The Synergic Entropy. An efficient frontier output derived from merged input units boosted by synergy and constrained by critical input - Henrique De Carvalho Videira (Financial Markets, Institutions and Risks)
The theory equates the maximum output deviations (efficient frontier) caused by combined inputs with affinity-synergy in a system, which leads to a parametric volatility whose curve can be compared to data envelopment analysis (DEA). The input is a cumulative variable (e.g.: merged assets), and the output is a flow variable (e.g.: combined incomes). Rather than being purely stochastic, volatility is estimated by a novel parameter for risk named synergy, which is constrained by critical input (scarce resources). The output acceleration derived from the mergers among inputs, boosted by synergy, is the main foundation of the approach, which particular case gives Shannon and Boltzmann-Gibbs entropies. Tests are done in the 11 USA Sectors over their quarterly financial statements, proving that synergy is significant for financial statements, whereas typical betas only present significance in stock market data. A practical application is a novel discount rate for valuation using synergy, whose results for each sector are stable and coherent with perceived risk. Systems that rely on causal relations between output and multiple inputs can be regressed under novel parameters, rather than reckoning exclusively in optimization procedures.