# Risk-Free Transactions

# Risk-Free Transactions

Black [1972] considered the case in which there is no risk-free asset. His model differed from the standard CAPM only in that it did not specify the relevant interest rate. This is often called the 'zero-*β*' (or two-factor) CAPM, as it provides the returns expected from a portfolio having a zero-*β* with the market.

Brennan [1971] analysed the situation where risk-free lending and borrowing is available, but at different rates. In this case, there are again two funds spanning all portfolios of risky assets held by individuals:

Equation (5.7) holds for all risky assets and thus for all portfolios composed entirely of risky assets. However, in this case λ, which replaces *r _{f}* in equation (5.5), will lie between the risk-free borrowing and lending rates. The same conclusion would apply if borrowing and lending rates differed amongst individuals.