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 rf 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.