Reading 28 - Pricing and Valuation of Forward Commitments Flashcards
Explain what the no-arbitrage principle is…..
That there should not be a riskless profit to be gained by a combination of a forward contract position with positions in other assets.
In simple terms,describe what a forward contract is….
An agreement between two parties in which one party, the buyer, agrees to buy from the other party, the seller, an underlying asset or other derivative, at a future date at a price established at the start of the contract.
What is the general formula for how to calculate the forward contract price?
***Critical Concept****
What are the 3 assumptions of the no-arbitrage principle?
- Transaction costs are zero
- There are no restrictions on short sales or on the use of short sale proceeds
- Both borrowing and lending can be done in unlimited amounts at the risk-free rate of interest.
Consider a 3-month forward contract on a zero-coupon bond with a face value of $1,000 is currently quoted at $500, and the risk free annual interest rate of 6%. Determine the price of the forward contract under the no-abitrage principle……
In a cash and carry arbitrage, what should be done if the FRA is overpriced?
***Critical Concept*****
- Short (sell) the forward
- Long (buy) spot asset
- Borrow money
In a cash and carry arbitrage, what should be done if the FRA is underpriced?
****Critical Concept*****
- long (buy) the forward
- short (sell) the spot asset
- invest (lend) money
What is the value of a forward contract calculated at its initiation???
****Critical Concept******
Value at initiation = 0. The contract is priced to prevent arbitrage.
How is the Long value of a forward contract calculated during the life of the contract???
****Critical Concept*****
simplified formula?
How is the Short value of a forward contract calculated during the life of the contract ???
***Critical Concept****
How is the value of a forward contract calculated at maturity for a long position ?
How is the value of a forward contract calculated at maturity for a short position???
What adjustment may we need to account for to calculate the price of an equity forward contract?
Since a stock, portfolio or equity index may have expected dividend payments over the life of the contract we have to account for these flows in one of two ways.
What formula is used to price an equity forward contract?
Explain in words
What is an alternative formula to calculate equity forward contract that does not include the PVD?
In words..
How do you calculate the value of a long position in a forward contract on a dividend-paying stock? What is the valuation dependent on?
***Critical Concept****
Explain words.
The valuation is dependent on the price of the underlying.
How do you calculate the price of an equity index forward contract whose dividends are paid continuously?
***Critical Concept****
in words…
The value of the S&P 500 index is 1,140. The continuously compounded risk-free rate is 4.6% and the continuous dividend yield is 2.1%. Calculate the no-arbitrage price of a 140 day forward contract on the index…..
The value of the S&P 500 index is 1,140. The continuously compunded risk-free rate is 4.6% and the continuous dividend yield is 2.1%. Calculate the no-arbitrage price of a 140 day forward contract on the index…..
Now, after 95 days, the value of the index is 1,025. Calculate the value to the long position of the forward contract……
How do you calculate the value of the forward contract on an equity index that is continuously compounded?
***Critical Concept****
What adjustment do we need to make to calculate the price of a forward contract on a fixed income security?
Similar to the adjustment we make for dividends in equity contracts, we must do the same for coupon payments by adusted be either:
- PV of expected coupon payments (PVC)
- Future value of coupon payments (FVC)
How do you calculate the forward price of a fixed income security prior to expiration?
Include alternative
How do you c_alculate the value of the forward contract_ of a fixed income security prior to expiration?
Calculate the price of a 250 day forward contract on a 7% US Treasury bond with a spot price of $1,050 (including accrued interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk free rate is 6%.
Previously:
Calculate the price of a 250 day forward contract on a 7% US Treasury bond with a spot price of $1,050 (including accrued interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk free rate is 6%.
Now:
After 100 days, the value of the bond is $1,090. Calculate the value of the forward contract on the bond to the long position, assuming the risk free rate is still 6%…….
What is a Eurodollar deposit?
The term for deposits in large banks outside the United States denominated in US dollars.
In a forward rate aggrement (FRA), is the long position the person the borrows the money or lends the money?
Borrows.
A FRA with the notation 2 X 3 means what?
***Critical Concept****
A 1 month loan 2 months from now
What are the 3 important things to remember about FRAs when you are pricing or valuing them?
- LIBOR rates are quoted on the 30/360 day basis
- The long position in an FRA, in effect, is long the rate and wins when the rate increases
- The payoff on the FRA occurs at the expiration of the FRA. The payoff is the present value of the interest savings on the loan.
Calculate the price of a 1 x 4 FRA. The current 30 day LIBOR is 4% and the 120 day LIBOR is 5%.
***Critical Concept***
1 x 4 means a 90 days loan, 30 days from now
What is the equation to calculate the price of a currency forward contract?
****Critical Concept*****
The risk-free rates are 6% in the US and 8% in Mexico. The current spot exchange rate is $0.0845 per Mexican peso. C_alculate the forward exchange rate_ for a 180-day forward contract……
What is the equation to value a currency forward contract at any time prior to maturity???????
****Critical Concept*****
Previously:
The risk-free rates are 6% in the US and 8% in Mexico. The current spot exchange rate is $0.0845 per Mexican peso. Calculate the forward exchange rate for a 180-day forward contract……
Now:
Calculate the value of the forward contract in the previous example, if, after 15 days the spot rate is $0.0980 per MXN.
In a forward contract, which party is exposed to the credit risk?
Whichever party has the position with a positive value if the contract would be terminated today.
It is customary in the forward market for the initial value to be set to zero.
If V0 =ST-F(0,T) 0
If amount is positive, who pays up front?
If amount is negative, who pays up front?
If positive: paid by the party going long the forward
If negative: paid by the party going short the forward
What is the name of a forward contract whose initial contract is intentionally set at a nonzero value?
an off-market FRA
What are some reasons we may want to know the value of a forward contract?
- It makes good business sense to know the monetary value of an obligation to do something at a later date
- Accounting rules require that a company mark its derivatives to their current market values and report the effects on this I/S and B/S.
- The market value can be used as a gauge of the credit exposure
- The market value can be used to determine how much money one party can pay to the other to terminate the contract.
Is the forward price a forecast of where the spot price is expected to go in the future?
No
If a forward price is higher than the spot price, it just indicates that the effect of the risk-free rate is greater than the effect of the dividends.
What is Interest Rate Parity?
a formula that expresses the equivalence, of spot and forward exchange rates, after adjusting for the differences in interest rates.
What is it called if the forward rate in the foreign exchange market does not equal the forward rate given by interest rate parity?
Covered Interest Arbitrage
Q. A portfolio returned 5% over one year, if continuously compounded, this is equivalent to ____?
A. ln 5
B. ln 1.05
C. e5
D. e1.05
The answer would be B based on the definition of continuous compounding. A financial function calculator or spreadsheet could yield the actual percentage of 4.879%, but wouldn’t be necessary to answer the question correctly on the exam.
