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on Risk Management |
| By: | Alejandro Balbas; Pedro Jimenez-Guerra |
| Abstract: | The paper introduces a new notion of vector-valued risk function. Both deviations and expectation bounded coherent risk measures are defined and analyzed. The relationships with both scalar and vector risk functions of previous literature are discussed, and it is pointed out that this new approach seems to appropriately integrate several preceding point of view. The framework of the study is the general setting of Banach lattices and Bochner integrable vector-valued random variables. Sub-gradient linked representation theorems, as well as portfolio choice problems, are also addressed, and general optimization methods are presented. Finally, practical examples are provided. |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wbrepe:wb066721&r=rmg |
| By: | Hanno Lustig; Stijn Van Nieuwerburgh |
| Abstract: | To explain the low-frequency variation in US equity and debt returns in the 20th century, we solve an equilibrium model in which households face housing collateral constraints. An increase in the ratio of housing to human wealth loosens these borrowing constraintsthus allowing for more risk sharing. The rate of return that households require for holding equity decreases as a result. Feeding the historical time series of US housing collateral into the model replicates four features of long-run asset returns. (1) It produces a fifteen percent equity premium during the 1930s and a slow decline of the equity premium from eleven percent in the 1960s to four percent in 2003. (2) It generates large unexpected capital gains for equity holders, especially in the 1990s. (3) The risk-free rate and the housing collateral ratio are strongly positively correlated at low frequencies. (4) The model mimics the slow decline in the volatility of stock returns and the riskless interest rate. |
| JEL: | G12 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:12766&r=rmg |