What is KVA (Capital Valuation Adjustment), and how does the cost of holding regulatory capital affect derivatives pricing?

KVA (Capital Valuation Adjustment) represents the cost of holding regulatory capital against a derivatives position over its lifetime. Unlike CVA (which reflects expected credit losses) or FVA (which reflects funding costs), KVA reflects the opportunity cost of equity capital that regulators require banks to set aside.\n\nThe Economic Logic:\n\nRegulatory capital (CET1 equity) is expensive -- shareholders demand returns of 10-15%. When a derivative trade consumes regulatory capital (through CVA capital charges, SA-CCR exposure, or market risk RWA), the bank must compensate shareholders for that locked-up equity.\n\nKVA = Integral from 0 to T of [(r_equity - r_f) x RC(t) x DF(t) dt]\n\nWhere:\n- r_equity = required return on equity (e.g., 12%)\n- r_f = risk-free rate\n- RC(t) = regulatory capital consumed at time t\n- DF(t) = discount factor\n\nWorked Example:\n\nBrookfield Securities executes a 5-year interest rate swap with Dalton Manufacturing ($500M notional). The trade consumes regulatory capital through multiple channels:\n\n| Capital Channel | Year 1 RC | Year 3 RC | Year 5 RC |\n|---|---|---|---|\n| CVA capital (SA-CVA) | $4.2M | $3.8M | $1.5M |\n| Counterparty credit (SA-CCR) | $2.1M | $1.9M | $0.8M |\n| Market risk (FRTB) | $0.5M | $0.5M | $0.5M |\n| Total RC | $6.8M | $6.2M | $2.8M |\n\nHurdle rate: 12%, Risk-free rate: 4.5%, Capital spread: 7.5%\n\nAnnual KVA contributions:\n- Year 1: 0.075 x $6.8M x 0.957 = $488,070\n- Year 3: 0.075 x $6.2M x 0.875 = $406,875\n- Year 5: 0.075 x $2.8M x 0.800 = $168,000\n\nTotal KVA (interpolated across all periods): approximately $1.85 million\n\nIs KVA a True Valuation Adjustment?\n\nThis is actively debated:\n\n| View | Rationale |\n|---|---|\n| Yes, it's a valuation adjustment | If the trade doesn't earn enough to cover capital costs, it destroys shareholder value. KVA makes this explicit. |\n| No, it's a profitability metric | Capital costs are firm-specific, not market-observable. Two banks with different capital structures would calculate different KVAs for the same trade. |\n| Pragmatic middle | KVA belongs in the hurdle rate or P&L attribution, not in fair value reported to accountants. |\n\nMost dealers include KVA in their internal pricing but exclude it from accounting fair value. KVA functions as a minimum profitability threshold: if a trade's margin doesn't cover KVA plus other XVAs, the trade is rejected.\n\nStudy KVA frameworks in our FRM Part II course.