Risk Management and Derivatives
Risk Management and Derivatives tests hedging rationale, derivative payoffs, and risk measures. Expect forwards, futures, options, swaps, duration, value at risk, and the distinction between market, credit, and liquidity risk.
Core rules
- A forward locks a price and carries counterparty credit risk; a futures contract is standardized, marked to market daily, and cleared, which reduces counterparty risk but introduces margin calls.
- Option payoffs: call payoff at expiry = max(S - K, 0); put payoff = max(K - S, 0). The buyer pays a premium; the maximum loss is the premium. Breakeven for a call is K + premium, for a put K - premium.
- A swap exchanges cash flows; an interest rate swap can convert fixed-rate debt to floating and changes duration exposure.
- Duration measures price sensitivity to yield: percentage price change ≈ -modified duration × yield change. Convexity improves the estimate for large moves.
- VaR estimates a loss threshold over a horizon at a confidence level; it says nothing about the size of losses beyond the threshold.
Worked example
A portfolio is worth 10 million with modified duration 5.0. If yields rise 50 basis points, the estimated price change is -5.0 × 0.005 = -2.5%, or a loss of 250,000. To hedge, the manager can short futures with the right DV01. If each futures contract has a DV01 of 50, the number of contracts is 10,000,000 × 5.0 × 0.0001 / 50 = 100 contracts. The hedge reduces, but does not eliminate, risk because of basis and convexity differences.
Traps
- Notional principal is not market value or exposure; a large notional can carry small market risk.
- Hedging with a correlated but non-identical instrument leaves basis risk.
- Time value erodes option positions even when the underlying moves favorably.
- VaR is not a worst-case loss; stress testing and expected shortfall cover tail risk.
- Speculative use of derivatives should be separated from hedging intent in risk disclosures.