Before revision:  Holding the Sharpe ratio constant, higher  volatility leads to superior returns through lower costs . For funds replicating benchmark multiples, such as leveraged ETFs, we identify the strategies that optimally trade off alpha against tracking error, and find that they depend on the target multiple and the benchmark's liquidity, but not its volatility .
After revision:  Holding the Sharpe ratio constant, higher volatility leads to superior returns through lower costs .