What specific kind of financial investing would give the greatest return based on a $2,500,000 investment? Stocks, bonds, mutual fund, etc?

If there were, why would anyone invest anywhere else?

If anyone tells you that they can get you 8% a year (or 5% or whatever) guaranteed or even pretty guaranteed, they're almost certainly lying to you. The stock market has historically averaged more than that. But it's wildly volatile, and cannot be counted on to get you that much in any given year or set of consecutive years. In fact it can lose you money year after year for a long time. If I was suddenly given $2.5 million, I would sock it away in a low fee mutual fund that tracks a broad stock market index such as the S&P 500. I would then withdraw no more that 4% of it out in any given year, and probably less. That should allow it to be a fairly safe -- not sure -- bet for perpetual income.

If you have 2.5 million bucks and this is the question you're asking, you need a reputable independent (likely fee-based) investment adviser to help figure out a strategy that makes sense for you. You'll need to figure out what levels of risk you're comfortable with, when you'll need access to the money, tax implications of different investment strategies, what kind of liquidity you need, etc... This is what an adviser helps you plan for. Your question focuses on return, but completely negates the risk side of the equation, which is phenomenally important. There is no zero-risk way to get a guaranteed 8% return, especially when your timespan and liquidity needs are undefined. If there were, everyone would pour all their money into said investment in a flash. The higher the return, the greater the risk and/or the lower the liquidity. That's why US Treasuries pay such little returns and why two-person garage startups make their investors filthy rich if they hit the big-time.

And by the way, if you go the "index tracking fund and forget about it" route, don't bother with some fancy-schmancey investment firm like Merrill Lynch or whatever. They exist only to slowly drain your money from you, and in the long run the advice they give isn't remotely likely to be particularly good. Just sign up for an online account at Vanguard.com, pick a low fee fund that tracks the S&P or whatever, transfer money into it, and forget about it. Maybe, for example, https://personal.vanguard.com/us/funds/snapshot?FundId=0540&FundIntExt=INT.

The kind that has professional advice, and possibly professional management. Fee-based professionals. On a 'what would tmotat do' basis ... Admiral shares from Vanguard, go with trying to match the market with a big, big chunk ( >80%) and use the rest for speculation.

Statistically? As with stories, the answer is all about when you end your time frame. The answer for 100 years will be different than the answer for 10 years or 5.

8% over time? Equities - maybe possibly. 8% year in year out, into perpetuity? No.

5% on a long-term horizon is very very reasonable. You can get that with a mix of equities and cash, but it will also be a function of how much liquidity you need.

It sounds like you are wanting to invest for income and to use this fund as a sort of money machine to turn out a fairly predictable income stream year after year. This is different from investing for growth (which long term could achieve 8%) or investing for wealth preservation. A good financial advisor will probably steer most investments toward dividend yielding stocks and bonds and target a 4 to 5% return annually. Really good advisors will spend time to really understand your goals and how much you need to earn to live and tell you if you your goal is a stretch.