A reference portfolio is a portfolio whose weights provide a baseline for constraining, comparing, or interpreting another portfolio. In practical Black–Litterman applications, it is generally the market portfolio, with asset weights proportional to market capitalizations and scaled to a chosen total weight or risk level. section 10.2.2 section 12.1.1
Optimization can limit how far portfolio weights move from the reference. The covariance-weighted variance of the return difference is (w − p)ᵀΣ(w − p); its square root is tracking error. A separate norm1 constraint limits the sum of absolute weight deviations, supporting controlled changes during rebalancing. section 10.2.2 section 10.2.2
Implied returns from a reference portfolio
If p is assumed to maximize expected return minus risk penalty, reverse optimization infers expected returns as μ = λΣp. This makes p the optimal solution without solving an optimization problem. section 12.1.1
constraints.append(cp.quad_form(w - p, Sigma) <= te_bound ** 2)
Inspect a cvxpy constraint that bounds tracking error relative to the reference weights. section 10.2.2
constraints.append(cp.norm1(w - p) <= dev_bound)
Inspect a cvxpy constraint that bounds total absolute deviations from the reference portfolio. section 10.2.2
def compute_equilibrium_ers(weights, sigma, risk_aversion): #1
return risk_aversion * sigma @ weights
Inspect the Python function that computes equilibrium expected returns from reference weights, covariance, and risk aversion. section 12.1.1
