8006 Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition - Practice Questions

Question 1

If r be the yield of a bond, which of the following relationships is true:

Select an option, then click Submit answer.

○
- Modified Duration / (1 + r) = Macaulay Duration
○
- Modified Duration x (1 + r) = Macaulay Duration
○
Modified Duration x (1 + r) = Macaulay Duration
○
Modified Duration / (1 + r) = Macaulay Duration

Question 2

Which of the following statements is false:

Select an option, then click Submit answer.

○
The value of an FRA at expiration is determined by the spot interest rate prevailing at expiration
○
The value of an FRA (forward rate agreement) at inception is zero.
○
An FRA can be valued at anytime in its lifetime using the spot interest rate for the period to which the FRA relates
○
Notional principals are exchanged at the start and the end of an FRA to eliminate credit risk

Question 3

What can the buyer of a 6 x 12 FRA expect to receive (or pay) if the contracted rate is 10% and the settlement rate is 12%? Assume contract notional is $100m.

Select an option, then click Submit answer.

○
Pay $1,000,000
○
Receive $1,000,000
○
Pay $943,396
○
Receive $943,396

Reference / correct answer:

Receive $943,396

:

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.

8006 – Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition