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# Optimization is about ranges rather than exact numbers

Updated: Jul 19, 2018

In business, we are always looking for optimization allowing us to save costs and boost margins. Optimization is often easy to find on paper but, harder to find in real applications. During the design phase we leave in a 2D world where the x independent variable can be moved in order to optimize the dependent variable y. That is rarely what happens in real life where the number of variables affecting the system is much higher. We are also optimistic about the accuracy of our estimates and we apply normal probability distribution even when we do not have a clue of the real distribution (we rarely do it on purpose relying on the central limit theorem).

When we apply quantitative indicators like the Net Present Value to calculate the expected return of the business initiative, the focus should be on the parameters rather than on the model. The correct estimate of the parameters and their dispersion would often show that initial higher investments on redundancy would result in higher final NPV.

A very practical example pointed out in The Black Swan and Antifragile by Nassim Taleb: consider 3 standard deviations in a normal distribution (the standard deviation is considered to be a representation of dispersion of outcomes and risk), in theory you are including about 99.8% of possible outcomes, a pretty solid margin. Consider now a mere 5% error in the estimate of the standard deviation and it results in about 60% to 40% error in the outlier probability (the error depends on the SD being 5% higher or lower). That is in part why we are often discussing failed private equity companies, loans unexpectedly not repaid, investment portfolios not yielding the expected return and so on.

It is not optimal to be close to the limit if we do not really know where that limit is. Being quantitative also means knowing the dispersion of numbers and it requires ranges rather than exact numbers.

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