Derivative Investments【Reading 54】Sample forward, price, contract, 2012

JoeyDVivre

The price of a forward contract:

A) is the settlement price for the underlying asset.

B) must be equal to the market price at contract termination.

C) is equal to the value of the contract in equilibrium.

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The price of a forward contract is the price of the underlying asset that the long will pay to the short at settlement (for a deliverable contract). The value of a forward contract comes from the difference between the forward contract price and the market price for the underlying asset. This difference between price and value is a key concept to understand. A forward contract has only one price, which applies to both the long and to the short.

kmf229

Credit risk to the long (position) in a forward contract will increase over the life of the contract due to all of the following EXCEPT the:

A) short party has deteriorating finances.

B) settlement date is getting closer.

C) contract value to the short is negative and decreasing.

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Deteriorating finances of the counterparty increase the probability of default. The amount owed to the long increases as the value of the underlying asset increases, which is the same as an increase in the value of the contract. An increase in the amount ‘owed’ and an increase in the probability of default can both be viewed as increasing credit risk. By itself, the passage of time does not necessarily increase credit risk.

kmf229

Over the life of a forward contract, the amount of credit risk is least likely to:

A) change signs.

B) stay the same.

C) increase.

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The amount of credit risk is least likely to stay the same. The amount of credit risk is based on the contract value, which is zero at contract initiation. For the value to stay the same (at zero), the expected future price of the asset must not change over the life of the contract, an unlikely circumstance. As the value of the contract to the long goes from positive to negative, the amount of credit risk changes in sign.

kmf229

The credit risk in a forward contract is:

A) positively related to the term of the contract.

B) only an issue for the long.

C) directly related to the contract value.

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The credit risk to the party with the position with the positive value (long or short) is greater, the greater the value of the forward contract at a point in time. A contract with a longer term may have a lower contract value.

kmf229

The best measure of the amount of credit risk exposure for a forward contract, at a point in time, is the:

A) liabilities of the counterparty.

B) value of the contract.

C) notional amount of the contract.

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The amount of credit risk is best measured by the contract value at a point in time. This is the present value of the settlement payment, based on current market prices, interest rates, or exchange rates. The party to whom the payment would be made has the credit risk, the risk that the payment will not be made or that the asset will not be delivered/purchased at contract expiration.

kmf229

Chantal DuPont is the CFO of Vetements Verdun, a manufacturer of specialty clothing and uniforms, located in northern France. The firm is currently undergoing an expansion which will require DuPont to draw down 25 million on Vetements Verdun’s credit line as a 90-day bridge loan before the mortgage closes. The money will not be needed for 60 days, at which point the interest rate will be determined. The interest rate on the loan will be based off 90-day LIBOR.DuPont is becoming concerned because of signs that interest rates may begin to rise. The firm cannot afford to have its borrowing costs increase significantly over current rates. In response to DuPont’s concerns, the company’s CEO, Viviane Lamarre, has asked DuPont to hedge the firm’s borrowing costs, even if that entails some near-term outlays. DuPont and Lamarre discuss entering into a forward rate agreement (FRA) to hedge Vetements Verdun’s interest rate exposure on the credit line. Current LIBOR rates are:

Libor rate
30-day	2.6%
60-day	2.8%
90-day	3.0%
120-day	3.2%
150-day	3.3%
180-day	3.4%

They decide to go forward with the hedge and DuPont enters into the appropriate FRA for the full amount of 25 million. In the first 30 days of the FRA, the fixed income markets rally sharply. The new set of LIBOR rates, on the thirtieth day of the FRA, is:

Libor rate
30-day	2.2%
60-day	2.4%
90-day	3.6%
120-day	3.8%
150-day	3.8%
180-day	3.8%

At the settlement date, the interest savings on the loan term is 23,750. DuPont tells Lamarre, “I am looking forward to cashing our settlement check for 23,750.” Lamarre adds, “Yes, and on top of that we get to borrow for 90 days at a below-market rate.” Both DuPont and Lamarre are pleased with their decision to hedge. Which statement most accurately describes a 2 x 3 forward rate agreement?

A) Underlying loan of two month maturity under a contract that expires in three months.

