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A study of total beta specification through symmetric regression: the case of the Johannesburg Stock Exchange


A topic of recent interest is risk management in equity investments from emerging markets. One traditional measure for systematic risk of an asset is beta, which is constructed through ordinary least squares (OLS) regression between historical returns on an individual asset and an index representing the overall market. OLS regression assumes all the error lies within the asset returns. Tofallis (Eur J Oper Res 187(3):1358–1367, 2008) made the case for constructing a systematic risk measure through symmetric regression, where error is assumed to be present in the returns of both the asset and the index. In this paper, we construct a systematic risk measure using symmetric regression for the case of the Johannesburg Stock Exchange (JSE). This paper makes the case that the so-called ‘total beta’ parameter provides a more realistic and stable estimator for market-related risk and return. The total beta estimate, explicitly allowing for error in both variables, is less likely to underestimate the magnitude of the beta parameter.

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  1. 1.

    In single-index model, such as the CAPM model, the idiosyncratic portion of firms’ returns are independent across firms. The diagonality assumption in a single-index model is that the errors between firms are not correlated.

  2. 2.

    While we have chosen the JSE in order to illustrate our work, this work is easily replicable for dichotomous markets such as the Australian and Canadian markets.

  3. 3.

    Tofallis (2015) shows analytical methods to obtain the regression coefficients exactly. Due to the timing of this paper, we followed Draper and Yang (1997).

  4. 4.

    We used the same measure as Francis (1979) as mentioned in Tofallis (2008).

  5. 5.

    It should be noted that consecutive periods in longer time frame scenario have more data in common that consecutive periods in a shorter time frame scenario.

  6. 6.

    The specification of the structural break points of the financial crisis in South Africa are reflective of tests, the results of which were forwarded in a private communication.


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This work is based on the research supported in part by the National Research Foundation (NRF) of South Africa for the Grant No. 93649. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors, and the NRF does not accept any liability in this regard. Additional funding was provided by the NWU-DST-ABSA Risk Research Initiative.

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Correspondence to Kanshukan Rajaratnam.


Appendix A

Table 4 Overall beta estimates

Appendix B

Table 5 Pre-crisis beta estimates

Appendix C

Table 6 Crisis beta estimates

Appendix D

Table 7 Post-crisis beta estimates

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Laird-Smith, J., Meyer, K. & Rajaratnam, K. A study of total beta specification through symmetric regression: the case of the Johannesburg Stock Exchange. Environ Syst Decis 36, 114–125 (2016).

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  • CAPM
  • APT
  • JSE
  • Beta
  • Systematic risk
  • Reduced major axis regression