EFF/KRF: The short answer: usually almost nothing. The longer answer depends on the specific investment and what you are trying to measure. Many decades of prior returns, for example, are not enough to make a precise estimate of the expected return on the stock market or of factor risk premiums. (See "Volatility and Premiums.") The answer is similar for investors trying to assess the prospects of a typical hedge fund. Five, 10, or even 20 years is almost certainly too short to say much about the manager’s skill or the fund’s future returns. On the other hand, one can quickly discover whether an index fund is reproducing its target index return because there is a perfect benchmark. Most investments are somewhere between hedge funds and index funds. One can use a benchmark (or asset pricing model) to eliminate some of the noise, but the randomness that remains usually makes it hard to determine whether good returns are the result of luck or skill, even with decades of past returns. (See "Luck versus Skill in Mutual Fund Performance.") This is especially true for active managers since active management almost by definition means low diversification and high volatility of unexpected returns (noise).
Eugene Fama and Ken French are members of the Board of Directors for and provide consulting services to Dimensional Fund Advisors LP.