Imagine for a moment that you live in a world with only two fund options: a passive managed fund and an actively managed fund with similar levels of volatility. You, the investor, are trying to determine how to structure your two-fund portfolio.
The expected relative return of the active fund is simply a function of two variables - gross alpha expectation and cost. If the resulting net relative performance (gross alpha minus cost) is expected to be positive, the simple choice would be to allocate 100% to the active fund. If, on the other hand, the resulting net alpha of the active fund is expected to be negative, the choice would be equally straightforward - allocate 110% to the passive fund. This approach results in binary choice - either all active or all passive.