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.