A note on portfolio selection with restrictions on leverage

This note focuses on a mean–variance asset allocation framework having restrictions on leverage, namely where investors are constrained either to hold funds in a risk-free asset (i.e. to lend) or to hold debt (i.e. to borrow). It is shown that the optimal portfolio in a constrained leverage situation will not have the same composition as the optimal portfolio in an unconstrained situation. We give formal justification for the intuitive notion that the more debt an investor is constrained to hold, the more the investor should tilt the remaining investments towards a portfolio of less risky assets. Conversely, the greater the proportion an investor is constrained to hold in a risk-free asset, the more the investor should tilt remaining investment towards a portfolio of more risky assets.