Many portfolio construction tasks in quantitative finance can be formulated as convex cone programs, notably linear programs (LP), second-order cone programs (SOCP), and semidefinite programs (SDP). In parallel, a line of work in quantum algorithms treats convex optimization-especially SDP-through multiplicative weights (MW) updates that implicitly form normalized matrix exponentials, i.e., Gibbs states. Recent developments show that SOCP structure can be exploited so that the Gibbs objects needed by MW decompose into direct sums of low-rank pieces, with algorithmic consequences for both quantum and classical ("quantum-inspired") models. This paper presents a self-contained mathematical bridge from: (i) cone programming formulations of core portfolio problems (mean-variance, risk budgeting, CVaR, robust and quasi-convex Sharpe-ratio constructions), to (ii) MW-style feasibility solvers on symmetric cones with explicit Jordan-algebraic structure, to (iii) the SOCP-specific "arrowhead" matrix representation of Lorentz cones and its implications for Gibbs-state preparation, and finally to (iv) a rigorous application-focused analysis of what these ideas do and do not imply for practical finance workloads (conditioning, data access, and discrete constraints such as cardinality). We provide complete proofs of all key results, explicit complexity bounds, and detailed algorithmic specifications suitable for implementation.