Financial leverage increases an investment position beyond the investor’s own capital by borrowing funds or scaling portfolio weights above 100%. It can raise expected return, but it also introduces borrowing costs, margin restrictions, collateral risk, and possible forced sales. section 11.3.1 section 2.4
Scaling a risk-parity portfolio
A risk-parity portfolio with 4.7% volatility can be scaled to match a 60/40 portfolio’s 10.3% volatility. Scaling its weights above 100% is leverage; achieving that exposure requires borrowing, and the scaled portfolio has an expected return of 4.36%. section 11.3.1
Leverage requires balancing exposure against financing and liquidation risks:
- Purchase securities on margin, using the purchased assets as collateral. section 11.3.1
- Account for borrowing rates, typically described as 2%–3% above the current risk-free rate. section 11.3.1
- Expect brokerage limits, cash-deposit requirements, or forced sales when portfolio values fall sufficiently. section 11.3.1
- Choose leverage according to the desired risk and return trade-off; no single amount is universally correct. section 11.3.1
w_rp_scaled = w_rp * 10.3 / 4.7
Scales risk-parity weights by the ratio between target volatility and unlevered volatility. section 11.3.1
w_rp_scaled @ mu
Calculates the expected return of the scaled portfolio from its adjusted weights and expected asset returns. section 11.3.1
