Jason Lemkin, the co-founder of EchoSign, has written a thoughtful piece about seed investing.
In it, he calculates that if you do 30 seed investments at $25K each (roughly the lower bound for a diversified portfolio), you'd need $750K in capital. (Even this is an underestimate, since it leaves out the need for follow-on investments)
In order for your $750K portfolio to represent a sane proportion of your wealth you'd need a net worth well into the tens of millions.
But it's worse than that--If you put that $750K into a fund instead of investing it yourself, you’d pay 2% a year for 10 years, plus 20% of the profits (I’m going to ignore hurdle rates for now to simplify the analysis). If the fund performed well and delivered a 3X return over that period, there would be $2.25 million in profit; 20% of that is $450,000. Meanwhile the management fees would come to $750K X 2% X 10 years, or $150,000. Overall then, you’d have paid your fund $600K, or $60K/year.
Essentially, a DIY seed investor deploying $750K is paying him or herself $60K/year to make investments. Does that sound like a good annual income for that much hard work?
To put it in perspective, that's roughly what a court reporter makes for typing in transcripts.