What determines the frequency domain properties of a stochastic process? How much risk comes from high frequencies, business cycle frequencies or low frequency swings? If these properties are under the influence of an agent, who is compensated by a principal according to the distribution of risk across frequencies, then the nature of this contracting problem will affect the spectral properties of the endogenous outcome. We imagine two thought experiments: in the first, the principal is myopic with regard to certain frequencies – his understanding of the true process is intermediated through a filter – and the agent chooses to hide risk by shifting power from frequencies to which the regulator is attuned to those to which he is not. Thus, the regulator is fooled into thinking there has been an overall reduction in risk when, in fact, there has simply been a frequency shift. In the second thought experiment, the regulator is not myopic, but simply cares more about risk from certain frequencies, perhaps due to the preferences of the constituents he represents or because certain types of market incompleteness make certain frequencies of risk more damaging. We model this intuition by positing a filter design problem for the agent and also by a particular type of portfolio selection problem, in which the agent chooses among investment projects with different spectral properties. While abstract, these models suggest important implications for macroprudential policy and regulatory arbitrage.
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