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
- Part VII Working with the full distribution
- Part VIII A framework for choice
- Part IX Numerical implementation
- Part X Analysis of portfolio allocation
- 26 The full allocation procedure: a case study
- 27 Numerical analysis
- 28 Stability analysis
- 29 How to use Bayesian nets: our recommended approach
- Appendix I The links with the Black–Litterman approach
- References
- Index
27 - Numerical analysis
from Part X - Analysis of portfolio allocation
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
- Part VII Working with the full distribution
- Part VIII A framework for choice
- Part IX Numerical implementation
- Part X Analysis of portfolio allocation
- 26 The full allocation procedure: a case study
- 27 Numerical analysis
- 28 Stability analysis
- 29 How to use Bayesian nets: our recommended approach
- Appendix I The links with the Black–Litterman approach
- References
- Index
Summary
In this chapter we review in detail the quality of the various numerical approximations we have introduced in Part IV of the book. As we shall see, the good news is that they tend to be surprisingly successful, and can therefore greatly lighten the computational burden of the optimization. They will also suggest an approach to asset allocation using Bayesian nets which is not only computationally lighter, but also intuitively more appealing.
We begin by looking at the quality of the mean-variance approximation.
How good is the mean-variance approximation?
In this section we are trying to ascertain how accurate the mean-variance Gaussian approximation presented in Sections 25.2 and 25.3 actually is, once the moments of the full distribution obtained by the Bayesian net are matched.
The answer is apparent from Figure 27.2, which shows the allocations as a function of (1 – k) obtained using the Gaussian approximation. This figure can be compared with the allocations obtained using the full Monte-Carlo optimization and the logarithmic utility function, shown again in Figure 27.1 for ease of comparison.
The similarity between the two sets of optimal weights is remarkable, and is shown even more clearly in Figure 27.3, which displays the allocations as a function of (1 – k) for the the three methods. Again, it is apparent that the Gaussian approximation, once the moments are matched, is extremely accurate.
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- Portfolio Management under StressA Bayesian-Net Approach to Coherent Asset Allocation, pp. 425 - 433Publisher: Cambridge University PressPrint publication year: 2014