CFM Derivatives & Hedging Strategies 4 — Questions and Answers
Question 1: A collar strategy on a long stock position is constructed by:
- Buying a call and selling a put at the same strike
- Buying a put and selling a call at a higher strike (Correct answer)
- Selling both a put and a call at the same strike
- Buying both a put and a call at different strikes
Correct answer: Buying a put and selling a call at a higher strike
A collar finances a protective put by selling an OTM call, capping upside while protecting downside at low or zero net cost.
Question 2: Vega measures an option's sensitivity to changes in:
- The underlying asset price
- Time to expiration
- Implied volatility (Correct answer)
- The risk-free rate
Correct answer: Implied volatility
Vega quantifies how much the option price changes for a 1% change in implied volatility.
Question 3: Under the Black-Scholes model, which assumption is most frequently violated in practice?
- Continuous trading is possible
- No dividends are paid during the option's life
- Volatility is constant over the option's life (Correct answer)
- The risk-free rate is known and constant
Correct answer: Volatility is constant over the option's life
In practice, implied volatility changes over time and across strikes (volatility smile/skew), violating the constant-volatility assumption.
Question 4: A fund manager wants to convert a fixed-rate bond portfolio to a synthetic floating-rate exposure without selling the bonds. The best approach is to:
- Buy interest rate caps on the portfolio notional
- Enter a pay-fixed, receive-floating interest rate swap (Correct answer)
- Enter a pay-floating, receive-fixed interest rate swap
- Sell bond futures equal to the portfolio duration
Correct answer: Enter a pay-fixed, receive-floating interest rate swap
By paying fixed and receiving floating in a swap, the manager offsets the fixed coupon income from bonds, creating a net floating-rate exposure.
Question 5: A variance swap pays the difference between realized variance and the swap's strike variance. Compared to a volatility swap, variance swaps are:
- Easier to replicate statically using vanilla options
- More difficult to replicate and have convex payoff relative to volatility (Correct answer)
- Identical in payoff when volatility is low
- Less sensitive to large market moves
Correct answer: More difficult to replicate and have convex payoff relative to volatility
Variance swaps have a convex payoff relative to volatility (since variance = vol²), making them more sensitive to large moves and harder to hedge linearly.
Question 6: The cheapest-to-deliver (CTD) bond in a Treasury futures contract is the bond that:
- Has the highest coupon among eligible bonds
- Maximizes the profit to the short futures position upon delivery (Correct answer)
- Has the longest duration of all eligible bonds
- Is selected by the exchange at random from eligible securities
Correct answer: Maximizes the profit to the short futures position upon delivery
The CTD bond is chosen by the short side to minimize delivery cost, effectively maximizing the profit (or minimizing the loss) on the delivery.
Question 7: A credit default swap (CDS) spread widening indicates that the market perceives the reference entity's credit risk has:
- Decreased, reducing protection cost
- Increased, raising the cost of default protection (Correct answer)
- Remained unchanged but liquidity has improved
- Improved due to a ratings upgrade
Correct answer: Increased, raising the cost of default protection
A wider CDS spread means buyers must pay more for protection, reflecting increased perceived probability of default.
CFM Derivatives & Hedging Strategies 4
A collar strategy on a long stock position is constructed by: