Which of the following relationships are true: I. Delta of Put = Delta of Call - 1 II. Vega of Call = Vega of Put III. Gamma of Call = Gamma of Put IV. Theta of Put > Theta of Call Assume dividends are zero.
Correct Answer: A
Explanation All the statements are correct, and represent the relationships between the values of the Greek variables for calls and puts for the same option. It is important to know why as the PRM exam often asks tough questions about the Greeks. Statement I is correct because of the put-call parity. According to the put-call parity, Value of call - Value of put = Spot price - Exercise price discounted to the present Now the delta of the spot is 1, and that of the discounted price is zero. Therefore Delta of Call - Delta of Put = 1 - 0, or by rearranging we get the equation in statement I. Statements II and III are correct as the gamma and vega of both the spot price and the discounted price are zero. Therefore using the put-call parity, we can say Gamma of Call - Gamma of Put = 0 - 0, and Vega of Call - Vega of Put = 0 - 0 Rearranging, we get statements II and III. Statement IV is correct because of the following relationship between theta of call and theta of put: Theta of Put = Theta of Call + rKe^(-rt). Since rKe^(-rt) can only be a positive number, theta of put can only exceed the theta of a call. However, since theta is generally negative, it often implies that the theta of a call is the larger absolute number. Additional explanation for the last point: Assume rKe^(-rt) =+1 and theta of a put is -5 (completely hypothetical) Now Theta of Put = Theta of Call + rKe^(-rt) Ie -5 = -6 + 1 Now -5 is the larger number than -6. In other words, theta of put exceeds that of the call in a pure mathematical sense, which is what I mean when I say "theta of put can only exceed the theta of call". But if you ignore the sign, then theta of call is larger at 6 when compared to 5. Therefore the theta of the put is greater than the theta of the call - which is what the answer says.
Question 2
In the context of futures contracts traded on an exchange, the term 'open interest' refers to:
Correct Answer: C
Explanation Open interest refers to the number of outstanding contracts, which is the same as the number of long positions or short positions held by market participants. Note that since for every long futures contract position held there is a seller who holds the short side, the open interest that is long is identical to the open interest that is short. (This is unlike the spot market where one could have long positions without anyone else needing to be symmetrically short). The total number of contracts traded refers to traded volumes, and not open interest. Other choices are irrelevant in the context.
Question 3
An asset has a volatility of 10% per year. An investment manager chooses to hedge it with another asset that has a volatility of 9% per year and a correlation of 0.9. Calculate the hedge ratio.
Correct Answer: D
Explanation The minimum variance hedge ratio answers the question of how much of the hedge to buy to hedge a given position. It minimizes the combined volatility of the primary and the hedge position. The minimum variance hedge ratio is given by the expression [ (x) / (y) ] * (x,y)]. Effectively, this is the same as the beta of the primary position with respect to the hedge. In this case, the hedge ratio is = 10%/9% * 0.9 = 1
Question 4
Which of the following are considered Credit Events under ISDA definitions? I. Bankruptcy II. Obligation Acceleration III. Obligation Default IV. Restructuring
Correct Answer: B
Explanation According to ISDA, a credit event is an event linked to the deteriorating credit worthiness of an underlying reference entity in a credit derivative. The occurrence of a credit event usually triggers full or partial termination of the transaction and a payment from protection seller to protection buyer. Credit events include - bankruptcy, - failure to pay, - restructuring, - obligation acceleration, - obligation default and - repudiation/moratorium. Therefore all four events listed are credit events and Choice 'b' is the correct answer.
Question 5
Given identical prices, a bond trader prefers dealing with Bank A over Bank B. Given a choice between Bank B and Bank C, he prefers Bank B. Yet, when given a choice between Bank A and Bank C, he prefers dealing with Bank C. What axiom underlying the utility theory is he violating?
Correct Answer: C
Explanation Remember the four basic axioms underlying the principal of maximum expected utility: - Transitivity, ie if A is preferred over B, and B is preferred over C, then A must be preferred over C; - Continuity, ie if A is preferred over B, and B is preferred over C, then B is on a continuum between A and C such that we can be indifferent between receiving B, or a lottery offering either A or C with probabilities p & 1-p respectively. - Independence, ie choices are not affected by the way they are presented - Stochastic dominance, ie a gamble that offers a greater probability of a preferred out come will be preferred. In this case, the first axiom is being violated. Therefore Choice 'c' is the correct answer.