19 Pages Posted: 28 Oct 2004 Last revised: 10 Jun 2016
Date Written: October 14, 2004
The cost of equity is required (besides various other basic data) for many financial applications such as capital budgeting decisions and performance measurements. A common procedure is to use the Capital Asset Pricing Model (CAPM), which involves estimation of an expected risk premium equal to beta times the expected risk premium on the 'market' portfolio, the portfolio containing all assets in the world. Since the market portfolio is not observable a proxy must be used. Typically beta is estimated using a particular index and another (arbitrary) estimate is chosen for the expected market risk premium. The estimates for beta and the expected market risk premium are then multiplied together. It is obvious that this procedure more than likely yields a biased estimate for the cost of equity. So far, the author agrees fully with what has been extensively described by Jan Bartholdy and Paula Peare in their paper entitled 'Estimating Cost of Equity', re http://ssrn.com/abstract=252270. Note: indeed estimating, the cost of equity cannot be calculated perfectly in each and every detail. What has been argued by Bartholdy and Peare cannot be allowed to pass without comment. They rightly criticise CAPM and their observation is correct, it is indeed surprising that CAPM is so widely used in the way it is. The very heart of the author's criticism relates to the discrete interest rates that are in use both within CAPM and by the two step procedure suggested by Bartholdy and Peare. The reasoning is simple: a discrete 'rate' is not a rate. Consequently, most if not all calculations making (risk-)additions to discrete rates do not fit. Outcomes from such artificial calculations are virtually worthless, notably if and when precise answers are necessary. CAPM is proven not valid. Initially, a given risk free discrete interest 'rate' must be translated into the corresponding continuous interest rate, in order to preserve sensible follow-up calculations.
Beta-values that are provided by commercial beta-providers are the input into dubious numerations and consequently the CAPM-outcome, the officially presented risk included 'rate'-figure, is artificial. The end outcomes are spurious. One has only to push the e-key on any simple pocket-calculator to defeat the entire financial community that is clinging to old traditions. Who is afraid of the e-power? Busy with all kinds of financial tools. Neither effective (not doing right things) nor efficient (not doing things right). Using PPR (Period Percentage Rate, any period, any rate) i.e. Discrete Compound Interest to rank investments is often deceptive. Financial tools - like the old CAPM - using PPR are dangerous since they lead to misallocation of funds and biased performance measures. It all can be done both finally and easily, as is demonstrated in this paper.
The paper is organized as follows. Section 1 discusses basic notions, followed by a close inspection of the central CAPM-problem in section 2. The solution i.e. the new CAPM relationship representing 'the state of the art' is the main subject of section 3. An exemplary problem in illustration is given in section 4. Finally, section 5 concludes.
Keywords: CAPM, Cost of Equity, Beta-values, Risk factors, Simple Interest, Discrete Compound Interest, Continuous Compound Interest
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