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

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86 Optimizing Optimization


Sophisticated quantitative analysis has the capacity to assist investors in
formulating and implementing appropriate investment strategies. The invest-
ment industry has concentrated on providing solutions for private investors
with finite investment horizons and liability management strategies for pen-
sion funds. In our analysis, we have highlighted characteristics of permanent
endowments that require a different approach to reconciling the balance
between risk and return. In particular, the requirement for intergenerational
equity can be expressed in the technical terms of Utility and we have demon-
strated that there can be a counterintuitive relationship between risk aversion
and expected future investment return.
Our conclusion is that the trustees of Foundations that intend to endure
in perpetuity require a formal expression of Utility that adequately captures
both risk aversion (theta) and subjective discounting of consumption over time
(delta) to determine a sustainable rate of consumption from the endowment.


3.8 Bespoke optimization — putting theory into practice


At BITA Risk, we see a whole range of tailored requests; the following sections
describe two examples. All have been successfully implemented using the range
of BITA Risk optimizers.


3.8.1 Request: produce optimal portfolio with exactly

50 long and 50 short holdings

Starting from a stock universe of several hundred stocks, the request was to
produce optimal mixes of stocks with exactly 50 long and exactly 50 short
positions. Clearly, this requires a heuristic approach since the analytical solu-
tion would be infeasible given the computational cost. Our solution was to
construct a hybrid methodology of two phases:


(i) On an iterative basis starting with the full candidate stock universe, eliminate a per-
centage of stocks on the basis of their lowest weight in the preceding optimal port-
folio, until the 50 long, 50 short constraint is first violated, i.e., the first step with
less than or equal to 50 stocks, both long and short.
(ii) Select and reinsert stocks individually on the basis of the highest marginal utility
until the exactly 50 long, exactly 50 short constraint is satisfied.


3.8.2 Request: how to optimize in the absence of forecast returns

A client required a long – short mix of stocks selected on the basis of absolute
betas rather than forecast returns, which were not available. In the absence
of forecast returns, it is obviously not possible to form a traditional efficient
frontier. However, the client could provide measures of beta, measured against
the market, for each stock. These absolute betas were used as a constraint in

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