# Equity Costs Some Conventions on Using the Capm

One of the starkest contrasts in finance is found in comparing the elegance of capital-asset pricing theory with the coarseness of its application. Although the capital-asset pricing model (CAPM) is well understood, the theory says nothing about which risk-free rates, market premia, and betas to use in the model. Possibilities abound, and any sampling of academicians and practitioners will summon up many combinations and permutations of methods. Rather than use all approaches, these notes cling to two:

Short-term risk-free rate and arithmetic market premium: The argument for this approach is that short-term rates are the best proxy for riskless rates: as obligations of the U.S. (or other) government, short-term rates are the closest to being default-risk free. As short-term rates, they suffer little risk of illiquidity or capital loss because of sudden rises in market yields. For the purposes of these notes, “short term” is defined as 90 to 360 days. The corresponding market premium used is the arithmetic average premium estimated over the long term (e.g., 1926 to the date of the case). For the period through 1992, this average was estimated to be 8.6 percent.2 If there is a bias in academia and in practice, it is toward the arithmetic premium, because, when compounded over many periods, an arithmetic mean return is the one that gives the expected value (i.e., mean) of the probability distribution of expected ending values.

Long-term risk-free rate and geometric-mean market premium: Partisans of the long-term risk-free rate argue that most corporate investments are for the long term and that the long rate better matches the term of the asset being valued. According to this view, investors want to earn a market-risk premium equal to the compound rate of return (over time) that the stock market has earned over and above returns on long-term bonds. For the purposes of these notes, “long term” is...

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