B) Contract expires in two months on an underlying loan settled in three months.

C) Two-month underlying interest rate on a contract settled in three months.

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A 2 x 3 forward rate agreement is a contract that expires in two months and the underlying loan is settled in three months. The underlying rate is a 30-day (1-month) rate on a 30-day (1-month) loan in 60 days (2 months). (Study Session 16, LOS 54.a)

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Which forward rate agreement would most effectively hedge Vetements Verdun’s exposure to LIBOR?

A) 2 x 3.

B) 3 x 2.

C) 2 x 5.

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Vetements Verdun needs to be hedged against 90-day LIBOR rates that will prevail 60 days from now. Such a hedge would require a two-month contract on three-month rates, to be settled in five months: a 2 x 5. (Study Session 16, LOS 54.c)

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Which value is closest to the price of the most effective hedge for Vetements Verdun?

A) 3.6%.

B) 3.3%.

C) 3.0%.

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The actual, unannualized rate on the 60-day loan is:
R60 = 0.028 × 60/360 = 0.00467
The actual, unannualized rate on the 150-day loan is:
R150 = 0.033 × 150/360 = 0.01375
So the rate on a 90-day loan to be made 60 days from now is:
FR (60,90) = ((1 + R150)/(1 + R60)) − 1
FR (60,90) = (1.01375/1.00467) − 1
FR (60,90) = 1.00904 − 1
FR (60,90) = 0.904%
We annualize this rate using the formula:
0.904% × (360/90) = 3.62%(Study Session 16, LOS 54.c)

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What must the 90-day LIBOR rate have been at the expiration of the contract?

A) 3.4%.

B) 4.0%.

C) 3.6%.

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Since Vetements Verdun is long the FRA, the market rate of interest at settlement must be higher than the price of the contract and the 23,750 has a positive value. The interest savings at the end of the loan term will be:
Interest savings = ( (market rate × (90/360)) − (0.0362 × (90/360)) ) × 25,000,000
23,750 = ((market rate × 90/360) − 0.00905) × 25,000,000
0.000950 = market rate × 90/360 − 0.00905
0.0100 = market rate × 0.25
0.0400 = market rate
The market rate must have been 4.0%.(Study Session 16, LOS 54.c)

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Regarding the statements made by Lamarre and DuPont about the ultimate value of their hedge:

A) Lamarre’s statement is correct; DuPont’s statement is incorrect.

B) Lamarre’s statement is incorrect; DuPont’s statement is incorrect.

C) Lamarre’s statement is incorrect; DuPont’s statement is correct.

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The interest savings at the end of the loan term must be discounted back to the present value on the FRA settlement date:
Settlement payment = Present value of interest savings
Settlement payment = 23,750 / (1 + (0.040 × 90/360))
Settlement payment = 23,750 / (1 + 0.010)
Settlement payment = 23,750 / 1.010
Settlement payment = 23,515
The settlement check would be for 23,515. DuPont’s statement is incorrect. Lamarre’s statement is also incorrect because the settlement check represents the value of the below-market loan. The actual loan will be at the prevailing rate, and the settlement on the FRA will offset the interest cost on the loan.(Study Session 16, LOS 54.c)

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Thirty days into the FRA, what is the value of the contract from Vetements Verdun’s perspective?

A) Due 45,000.

B) Owes 43,943.

C) Due 43,943.

