What trading restrictions/rules are there for IRAs? The only universal restriction is tied to IRS rules that do not allow borrowing from an IRA account.
This restriction blocks short selling, leverage using margin, and the sale of naked put or call options. Brokerage firms vary in what they allow, but generally, you can trade all stocks and exchange-traded products (ETFs & ETNs) including leveraged (SSO), inverse (e.g., SH), and volatility funds (e.g., VXX, SVXY, ZIV).
Some trades such as options, leveraged/inverse funds, volatility funds, or futures will likely require extra paperwork/qualification.