# The applicability of the risk-free rate proxy in South Africa : a zero-beta approach.

## Date

2009

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## Abstract

## Description

Thesis (M.Comm.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.

The Capital Asset Pricing Model (CAPM), despite criticism and debate regarding its validity, remains the most widely employed model to estimate the cost of equity for use in capital budgeting decisions, both in the U.S. and in South Africa. The risk-free rate specified in the model is generally estimated with the use of a government security, but there is some concern as to the appropriateness of this practice in the South African market. An alternative approach was derived by Black (1972), known as the minimum-variance zero-beta portfolio returns; but the suitability of this parameter in the South African market has not yet been examined. The objective of this study therefore is to determine the best method to estimate the risk-free rate for applications of the CAPM in South Africa. A set of theoretical requirements that an asset must closely satisfy to be considered a suitable proxy for the risk-free rate are derived, with the most commonly employed proxies being compared to these criteria to ascertain their appropriateness. The zero-beta portfolio returns are computed, in conjunction with the rate that investors have historically viewed as the minimum required return, denoted by the intercept of the CAPM. Hypothesis tests of the equality of the two estimates of the risk-free rate and the minimum required return are conducted, as well as a comparison of the forecasting accuracy of the model using the different risk-free rate values. The results of the analysis indicate that the South African proxies diverge substantially from the criteria, and are likely to overstate the true-risk-free rate. In complete contrast to this, the hypothesis tests reveal that the proxies understate the intercept estimate, whilst the zero-beta portfolio returns closely approximate this value. This finding that the zero-beta portfolio returns, which are larger than the proxy yields, are more suitable appears counter-intuitive given the goal to identify the minimum return from investing. This result can possibly be explained by the fact that the CAPM intercept represents the average of the riskless lending and borrowing rates, whilst the proxy only denotes the former. The borrowing rate is likely to be higher than the lending rate; thus giving reason for the average being greater. However, the possibility also remains that the results observed may be a consequence of the incorrect specification of the market portfolio, that the tests employed are inapt, or that the model itself is inappropriate. The forecasting analysis confirms the greater accuracy associated with employing the zero-beta portfolio returns as the risk-free rate compared to the use of a proxy, but the improvement is small. Thus the choice for the practitioner is whether the increase in accuracy is justified by the difficulty and time involved with estimating the zero-beta portfolio returns.

The Capital Asset Pricing Model (CAPM), despite criticism and debate regarding its validity, remains the most widely employed model to estimate the cost of equity for use in capital budgeting decisions, both in the U.S. and in South Africa. The risk-free rate specified in the model is generally estimated with the use of a government security, but there is some concern as to the appropriateness of this practice in the South African market. An alternative approach was derived by Black (1972), known as the minimum-variance zero-beta portfolio returns; but the suitability of this parameter in the South African market has not yet been examined. The objective of this study therefore is to determine the best method to estimate the risk-free rate for applications of the CAPM in South Africa. A set of theoretical requirements that an asset must closely satisfy to be considered a suitable proxy for the risk-free rate are derived, with the most commonly employed proxies being compared to these criteria to ascertain their appropriateness. The zero-beta portfolio returns are computed, in conjunction with the rate that investors have historically viewed as the minimum required return, denoted by the intercept of the CAPM. Hypothesis tests of the equality of the two estimates of the risk-free rate and the minimum required return are conducted, as well as a comparison of the forecasting accuracy of the model using the different risk-free rate values. The results of the analysis indicate that the South African proxies diverge substantially from the criteria, and are likely to overstate the true-risk-free rate. In complete contrast to this, the hypothesis tests reveal that the proxies understate the intercept estimate, whilst the zero-beta portfolio returns closely approximate this value. This finding that the zero-beta portfolio returns, which are larger than the proxy yields, are more suitable appears counter-intuitive given the goal to identify the minimum return from investing. This result can possibly be explained by the fact that the CAPM intercept represents the average of the riskless lending and borrowing rates, whilst the proxy only denotes the former. The borrowing rate is likely to be higher than the lending rate; thus giving reason for the average being greater. However, the possibility also remains that the results observed may be a consequence of the incorrect specification of the market portfolio, that the tests employed are inapt, or that the model itself is inappropriate. The forecasting analysis confirms the greater accuracy associated with employing the zero-beta portfolio returns as the risk-free rate compared to the use of a proxy, but the improvement is small. Thus the choice for the practitioner is whether the increase in accuracy is justified by the difficulty and time involved with estimating the zero-beta portfolio returns.

## Keywords

Capital assets pricing model., Capital budget., Theses--Economics.