3, pages 253-274.
    17. Ivancic, Lorraine & Erwin Diewert, W. & Fox, Kevin J., 2011. "Scanner data, time aggregation and the construction of price indexes," Journal of Econometrics, Elsevier, vol. 161(1), pages 24-35, March.
    18. William A. Barnett & Milka Kirova & Meenakshi Pasupathy & Piyu Yue, 1996. "Estimating Policy-Invariant Technology and Taste Parameters in the Financial Sector, When Risk and Growth Matter," Macroeconomics 9602002, University Library of Munich, Germany.
    19. Ryan S. Mattson & Philippe de Peretti, 2014. "Investigating the Role of Real Divisia Money in Persistence-Robust Econometric Models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00984827, HAL.
    20. Deb Kusum Das, 2003. "Manufacturing productivity under varying trade regmies: India in the 1980s and 1990s," Indian Council for Research on International Economic Relations, New Delhi Working Papers 107, Indian Council for Research on International Economic Relations, New Delhi, India.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1501.03768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.