Book contents
- Frontmatter
- Dedication
- Contents
- List of figures
- List of tables
- Acknowledgements
- Part I Our approach in its context
- Part II Dealing with extreme events
- Part III Diversification and subjective views
- Part IV How we deal with exceptional events
- Part V Building Bayesian nets in practice
- Part VI Dealing with normal-times returns
- 17 Identification of the body of the distribution
- 18 Constructing the marginals
- 19 Choosing and fitting the copula
- Part VII Working with the full distribution
- Part VIII A framework for choice
- Part IX Numerical implementation
- Part X Analysis of portfolio allocation
- Appendix I The links with the Black–Litterman approach
- References
- Index
19 - Choosing and fitting the copula
from Part VI - Dealing with normal-times returns
Published online by Cambridge University Press: 18 December 2013
- Frontmatter
- Dedication
- Contents
- List of figures
- List of tables
- Acknowledgements
- Part I Our approach in its context
- Part II Dealing with extreme events
- Part III Diversification and subjective views
- Part IV How we deal with exceptional events
- Part V Building Bayesian nets in practice
- Part VI Dealing with normal-times returns
- 17 Identification of the body of the distribution
- 18 Constructing the marginals
- 19 Choosing and fitting the copula
- Part VII Working with the full distribution
- Part VIII A framework for choice
- Part IX Numerical implementation
- Part X Analysis of portfolio allocation
- Appendix I The links with the Black–Litterman approach
- References
- Index
Summary
The purpose of this chapter
The procedure described in Chapter 18 produces univariate marginal distributions for each risk factor. These marginals may well display fatter tails than Gaussians, but nonetheless refer to non-extreme market conditions. The next step to characterize the normal-times joint distribution is to conjoin them using a copula. We are going to choose a copula that provides an acceptable fit to the data. We are aware that estimating the marginal distributions first, and then the copula, is statistically sub-optimal, as a joint maximum-likelihood would in general give a different solution. We justify our two-step approach by pointing to the computational advantages and the conceptually ‘neat’ decomposition afforded by this standard decomposition of the estimation problem. As we shall see, this two-step procedure will also greatly facilitate the construction of the spliced distribution – see Chapter 20, Section 20.5 in particular.
If for each risk factor the normal-times portion of the data can be satisfactorily described by a Gaussian distribution and if all the risk factors can be joined by a Gaussian copula, we shall see that important computational savings can be achieved (because a simple closed-form expression can be obtained in some cases by linking the distribution of portfolio returns and the weights of the individual sub-portfolios). If this is not the case, the procedure described in the following can still be applied, but the final numerical search becomes somewhat more burdensome. Conceptually, however, nothing changes.
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- Portfolio Management under StressA Bayesian-Net Approach to Coherent Asset Allocation, pp. 278 - 290Publisher: Cambridge University PressPrint publication year: 2014