In this paper, it is argued that previous estimates of the UK arithmetic risk premium show a degree of upward bias. Given the importance of the risk premium in regulatory cost of capital in the UK, this has important policy implications. There are three reasons why previous estimates could be upward biased. The first two arise from the comparison of estimates of the realised returns on Government Bond ( Gilt ) to realised returns on equities. These estimates are frequently used to infer a risk premium relative to the current yield on index-linked gilts. This is incorrect on two counts; first, inconsistent estimates of the risk free rate are implied on the right hand side of the CAPM (Jenkinson, 1993); second, they compare realised returns from a bond which carried inflation risk with realised returns from equities which may be expected to have at least some protection from inflation risk. The second source of bias arises from the difference between arithmetic and geometric premia. If markets exhibit excess volatility (Shiller 1981), or if part of the historical return arises because of revisions to expected future cash flows, then estimates of variance derived from historical returns or price growth must be used with great care when uplifting geometric averages to arithmetic averages. Adjusting expected returns for the effect of such biases leads to lower ex ante premia than those that are typically quoted. At current market values, the arithmetic premium ranges between 2% and 4.3%, although the higher estimates require optimistic assumptions concerning growth; the geometric equivalent ranges between 1.5% and 3.3%.
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