Monica Lewis, CFA, has been hired to review data on a series of forward contracts for a major client. The client has asked for an analysis of a contract with each of the following characteristics:
- A forward contract on a U.S. Treasury bond
- A forward rate agreement (FRA)
- A forward contract on a currency
Information related to a forward contract on a U.S. Treasury bond: The Treasury bond carries a 6% coupon and has a current spot price of $1,071.77 (including accrued interest). A coupon has just been paid and the next coupon is expected in 183 days. The annual risk-free rate is 5%. The forward contract will mature in 195 days.
Information related to a forward rate agreement: The relevant contract is a 3 × 9 FRA. The current annualized 90-day money market rate is 3.5% and the 270-day rate is 4.5%. Based on the best available forecast, the 180-day rate at the expiration of the contract is expected to be 4.2%.
Information related to a forward contract on a currency: The risk-free rate in the U.S. is 5% and 4% in Switzerland. The current spot exchange rate is $0.8611 per Swiss France (SFr). The forward contract will mature in 200 days.
Based on the information given, what initial price should Lewis recommend for a forward contract on the Treasury bond?
The forward price (FP) of a fixed income security is the future value of the spot price net of the present value of expected coupon payments during the life of the contract. In a formula:
FP = (S0 ? PVC) × (1 + Rf)T
A 6% coupon translates into semiannual payments of $30. With a risk-free rate of 5% and 183 days until the next coupon we can find the present value of the coupon payments from:
PVC = $30 / (1.05)183/365 = $29.28.
With 195 days to maturity the forward price is:
FP = ($1,071.77 – $29.28) × (1.05)195 / 365 = $1,070.02.
(Study Session 16, LOS 58.c)
Suppose that the price of the forward contract for the Treasury bond was negotiated off-market and the initial value of the contract was positive as a result. Which party makes a payment and when is the payment made?
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A) |
The short pays the long at the maturity of the contract. | |
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B) |
The long pays the short at the initiation of the contract. | |
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C) |
The long pays the short at the maturity of the contract. | |
If the value of a forward contract is positive at initiation then the long pays the short the value of the contract at the time it is entered into. If the value of the contract is negative initially then the short pays the long the absolute value of the contract at the time the contract is entered into. (Study Session 16, LOS 58.a)
Suppose that instead of a forward contract on the Treasury bond, a similar futures contract was being considered. Which one of the following alternatives correctly gives the preference that an investor would have between a forward and a futures contract on the Treasury bond?
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A) |
The forward contract will be preferred to the futures contract. | |
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B) |
The futures contract will be preferred to the forward contract. | |
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C) |
It is impossible to say for certain because it depends on the correlation between the underlying asset and interest rates. | |
The forward contract will be preferred to a similar futures contract precisely because there is a negative correlation between bond prices and interest rates. Fixed income values fall when interest rates rise. Borrowing costs are higher when funds are needed to meet margin requirements. Similarly reinvestment rates are lower when funds are generated by the mark to market of the futures contract. Consequently the mark to market feature of the futures contract will not be preferred by a typical investor. (Study Session 16, LOS 58.a)
Based on the information given, what initial price should Lewis recommend for the 3 × 9 FRA?
The price of an FRA is expressed as a forward interest rate. A 3 × 9 FRA is a 180-day loan, 90 days from now. The current annualized 90-day money market rate is 3.5% and the 270-day rate is 4.5%. The actual (unannualized) rates on the 90-day loan (R90) and the 270-day loan (R270) are:
R90 = 0.035 × (90 / 360) = 0.00875
R270 = 0.045 × (270 / 360) = 0.03375 The actual forward rate on a loan with a term of 180 days to be made 90 days from now (written as FR (90, 180)) is:
Annualized = 0.02478 × (360 / 180) = 0.04957 or 4.96%.
(Study Session 16, LOS 58.c)
Based on the information given and assuming a notional principal of $10 million, what value should Lewis place on the 3 × 9 FRA at time of settlement?
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A) |
$37,218 paid from long to short. | |
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B) |
$38,000 paid from short to long. | |
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C) |
$19,000 paid from long to short. | |
The value of the FRA at maturity is paid in cash. If interest rates increase then the party with the long position will receive a payment from the party with a short position. If interest rates decline the reverse will be true. The annualized 180-day loan rate is 4.96%. Given that annualized interest rates for a 180-day loan 90 days later are expected to drop to 4.2%, a cash payment will be made from the party with the long position to the party with the short position. The payment is given by:
The present value of the FRA at settlement is:
38,000 / {1 + [0.042 × (180 / 360)]} = 38,000 / 1.021 = $37,218
(Study Session 16, LOS 58.c)
Based on the information given, what initial price should Lewis recommend for a forward contract on Swiss Francs based on a discrete time calculation?
The value of a forward currency contract is given by:
Where F and S are quoted in domestic currency per unit of foreign currency. Substituting:
(Study Session 16, LOS 58.c)
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发表于 2011-3-25 11:05
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