Abstract
Intertemporal equilibrium models of the kind discussed in (Asset pricing, Princeton University Press, Princeton, 2001) have become the standard paradigm in most advanced asset pricing courses. The purpose of this chapter is to explain the relationship between this paradigm and the portfolio theory paradigm common in most of the prior asset pricing literature. We show that these paradigms are merely different ways of looking at the same economic phenomena, and that insights can be gained from each approach.
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Notes
- 1.
Cochrane [2001] along with many economists define return as the growth in value of one dollar invested, or the gross return \(1 + {R}_{i,t+j}\) where R i, t + j is the “net return” or total return (income plus capital gain) in period t + j for security i. This leads to some confusion, as Cochrane uses the symbol R to denote gross return, whereas much of the finance literature uses the same symbol to signify net return. We use the net return convention most commonly employed in the financial economics literature.
- 2.
Note that this system of equations corresponds to the first order conditions \(\mu - {R}_{f} = \Sigma z\) for a maximum value of the Sharpe ratio \(\theta = ({x}^{{\prime}}\mu - {R}_{f})/\sqrt{{x}^{{\prime}} \Sigma x}\), where x is the vector of portfolio weights, Σ is the covariance matrix of returns, and z is proportional to the portfolio weight vector x that maximizes the Sharpe ratio.
- 3.
See for example Gibbons et al. (1989).
References
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Cochrane, J. 2001. Asset pricing, Princeton University Press, Princeton.
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Brown, S.J. (2010). Intertemporal Equilibrium Models, Portfolio Theory and the Capital Asset Pricing Model. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_18
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DOI: https://doi.org/10.1007/978-0-387-77117-5_18
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