The CAPM equation is expressed as:

$E(R_i) = R_f + \beta [E(R_m) - R_f]$

Given that the security's expected return equals the market's risk premium, we can deduce:

$E(R_i) = E(R_m) - R_f$

Substituting into the CAPM equation:

$E(R_m) - R_f = R_f + \beta [E(R_m) - R_f] - R_f$

Simplifying:

$E(R_m) - R_f = \beta [E(R_m) - R_f]$

For this equality to hold when the risk-free rate ($R_f$) is positive, the beta ($\beta$) must be less than 1. If beta were equal to or greater than 1, the security's return would exceed the market risk premium, which contradicts the given condition.