PRMIA 8006 Exam Questions

The key point in this question is that the bond is zero coupon, and can only be called at face value. Since the bond is zero coupon, its value will always be less than its par value at any time during its existence (as any interest rate will be a positive number). Therefore the issuer will never exercise the call. Thus the bond will have a duration equal to what an equivalent non-callable bond would have.

Since zero coupon bonds have a duration equal to their maturity, the bond's duration is 10 years.

An m x n FRA is an agreement to borrow money for a period starting at time m and ending at time n at the contracted rate. Therefore, the buyer of the 3 x 6 FRA has committed to borrow $1m at the beginning of 3 months and return it at the end of 6 months, ie a total borrowing period of 3 months at a rate of 5%. Of course, the $1m is never actually exchanged, and at the beginning of the 3 month period when the next three months' interest rate is known (6%), the parties merely exchange the difference in the interest. SInce this interest was only due at the end of the 6 months and is being exchanged at the 3 month time point, it will have to be discounted to its present value.

The correct answer to this question is =(1,000,000 * (6% - 5%) * 3/12)/(1 + (6%*3/12))=$2463.05. Since interest rates rose, the borrower gained as he has the right to borrow at a lower rate, and therefore the seller will pay the borrower.

(Here:

- $1m is the notional

- 6% - 5% represents the difference between the contracted and the realized interest rates

- 3/12 is the 3 month period from month 3 to 6

- Finally, we divide by the current interest rate for 3 months to present value the payment from month 6 to month 3)

Given covered interest parity, the currency with a lower interest rate will trade at a forward premium. Choice 'b' is the correct answer.

For an intuitive reasoning, consider a currency forward contract that matures in 3 months. The seller has agreed to sell, say JPY 1,000,000 in exchange for USD 10,000 in the future. In order to cover himself, he borrows the USD right now and converts it to JPY at spot which he puts in a JPY deposit. Assuming JPY interest rates are less than USD interest rates, he pays more on his USD borrowing than he receives on his JPY deposit. Therefore he has to price the forward contract at a premium to spot to cover the interest rate differential.

The correct answer is the index value times the contract size, in this case 1500 x 50.

One way to think about index futures is this: Consider equity index trading as trading in the shares of a company whose share price is equal to a number of dollars which is the same as the index. If the 'contract multiplier' for a index futures contract is 50, that means the futures contract is for 50 shares of such a fictitious company. Therefore the notional value of the contract will be 15000 x 50, and Choice 'a' is the correct answer.

Futures contracts carry no gamma. Only options have gamma. Choice 'a' is the correct answer. Any instrument whose price varies in a linear fashion with respect to the underlying will have gamma equal to zero.