We develop a toy model of completely rational and informed agents which are
bounded “by law” to use investment strategies from a simple set as a set of strategies of
constant debt to invested capital ratio or constant leverage (ratio of invested capital to
difference invested one and debt (own capital), means constant debt to invested capital ratio).
Economic agent is able to set any leverage he should follow during all the game.
So we get Nash equilibrium where every economic agent is able to predict all the
trajectory of all parameters after he understands the rational strategies of all other partners.
We show that if credit leverage high enough oscillations appear due to price
equilibrium destabilization.
We show that in real market under certain natural conditions there is only one source
of bounding leverage that connected with impossibility of fast contraction of invested capital
finally bonded by depreciation rate of physical capital (at leverage more than 1 at low return
physical capital rate investor may need to disinvest faster to hold his leverage constant). After physical capital IRR got
negative valleys at certain leverage bankruptcy is unavoidable.
Before that own capital IRR linearly depends on leverage & the maximum of this
curve is best response of economic agent & at corresponding Nash equillibrium we obtain equilibrium volatility or
oscillation amplitude at real market.