Ms. [Ivy Zelman], 41 years old, says she has turned down several opportunities because her position as an equity analyst wouldn’t allow her to pursue them. A private-equity fund asked her to be an adviser and equity investor in a land fund and a private home builder asked her to sit on its board, she says. “As the down market continues, more people are asking for my advice,” she adds. “I want to capitalize on what I’ve built.”