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
- 24 Optimizing the expected utility over the weights
- 25 Approximations
- Part X Analysis of portfolio allocation
- Appendix I The links with the Black–Litterman approach
- References
- Index
25 - Approximations
from Part IX - Numerical implementation
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
- 24 Optimizing the expected utility over the weights
- 25 Approximations
- Part X Analysis of portfolio allocation
- Appendix I The links with the Black–Litterman approach
- References
- Index
Summary
The purpose of this chapter
The results presented in the previous chapter provide a general, if rather brute-force, solution to the optimization problem which has been set up throughout the book. If some approximations are made, the optimization and the sensitivity analysis described in Chapter 28 can be carried out very efficiently. In particular, we intend to show in this chapter:
how to calculate the weights if we are happy to expand the chosen power utility function to second order;
how to calculate the weights if we are happy to match the first two moments of the true spliced distribution and the first two moments of a multivariate Gaussian;
how to deduce at trivial computational cost the optimal allocation weights once the optimization has been carried out for one particular value of the normalization constant, k.
These approximations are useful in their own rights. However, they also give us the tools to explore deeper questions, namely, why second-order expansions turn out to be so effective. Once we understand why this is the case, it will become apparent that a much simpler approach than the full expected-utility optimization can produce results which are almost as accurate, and far more intuitive, than the ‘full’ solution.
We present the theory behind these approximations in the remainder of the chapter, and we discuss how well they work in the next chapter.
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- Portfolio Management under StressA Bayesian-Net Approach to Coherent Asset Allocation, pp. 384 - 398Publisher: Cambridge University PressPrint publication year: 2014