One thing that you have to keep in mind is that the 20% part is effectively a European call option on the fund's portfolio, with strike equal to the fund's initial value (so ATM - At The Money - when the fund starts) and notional amount of 20% of the fund's value. The manager gets that option for free, in fact he's paid 2% a year to hold that long option (and do his/hers job). Call options are more valuable if the un…
Call options are more valuable if the underlying security is more volatile (because there's higher chance of ending in the money) Whatever the volatility is you still (in Black-Scholes) have a 50/50 of the option ending ITM (stock returns are normally distributed, higher volatility just means higher std. deviation). One reason why ATM options are more valuable with higher volatility is because there's a greater chanc…
And, to nitpick back: the logarithm of stock return is normally distributed under B-S.