모호성 회피를 고려한 가상자산 편입 로버스트 자산배분 모델: 쿼드라틱 리스크 제약과 SOCP 프레임워크를 중심으로

초록

Incorporating cryptocurrencies into institutional portfolios can amplify estimation error under conventional mean-variance optimization (MVO), often producing corner solutions. This paper proposes a dual-layer robust allocation framework. The first layer models ambiguity aversion by imposing an ellipsoidal uncertainty set on expected returns, while the second layer introduces a quadratic risk contribution constraint that directly limits each asset’s contribution to total portfolio variance. Because the original problem is generally nonconvex, we solve it through a sequential convex approximation procedure that yields a sequence of SOCP subproblems. Using monthly data on seven asset classes, including Bitcoin, from 2016 to 2025, we find that the proposed model achieves a Sharpe ratio of 1.28 and a maximum drawdown of -8.93% over a 60-month out-of-sample period, showing comparatively favorable risk-adjusted performance relative to six benchmark strategies. A notable result is an asymmetric inclusion effect: adding Bitcoin improves risk-adjusted returns within the robust framework (+0.27), but worsens them under traditional MVO (−0.24). These findings suggest that combining ambiguity-aware robust optimization with a quadratic risk constraint may help mitigate estimation error amplification and risk transmission, although the results should be interpreted within the limits of this sample.

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