What type of risk could theoretically be eliminated completely by buying a portfolio of shares...

Specific risk, also called unsystematic or diversifiable risk, is the risk associated with individual companies or industries. It includes risks such as poor management decisions, product failures, labour disruptions, litigation, or company-specific earnings weakness. By holding a broadly diversified portfolio such as all stocks in the S & P/TSX Composite Index, an investor can theoretically diversify away company-specific risk because negative events affecting one company may be offset by performance from others. Systematic risk cannot be eliminated through diversification because it affects the whole market, such as interest rate changes, recessions, inflation shocks, or broad market declines. Default risk is more directly associated with credit instruments. Therefore, the risk theoretically eliminated through broad equity diversification is specific risk.