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# Finance Dictionary - J Terms

# Johnson Hedge Model

Developed within the framework of modern portfolio theory. The Johnson hedge model (Johnson, 1960) retains the traditional objective of risk minimization but defines risk as the variance of return on a two-asset hedge portfolio. As in the two-parameter world of Markowitz’s (1959), the hedger is assumed to be infinitely risk averse (that is, the investor desires zero variance). Moreover, with portfolio optimization, the risk-minimization objective defined as the variance of return on the combined spot and futures position, the Johnson hedge ratio is expressed in terms of expectations of variance and covariances for price changes in the spot and futures markets. The Johnson hedge model can be expressed in regression from as: DSt ¼ a þ HDFt þ et, where DSt ¼ change in the spot price at time t; DFt ¼ change in the futures price at time t; a ¼ constant; H ¼ hedge ratio; and et ¼ residual term at time t.