Skip to main content

A Diversification Measure for Portfolios of Risky Assets

  • Chapter
Advances in Financial Risk Management

Abstract

The benefits of diversification are well known and indeed diversification is frequently applied in real-life portfolio optimization. The first proof of portfolio diversification is given by Markowitz (1952). In his seminal paper, Markowitz provides a normative basis of portfolio choice which has led to modern portfolio theory. The mean-variance framework has become standard knowledge in finance theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bera, A. K. and Park, S. Y. (2008). Optimal portfolio diversification using maximum entropy. Econometric Reviews, 27(4–6): 484–512.

    Article  Google Scholar 

  • Best, M. J. and Grauer, R. R. (1991). On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results. The Review of Financial Studies, 4(2): 315–42.

    Article  Google Scholar 

  • Black, F. and Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48: 28–43.

    Article  Google Scholar 

  • Bouchaud, J.-P., Potters, M., and Aguilar, J.-P. (1997). Missing information and asset allocation. http://econpapers.repec.org/RePEc:sfi:sfiwpa:500045.

  • Chopra, V. K. and Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. The Journal of Portfolio Management, 19(2): 6–11.

    Article  Google Scholar 

  • DeMiguel, V., Garlappi, L., Nogales, F. J., and Uppal, R. (2009a). A generalized approach to portfolio optimization: improving performance by constraining portfolio norms. Management Science, 55(5): 798–12.

    Article  Google Scholar 

  • DeMiguel, V., Garlappi, L., and Uppal, R. (2009b). Optimal versus naive diversification: how inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22(5): 1915–53.

    Article  Google Scholar 

  • Evans, J. L. and Archer, S. H. (1968). Diversification and the reduction of dispersion: an empirical analysis. The Journal of Finance, 23(5): 761–7.

    Google Scholar 

  • Fisher, L. and Lorie, J. H. (1970). Some studies of variability of returns on investments in common stocks. The Journal of Business. 43(2): 99–134.

    Article  Google Scholar 

  • Fletcher, J. (2011). Do optimal diversification strategies outperform the 1/N strategy in U.K. stock returns? International Review of Financial Analysis. 20: 375–85.

    Article  Google Scholar 

  • Frahm, G. (2011). The determinants of the risk functions of estimators for expected asset returns. Technical report, University of Cologne.

    Google Scholar 

  • Frahm, G. (2012). Capital allocation under risk and uncertainty. Technical report, Helmut Schmidt University.

    Google Scholar 

  • Frahm, G. and Memmel, C. (2010). Dominating estimators for minimum-variance portfolios. Journal of Econometrics, 159: 289–302.

    Article  Google Scholar 

  • Frahm, G., Wickern, T., and Wiechers, C. (2011). Multiple tests for the performance of different investment strategies. Advances in Statistical Analysis, 96: 343–83.

    Article  Google Scholar 

  • Jagannathan, R. and Ma, T. (2003). Risk reduction in large portfolios: why imposing the wrong constraints helps. The Journal of Finance, 58(4): 1651–84.

    Article  Google Scholar 

  • Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis, 21(3): 279–92.

    Article  Google Scholar 

  • Klein, R. W. and Bawa, V. S. (1976). The effect of estimation risk on optimal portfolio choice. Journal of Financial Econometrics, 3: 215–31.

    Article  Google Scholar 

  • Ledoit, O. and Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5): 603–21.

    Article  Google Scholar 

  • Lintner, J. (1965). The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, 47(1): 13–37.

    Article  Google Scholar 

  • Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7(1): 77–91.

    Google Scholar 

  • Memmel, C. (2004). Schï£itzrisiken in der Portfoliotheorie. PhD thesis, University of Cologne.

    Google Scholar 

  • Meucci, A. (2009). Managing diversification. Risk, 22(5): 74–9.

    Google Scholar 

  • Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4): 768–83.

    Article  Google Scholar 

  • Muirhead, R. J. (1982). Aspects of Multivariate Analysis. Wiley Series in Probability and Mathematical Statistics, New York.

    Google Scholar 

  • Pafka, S. and Kondor, I. (2003). Noisy covariance matrices and portfolio optimization II. Physica A, 319: 487–94.

    Article  Google Scholar 

  • Partovi, M. H. and Caputo, M. (2004). Principal portfolios: recasting the efficient frontier. Economics Bulletin, 7(3): 1–10.

    Google Scholar 

  • Rudin, A. M. and Morgan, J. S. (2006). A portfolio diversification index. The Journal of Portfolio Management, 32(2): 81–9.

    Article  Google Scholar 

  • Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1): 119–38.

    Article  Google Scholar 

  • Woerheide, W. and Persson, D. (1993). An index of portfolio diversification. Financial Services Review, 2: 73–85.

    Article  Google Scholar 

  • Zhang, S. (1998). Fourteen homogeneity of variance tests: when and how to use them. Anual Meeting of the American Educational Research Association (San Diego, CA, April 13–17).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Copyright information

© 2013 Gabriel Frahm and Christof Wiechers

About this chapter

Cite this chapter

Frahm, G., Wiechers, C. (2013). A Diversification Measure for Portfolios of Risky Assets. In: Batten, J.A., MacKay, P., Wagner, N. (eds) Advances in Financial Risk Management. Palgrave Macmillan, London. https://doi.org/10.1057/9781137025098_13

Download citation

Publish with us

Policies and ethics