A portfolio manager generates a 20% rate of return on a "small cap" portfolio, compared to a 15% rate of return on the benchmark portfolio and a 10% rate of return on the Standard and Poor's 500 index over the same period. The passive rate of return on the portfolio is:

15%

Explanation:

A passive portfolio management is an act of running a portfolio to meet the performance  and requirements of a benchmark portfolio.

Given that:

A portfolio manager generates = 20% rate of return

Benchmark portfolio = 15% rate of return

Standard and Poor's 500 index = 10% rate of return.

The passive rate of return  will be 15%. This is because a passive rate of return is attained by putting money into the right index fund, From the information given; the benchmark index has an 15% rate of return. As such,  that is the return any passive investor could attain as a result of putting money in an index fund.