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Over 700 finance terms, Shmooped to perfection.
In a portfolio which is actively managed (like a mutual fund or a hedge fund but not an index fund or ETF), "active risk" is the risk in the portfolio taken on by the investments (and the analysts and portfolio managers who put together the fund).
See, risk is a fine line. The riskier stocks might explode and help a fund do really well... or they might tank and pull down the fund with them. Good managers balance risk so that the fund doesn't tank but also has a chance to grow. Investment companies usually put together products with different risk levels: higher risk investments for those who like the money equivalent of skydiving and want a shot at big cash and lower risk investments for those who want fewer late nights with antacids because they're worried about their mutual fund.