assumer wrote:It seems to me that a rational thing to maximize in a portfolio is the Sharpe ratio (mean divided by standard deviation)

The Sharpe ratio is not the mean (return) divided by the standard deviation (of returns); the numerator is the mean return

minus the risk-free rate. Maximizing the Sharpe ratio is one approach to deciding the asset mix in one's portfolio, but it is not the only one. A lot depends on the risk aversion of the investor.

assumer wrote:Let us assume that Investment A has a higher Sharpe ratio than Investment B but a lower mean [return]. I've heard it state that "leverage" can bring up the mean, or somehow normalize this. In my understanding leverage is simply borrowing to invest.

Yes, by borrowing (at a rate less than the return on your investment) you can increase the overall return.

assumer wrote:My questions are:

1. How does the interest rate on the borrowed money affect the Sharpe ratio?

If you can borrow at the risk-free rate, the Sharpe ratio of the leveraged portfolio will be the same as the Sharpe ratio of the unleveraged portfolio. If, in the more likely case, the rate at which you can borrow is higher than the risk-free rate, the Sharpe ratio of the leveraged portfolio will be lower than the Sharpe ratio of the unleveraged portfolio.

assumer wrote:2. How do/could institutional investors (e.g. hedge funds, pensions) employ leverage?

They can do it by borrowing money (e.g., buying on margin), or by using various derivative securities (e.g., futures or forwards).

assumer wrote:3. How do/could retail investors (e.g. average Joe and Jane) employ leverage?

Buying on margin or entering into futures contracts would probably be the simplest way.

Note: that isn't intended as an endorsement of these investments.

Simplify the complicated side; don't complify the simplicated side.