Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

Novel approaches to portfolio construction 51

Indeed , one can do all of these steps manually without the aid of tools and
concepts developed in this section. The resulting enterprise, however, will be
tedious, vulnerable to trial and error, and most importantly deprive the PM
from exploiting the latest developments in computing technology. By system-
atically automating various steps in this procedure and augmenting them with
specifically tailored proprietary algorithms, we shoulder the computational
burden of a PM thereby allowing him or her to focus exclusively on his or her
central goal — portfolio design and analysis.

2.4 Conclusions

This chapter has presented several new methods for approaching portfolio con-
struction. The high-level conclusions are the following:

1. The addition of a second risk model can lead to better performance than using one
   risk model alone when the second risk model constraint is calibrated so that both
   risk model constraints are simultaneously binding. In many cases, a good calibration
   tightens the second risk model constraint until the primary risk model constraint
   just remains binding. Calibration of the other portfolio construction parameters is
   essential. In particular, since the region over which both risk models are binding
   can be narrow, guessing what value to use (for X and Y in our examples) can lead
   to only one risk model being binding for the optimal solution, even when both risk
   models are comparable. The other constraints in the portfolio construction strategy
   can greatly influence the region over which both risk models are binding.


2. Rebalancing a portfolio is a complex activity that goes beyond solving an optimiza-
   tion problem. It entails a systematic attempt by the PM to understand the impact of
   constraints on the choice of the optimal portfolio, to evaluate the effect of changing
   one or more constraint bounds, and to gain insights in the resulting trade-offs. The
   concept of constraint elasticity gives a natural ordering of constraints to examine

Table 2.9 Portfolio P3

Summary statistic Value

Expected return 0.2733%

Transfer coefficient 0.6643

Implied beta 1.0094

Tracking error 1.84%

Tax liability $3,616.29

Turnover 13.00%

Realized short-term gains $11,687.70

Realized short-term losses $13,594.12

Net realized short-term gains/losses ($1,906.41)

Realized long-term gains $42,114.52

Realized long-term losses $16,099.53

Net realized long-term gains/losses $26,014.99