Free PRMIA 8006 Practice Exam with Questions & Answers

A cash or nothing call is one that pays a fixed amount if the underlying exceeds a certain threshold, or nothing. An asset or nothing call is the same as the cash or nothing call except that instead of paying a fixed amount, it 'pays' the asset. Therefore the payoff profile of a long asset or nothing call has the same payoff as a long cash or nothing call and a long vanilla call.

This is best considered by building payoff diagrams which will show how the two positions are economically equivalent. Choice 'd' is the correct answer, and the rest are not.

This is a straightforward bond valuation problem where all variables required are known. The coupon payments will be $1.50 in 6 months and 1 year from now, and a final paymento of $101.50 will be received in an year's time. This can be discounted at the yield provided as follows, and summed together to get the bond price.

Bootstrapping is not one of the various approaches to try to value a convertible security. The rest of them are, and therefore Choice 'b' is the correct answer.

The investor's needs to sell futures contracts, as his current position is long. He needs to sell ($1,000,000 x (2.5-1)) / ($240,000 x 1.2) = 5.2 contracts, or rounded to 5 contracts.

It is important to note here that the investor wishes to retain a beta of 1, and does not want to get rid of all market exposure.

Generally, it is not a good idea to exercise an option early as any more upside in the remaining period to expiry is being sacrificed. However, if an extraordinarily large dividend is coming due, and this dividend is larger than the interest foregone from holding the option, it may be a good idea to exercise the option early. In such cases, the exercise needs to happen before the ex-dividend date and not afterwards. Choice 'b' is therefore the correct answer.

Even if the option is deep in the money and delta is approaching 1, and exercise upon maturity is almost a certainty, it would still always be better to sell the option than exercise it . Therefore Choice 'a' is incorrect. Choice 'c' is correct in all cases except when a large dividend is coming in. Choice 'd' is not correct because an early exercise needs to happen prior to the ex-dividend date and not afterwards.

A fixed for floating interest rate swap is identical to a series of forward rate agreements coinciding with the settlement periods. For example, a 2 year fixed for floating interest rate swap where the investor pays fixed at 6 monthly rests is equivalent to a long position in 3 FRAs ( a 6 x12, a 12 x 18 and an 18 x 24 FRA). Thus I represents a correct replication of the swap.

An obligation to pay fixed is identical to a short position in a fixed rate bond, and receiving the floating rate is akin to a long position in a floating rate note. Thus II also correctly replicates the swap.

A long position in an FRN correctly replicates the floating cash flow from the swap, but a short position in the FRA obliges the investor to receive fixed and pay floating - which is not equivalent to the flows from the interest rate swap. Thus III is not a correct replication of the interest.

A long position in a cap means the investor will receive the difference between the floating and the cap rate if the floating rate is greater than the cap rate. Effectively, the investor will receive floating. A short postion in a floor at the same strike rate would mean the investor would end up paying the floor rate, effectively equivalent to the obligation to pay a fixed rate. Therefore this replication also correctly replicates the swap, and IV can also be used to replicate the investor's position.

Therefore Choice 'a' is the correct answer and the rest are incorrect.

(For statement IV, let me explain with an example. Recall that the buyer of a cap receives the difference between the current interest rate and the agreed exercise rate if the current interest rate goes above the exercise rate. A cap can be used by a floating rate borrower to limit their exposure to a rise in interest rates. In the same way, the seller of a floor pays the buyer the difference between the current interest rate and the exercise rate if the current interest rate falls below the exercise rate. A floor can be used by a lender to protect against a fall in interest rates.

Now assume the exercise rate is r. Also assume that the current floating interest rate is r'. the holder of the interest rate swap in the example in the question receives r and pays r'. Therefore the net payout is r' - r (pays fixed, ie -r, and receives floating, ie +r).

Now consider the long position in the cap and the short position in the floor.

Case 1: If r > r', the following will happen:

a. The long position in the cap will pay nothing, ie 0.

b. The short position in the floor will require a payment of r - r' to the buyer of the floor, and because it is a payment, the cash flow will be -(r - r') = r' - r

Case 2: If r < r', the following will happen:

a. The long position in the cap will mean the investor receives r' - r.

b. The short position in the floor will pay nothing as the interest rate is higher than the exercise rate.

In both cases, the net cash flow for the investor is r' - r, which is the same as for the swap where the investor pays fixed and receives floating.)

The buyer of the FRA gets to borrow $100m at 10% per annum for 6 months at the end of 6 months from the contract date. Thus, the interest due is $100m * 10% * 6/12 = $5m. However, at the end of the 6 months (when the notional borrowing period begins), the spot rate is 12%. The interest due on a borrowing at the spot rate would be $100m * 12% * 6/12 = $6m. Since the buyer gets to borrow cheaper than the going rate, he or she has made a gain of $1m on the FRA. However, this amount is not due immediately, it is due at the end of the 6 month borrowing period (ie, 12 months from the date the contract was entered into). The seller of the FRA can make the buyer whole by paying the buyer the present value of $1m due in 6 months time, which is $1m/(1 + 12%*6/12) = $1m/1.06 = $943,396.

Thus, Choice 'd' is the correct answer. Remember that the FRA gets settled at the beginning of the notional borrowing period as all future cash flows, and the applicable discount rates are known with certainty. The buyer and the seller do not need to wait for the entire period to get over first. The cash settlement allows the buyer to borrow at the market rate and still have the same net borrowing cost as he or she had initially contracted for in the FRA.

The duration of a perpetuity is 1/running yield. Therefore the correct answer is 1/.05 = 20 years

Explanation:

In an American option, early exercise of the option is permitted. In a European option, early exercise is not permitted. Therefore Choice 'b' is the correct answer.

Explanation:

Straddles and strangles are strategies that would benefit from sharp movement in option prices, regardless of direction. These comprise a long call and a long put, which would benefit regardless of whether prices rise or fall. The only time they would lose money would be when prices stay constant.

A collar would gain when stock prices fall, and not when they rise. Since our investor does not have a view on the direction of the movement, this strategy will not work for him.

A butterfly spread or a condor would gain when prices stay range-bound, so that cannot be a useful strategy.

Therefore Choice 'd' is the correct answer.