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Risk Premia: Exact Solutions vs. Log-Linear Approximations

Vilhelmsson, Anders LU and Lundtofte, Frederik LU (2013) In Journal of Banking & Finance 37(11). p.4256-4264
Abstract
We derive exact expressions for the risk premia for general distributions in a Lucas economy and show that the errors when using log-linear approximations can be economically significant when the shocks are nonnormal. Assuming growth rates are Normal Inverse Gaussian (NIG) and fitting the distribution to the data used in Mehra and Prescott (1985), the coefficient of relative risk aversion required to match the equity premium is more than halved compared to the finding in their article. We also consider a standard long-run risk model and, by comparing our exact solutions to the log-linear approximations, we show that the approximation errors are substantial, especially for high levels of risk aversion.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Log-linear approximations, Equity premium puzzle, Cumulants, NIG distribution, Long-run risk
in
Journal of Banking & Finance
volume
37
issue
11
pages
4256 - 4264
publisher
Elsevier
external identifiers
  • wos:000326212100019
  • scopus:84882802991
ISSN
1872-6372
DOI
10.1016/j.jbankfin.2013.07.035
language
English
LU publication?
yes
id
46e247cb-409e-4043-b01b-333829f73475 (old id 4016671)
date added to LUP
2016-04-01 10:37:55
date last changed
2022-02-17 19:53:47
@article{46e247cb-409e-4043-b01b-333829f73475,
  abstract     = {{We derive exact expressions for the risk premia for general distributions in a Lucas economy and show that the errors when using log-linear approximations can be economically significant when the shocks are nonnormal. Assuming growth rates are Normal Inverse Gaussian (NIG) and fitting the distribution to the data used in Mehra and Prescott (1985), the coefficient of relative risk aversion required to match the equity premium is more than halved compared to the finding in their article. We also consider a standard long-run risk model and, by comparing our exact solutions to the log-linear approximations, we show that the approximation errors are substantial, especially for high levels of risk aversion.}},
  author       = {{Vilhelmsson, Anders and Lundtofte, Frederik}},
  issn         = {{1872-6372}},
  keywords     = {{Log-linear approximations; Equity premium puzzle; Cumulants; NIG distribution; Long-run risk}},
  language     = {{eng}},
  number       = {{11}},
  pages        = {{4256--4264}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Banking & Finance}},
  title        = {{Risk Premia: Exact Solutions vs. Log-Linear Approximations}},
  url          = {{http://dx.doi.org/10.1016/j.jbankfin.2013.07.035}},
  doi          = {{10.1016/j.jbankfin.2013.07.035}},
  volume       = {{37}},
  year         = {{2013}},
}