2013年9月23日月曜日

Roll's critique

http://en.wikipedia.org/wiki/Roll%27s_critique

Epstein-Zin(1991)JPE
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The nominal return on the optimal portfolio is measured with the value-weighted index of shares traded on the New York Stock Exchange. A number of issues arise from the use of this measure, but the primary concern for our purposes is whether it is sufficiently broad to capture the relevant part of actual holdings of wealth; that is, Roll's (1977) critique of CAPM is relevant here. If stochastic wages are a large factor in the wealth constraint of the typical agent, then, as discussed in Section II, the return on the optimal portfolio of the agent should reflect the shadow return of the agent's human capital. Rather than attempt a lengthy analysis of this issue at this time, we shall simply assume that factors that may not be properly measured by the value- weighted index of stock returns do not affect the empirical analysis in an appreciable way. The appropriateness of this assumption, vis-a-vis the empirical results below, remains an open question.
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Campbell(1996)JPE
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In response to the Roll (1977) critique, I extend the Campbell (1993) model to allow for human capital as a component of wealth. I impute the return on human capital from data on aggregate labor income and asset returns. Finally, I develop an econometric frame- work in which the model can be confronted with historical data.

The asset pricing model developed in Section II is empirically testable only if one can measure the return on the market portfolio. Financial economists commonly proxy the market portfolio by a value-weighted index of common stocks, but this practice is questionable. Even if the stock index return captures the return on financial wealth, as argued by Stambaugh (1982), it may not capture the return on human wealth. Approximately two-thirds of gross national product goes to labor and only one-third to capital, so human wealth is likely to be about two-thirds of total wealth and twice financial wealth. This suggests that the omission of human wealth may be a serious matter.

Increases in expected future labor income cause a positive return on human capital, but increases in expected future asset returns cause a negative return on human capital because the labor income stream is now discounted at a higher rate and is therefore worth less today.
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