Question about student loans

[DeathDonkey]

I'm just starting grad school and was offered student loans of around $20,000 to cover food/rent/miscellaneous expenses. I declined as I don't need the money, but at the same time I will be eating into savings to live through the school year. I had a genius moment where I thought I could take the loans anyway, invest them in something, and by the time I have to pay them back have made some decent money in interest, returns, or whatever. Where is the hole in my reasoning? I think it has something to do with needing to pay taxes on the loans as if they were income for the year? Will I make money with this plan or am I being shortsighted?

Thanks,
DeathDonkey