Abstract
In the previous chapter, we discussed different approaches to forming expectations about future returns of the main asset classes but made only casual reference to the question of risk. In this chapter, we examine the issue of integrating risk and return, that is, optimizing the SAA. The mechanics of standard mean-variance optimization (MVO) are outlined in the Appendix to the book. Here we will focus on some of the challenges when applying MVO, possible remedies and alternative approaches.
“It is better to be approximately right than precisely wrong.”
—Warren Buffet
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- 1.
- 2.
Sample skewness is calculated as \( \frac{n}{\left(n-1\right)\left(n-2\right)}{\sum}_{i=1}^n{\left(\frac{x_i-\overline{x}}{\sigma_s}\right)}^3, \) where n is the number of observations, \( \overline{x} \) is the mean of the sample and σs is the standard deviation of the sample. As n becomes large, this expression can be approximated by \( \frac{1}{n}\kern0.1em {\sum}_{i=1}^n{\left(\frac{x-\overline{x}}{\sigma_s}\right)}^3. \) Excess kurtosis is calculated as \( \frac{n\left(n+1\right)}{\left(n-1\right)\left(n-2\right)\left(n-3\right)}{\sum}_{i=1}^n{\left(\frac{x_i-\overline{x}}{\sigma_s}\right)}^4-3 \) which can be approximated by \( \frac{1}{n}{\sum}_{i=1}^n{\left(\frac{x_i-\overline{x}}{\sigma_s}\right)}^4-3 \) for a large n.
- 3.
Corresponding to a one-sided 99.73% confidence interval.
- 4.
This value can be calculated in Excel by using the NORMSINV function.
- 5.
See also Artzner et al. (1999).
- 6.
See further Rockafellar and Uryasev (2002).
- 7.
We provide an illustration of how weights are calculated using RP in the note at the end of the chapter.
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Lumholdt, H. (2018). Optimizing the Strategic Asset Allocation. In: Strategic and Tactical Asset Allocation. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-89554-3_5
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