Question

Suppose that a fund manager runs an active fund with an expected return of 12% and standard deviation of 30%. Given the performance metrics of the passive index, expected return = 9,24% and standard deviation = 17.24%, what is the maximum percentage fee the active fund manager could charge so that investors would be indifferent between investing in the active fund and investing in the passive index? Does the fee the manager can charge depend on investors’ level of risk aversion?

Answer 1

Risk adjusted return places main role in funds having different standard deviations.

Here active fund is providing better returns with more standard deviation. By taking risk free rate as 6.35%. Risk adjusted return(sharp ratio) for active fund is 18% and passive fund is 16%.

By taking the fact active funds trades more often than passive fund and managed by professional fund managers it is better to invest in active fund and to offset the return of both funds passive funds managers should charge 1.125x times active fund managers

Yes, fee charged by managers depends on the risk aversion of rhe investors. More risk means more returns and managers which provide extra returns charge, fund fee/management fee and incentive fee of 20% for over and above returns than the mentioned returns earlier.