Yep. Depending on how the study is conducted, you can make the fund managers look very, very, bad indeed.
The thing is, if the fund managers were very good at stock picking, they would still sometimes lose to the monkey, but most of the time an average fund manager will beat the monkey. However, he won't beat it by much. He'll beat it consistently by one or two percent The thing is, if you give him your money to invest, he will keep three percent of your money. You do the math. Monkey chow is cheaper.
Something like that happens with CEOs too. I worked for a company that hired a "celebrity CEO". The company was Hughes Aircraft and the CEO was C. Michael Armstrong. This guy was good. How do we know? Because he had done fantastic things while he was at some other company. (Lucent, I think.) Yet, somehow, when he was getting a zillion dollars per year to run our company, we nearly collapsed, and ultimately ended up being purchased by Raytheon. (And in this case, I can even point to specific very bad decisions he made that caused the collapse.) C. Mike ended up going to AT&T, which also did very, very, badly under his guidance.
The fact is that he had gotten lucky at Lucent. I'm sure he was a fine manager and all that, but he wasn't a superstar. I'm of the opinion that there really are no general purpose superstar CEOs. I don't think the ability to run one company well necessarily translates to running some other company. I'm also of the opinion that one guy at the top has limited powers to make a company perform well. If he is surrounded by idiots, the company won't do well. If he is surrounded by geniuses, he probably won't be able to ruin the company. However, if everything comes together just right, he can look like he's a genius, and get hired by some other company who thinks that the superstar can save them from whatever bad situation they are in.