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Since we have moved 30 days into the FRA, the new rate for the end of the contract is the 30-day rate (60 days originally minus 30 days passed) and the new rate for the settlement of the loan is the 120-day rate (150 days originally minus 30 days passed).
With that information, the pricing is straightforward:
The actual, unannualized rate on the 30-day loan is:
R30 = 0.022 × 30/360 = 0.00183
The actual, unannualized rate on the 120-day loan is:
R120 = 0.038 × 120/360 = 0.01267
The rate on a 90-day loan to be made 30 days from now is:
FR (30,90) = ((1 + R120) / (1 + R30)) − 1
FR (30,90) = ((1 + 0.01267) / (1 + 0.00183)) − 1
FR (30,90) = (1.01267 / 1.00183) − 1
FR (30,90) = 1.010820 − 1
FR (30,90) = 1.0820%
We annualize this rate using the formula:
1.082% × (360/90) = 4.33%
The interest saving is:
Interest saving = ( (0.0433 × 90/360) − (0.0362 × 90/360) ) × 25,000,000
Interest saving = (0.01083 − 0.00905) × 25,000,000
Interest saving = 0.00178 × 25,000,000
Interest saving = 44,500
The interest “saving” is a positive 44,500. Discounting that back at the current 120-day rate we have:
FRA value = 44,500 / (1 + ( 0.038 × 120/360) )
FRA value = 44,500 / (1 + ( 0.012667) )
FRA value = 44,500 / 1.012667
FRA value = 43,943
The value of the FRA to Vetements Verdun 30 days into the contract is 43,943. In other words, they are due 43,943. (Study Session 16, LOS 54.c)

kmf229

Consider a forward contract on 1 million Mexican Pesos at $0.08254/MXN. 60 days prior to expiration the U.S. risk-free rate is 5%, the Mexican risk-free rate is 6%, and the spot rate is $0.08211/MXN. The value of the contract to the long is closest to:

A) $553.

B) -$553.

C) -$297.

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The formula is:
Vt = St / (1 + Rfor)(T − t) − FT / (1 + Rdom)(T − t) .

The value is 0.08211 / 1.0660/365 − 0.08254/1.0560/365 = 0.08132763 − 0.08188065 = -0.00055302.

The answer is in USD/ Peso, because when multiplying by Pesos, the answer is in USD.
0.00055302 × 1 million Pesos = -$553.02.

kmf229

Calculate the price (expressed as an annualized rate) of a 1x4 forward rate agreement (FRA) if the current 30-day rate is 5% and the 120-day rate is 7%.

A) 7.63%.

B) 6.86%.

C) 7.47%.

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A 1x4 FRA is a 90-day loan, 30 days from today.
The actual rate on the 30-day loan is: R30 = 0.05 x 30/360 = 0.004167
The actual rate on the 120-day loan is: R120 = 0.07 x 120/360 = 0.02333
FR (30,90) = [(1+ R120)/(1+ R30)] – 1 = (1.023333/1.004167) – 1 = 0.0190871
The annualized 90-day rate = 0.0190871 x 360/90 = .07634 = 7.63%

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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?

A) $1,073.54.

B) $1,035.12.

C) $1,070.02.

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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 54.c)

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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?

A) The long pays the short at the initiation of the contract.

B) The short pays the long at the maturity of the contract.

C) The long pays the short at the maturity of the contract.

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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 54.a)

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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?

A) The futures contract will be preferred to the forward contract.

B) It is impossible to say for certain because it depends on the correlation between the underlying asset and interest rates.

C) The forward contract will be preferred to the futures contract.

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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 54.a)

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Based on the information given, what initial price should Lewis recommend for the 3 × 9 FRA?

A) 5.66%.

B) 4.96%.

C) 4.66%.

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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) = 0.03375The 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 54.c)

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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?

A) $37,218 paid from long to short.

B) $38,000 paid from short to long.

C) $19,000 paid from long to short.

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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 54.c)

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Based on the information given, what initial price should Lewis recommend for a forward contract on Swiss Francs based on a discrete time calculation?

A) $0.8656.

B) $1.1552.

C) $1.0053.

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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 54.c)

kmf229

What is the value of a 6.00% 1x4 (30 days x 120 days) forward rate agreement (FRA) with a principal amount of $2,000,000, 10 days after initiation if L10(110) is 6.15% and L10(20) is 6.05%?

A) $767.40.

B) $700.00.

C) $745.76.

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The current 90-day forward rate at the settlement date, 20 days from now is:
([1+ (0.0615 x 110/360)]/[1+ (0.0605 x 20/360)] – 1) x 360/90 = 0.061517 The interest difference on a $2 million, 90-day loan made 20 days from now at the above rate compared to the FRA rate of 6.0% is:
[(0.061517 x 90/360) – (0.060 x 90/360)] x 2,000,000 = $758.50
Discount this amount at the current 110-day rate:
758.50/[1+ (0.0615 x 110/360)] = $745.76