Hedge fund managers are typically compensated by deducting management fees from fund assets and receiving incentive bonuses for beating a specified benchmark. This is often referred to as the '2 and 20' structure, where the management fee is usually 2% of the fund's net asset value, and the incentive fee is 20% of the fund's profits above a certain benchmark. The management fee is meant to cover the operational costs of the fund, while the incentive fee aligns the interests of the fund managers with those of the investors, as the managers stand to gain significantly if the fund performs well. This structure is designed to motivate the managers to generate high returns, but it also means that they stand to earn substantial amounts even if the fund's performance is mediocre, as the management fee is charged regardless of the fund's performance.

Choice B is incorrect. While hedge fund managers do often receive a percentage of the gains in asset value, this is typically in addition to a management fee and not deducted from the gains themselves. This compensation structure is known as "two and twenty", where the manager receives a 2% management fee and 20% of any profits.

Choice C is incorrect. Hedge fund managers do not typically buy shares in their own funds at a discount as part of their compensation. While they may invest their own money into the fund to align their interests with those of the investors, this is not considered part of their compensation structure.

Choice D is incorrect. Charging portfolio turnover fees isn't typical for hedge funds' compensation structures. Portfolio turnover fees are more commonly associated with mutual funds, where they are used to cover transaction costs associated with buying and selling securities within the fund's portfolio.