Kerry E. Back
- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190241148
- eISBN:
- 9780190241179
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190241148.003.0005
- Subject:
- Economics and Finance, Financial Economics
The mean‐variance frontier is characterized with and without a risk‐free asset. The global minimum variance portfolio and tangency portfolio are defined, and two‐fund spanning is explained. The ...
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The mean‐variance frontier is characterized with and without a risk‐free asset. The global minimum variance portfolio and tangency portfolio are defined, and two‐fund spanning is explained. The frontier is characterized in terms of the return defined from the SDF that is in the span of the assets. This is related to the Hansen‐Jagannathan bound. There is an SDF that is an affine function of a return if and only if the return is on the mean‐variance frontier. Separating distributions are defined and shown to imply two‐fund separation and mean‐variance efficiency of the market portfolio.Less
The mean‐variance frontier is characterized with and without a risk‐free asset. The global minimum variance portfolio and tangency portfolio are defined, and two‐fund spanning is explained. The frontier is characterized in terms of the return defined from the SDF that is in the span of the assets. This is related to the Hansen‐Jagannathan bound. There is an SDF that is an affine function of a return if and only if the return is on the mean‐variance frontier. Separating distributions are defined and shown to imply two‐fund separation and mean‐variance efficiency of the market portfolio.
Kerry E. Back
- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190241148
- eISBN:
- 9780190241179
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190241148.003.0014
- Subject:
- Economics and Finance, Financial Economics
The Euler equation is defined. The static approach can be used to derive an optimal portfolio in a complete market and when the investment opportunity set is constant. In the latter case, the optimal ...
More
The Euler equation is defined. The static approach can be used to derive an optimal portfolio in a complete market and when the investment opportunity set is constant. In the latter case, the optimal portfolio is proportional to the growth‐optimal portfolio and two‐fund separation holds. Dynamic programming and the Hamilton‐Jacobi‐Bellman equation are explained. An optimal portfolio consists of myopic and hedging demands. The envelope condition is explained. CRRA utility implies a CRRA value function. The CCAPM and ICAPM are derived.Less
The Euler equation is defined. The static approach can be used to derive an optimal portfolio in a complete market and when the investment opportunity set is constant. In the latter case, the optimal portfolio is proportional to the growth‐optimal portfolio and two‐fund separation holds. Dynamic programming and the Hamilton‐Jacobi‐Bellman equation are explained. An optimal portfolio consists of myopic and hedging demands. The envelope condition is explained. CRRA utility implies a CRRA value function. The CCAPM and ICAPM are derived.
Kerry E. Back
- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780190241148
- eISBN:
- 9780190241179
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190241148.003.0004
- Subject:
- Economics and Finance, Financial Economics
Pareto optima and competitive equilibria are defined. Allocations are functions of market wealth (sharing rules) in Pareto optima, which means that all risks except market wealth are perfectly ...
More
Pareto optima and competitive equilibria are defined. Allocations are functions of market wealth (sharing rules) in Pareto optima, which means that all risks except market wealth are perfectly shared. Equilibria in complete markets are shown to be equivalent to Arrow‐Debreu equilibria and to be Pareto optimal. If investors all have linear risk tolerance with the same cautiousness parameter, then equilibria are Pareto optimal, equilibrium prices are independent of the initial wealth allocation (Gorman aggregation), and two‐fund separation holds (all investors hold the risk‐free asset and the market portfolio).Less
Pareto optima and competitive equilibria are defined. Allocations are functions of market wealth (sharing rules) in Pareto optima, which means that all risks except market wealth are perfectly shared. Equilibria in complete markets are shown to be equivalent to Arrow‐Debreu equilibria and to be Pareto optimal. If investors all have linear risk tolerance with the same cautiousness parameter, then equilibria are Pareto optimal, equilibrium prices are independent of the initial wealth allocation (Gorman aggregation), and two‐fund separation holds (all investors hold the risk‐free asset and the market portfolio).
