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To reduce the beta of an equity portfolio from 1.5 to 0.7 using S&P 500 futures, a portfolio manager should take a short position in index futures.

A trader buys a call and a put on the same stock with the same strike price ($50) and expiration. The call premium is $3 and the put premium is $2.50. This strategy is called a:

CDS Valuation and Default ProbabilityA 5-year CDS on a corporate bond has a spread of 180 basis points. The assumed recovery rate is 45%.(a) Estimate the implied annual default probability.(b) If the notional is $20 million, calculate the quarterly premium payment (assuming the annual premium is split into equal quarterly installments).(c) If the reference entity defaults when the bond is worth 45% of par, what payment does the protection buyer receive on a $20 million notional?

An investor entered a long forward contract to buy a non-dividend-paying stock at $55 nine months ago. The stock now trades at $62, and the risk-free rate is 4% (continuously compounded). The contract has 3 months remaining. The value of the forward to the long position is closest to:

A trader simultaneously enters a long forward and a short forward on the same asset with the same delivery date but with different counterparties. This strategy is:

Equity Beta HedgingA fund manager holds a $40 million portfolio with β = 1.3. The manager wants to temporarily reduce the portfolio beta to 0.5 using S&P 500 futures. The current S&P 500 futures price is 4,800 and the multiplier is $250.(a) Calculate the number of contracts and state whether the manager should go long or short.(b) If the S&P 500 subsequently falls by 3%, estimate the approximate change in the hedged portfolio’s value.

An airline uses crude oil futures to cross-hedge its jet fuel purchases. The optimal hedge ratio is 0.78. Which of the following explains why the optimal hedge ratio is less than 1.0?

A European call on a non-dividend-paying stock is priced at $9. The stock price is $65, K = $60, r = 4% (continuously compounded), and T = 1 year. According to put-call parity, the European put price should be:

A trader is long 3 natural gas futures contracts (each for 10,000 MMBtu) at $3.50/MMBtu. The initial margin is $4,000 per contract and the maintenance margin is $3,000 per contract. After two days of trading, the settlement prices are Day 1: $3.44, Day 2: $3.38. What is the trader’s margin account status at the end of Day 2 (before any margin call action)?

Implied volatility is the value of σ that, when substituted into the Black-Scholes formula, produces a model price equal to the observed market price of the option.