Reading 28 - Pricing and Valuation of Forward Commitments

Question 1

Explain what the no-arbitrage principle is…..

Answer 1

That there should not be a riskless profit to be gained by a combination of a forward contract position with positions in other assets.

Question 2

In simple terms,describe what a forward contract is….

Answer 2

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.

Question 3

What is the general formula for how to calculate the forward contract price?

***Critical Concept****

Answer 3

Question 4

What are the 3 assumptions of the no-arbitrage principle?

Answer 4

1. Transaction costs are zero
2. There are no restrictions on short sales or on the use of short sale proceeds
3. Both borrowing and lending can be done in unlimited amounts at the risk-free rate of interest.

Question 5

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……

Answer 5

Question 6

In a cash and carry arbitrage, what should be done if the FRA is overpriced?

***Critical Concept*****

Answer 6

1. Short (sell) the forward
2. Long (buy) spot asset
3. Borrow money

Question 7

In a cash and carry arbitrage, what should be done if the FRA is underpriced?

****Critical Concept*****

Answer 7

1. long (buy) the forward
2. short (sell) the spot asset
3. invest (lend) money

Question 8

What is the value of a forward contract calculated at its initiation???

****Critical Concept******

Answer 8

Value at initiation = 0. The contract is priced to prevent arbitrage.

Question 9

How is the Long value of a forward contract calculated during the life of the contract???

****Critical Concept*****

simplified formula?

Answer 9

simplified: PV (S @ time ) - PV(FP)

Question 10

How is the Short value of a forward contract calculated during the life of the contract ???

***Critical Concept****

Answer 10

Question 11

How is the value of a forward contract calculated at maturity for a long position ?

Answer 11

Question 12

How is the value of a forward contract calculated at maturity for a short position???

Answer 12

Question 13

What adjustment may we need to account for to calculate the price of an equity forward contract?

Answer 13

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.

Question 14

What formula is used to price an equity forward contract?

Explain in words

Answer 14

Grow the spot and PVD at the risk free rate

Question 15

What is an alternative formula to calculate equity forward contract that does not include the PVD?

In words..

Answer 15

Grow spot at the risk free rate, deduct the FV of dividends. Note FV of D = PVD grown at Rf

Question 16

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.

Answer 16

The valuation is dependent on the price of the underlying.

Value = what you agreed to buy a.k.a. u/l, knock out the CFs, then deduct that whole thing by the PV of the forward prive.

Question 17

How do you calculate the price of an equity index forward contract whose dividends are paid continuously?

***Critical Concept****

in words…

Answer 17

The price is reduced by the continuous dividends missed out on and grown at the continuously compounded risk free rate.

Question 18

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…..

Answer 18

Question 19

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……

Answer 19

Question 20

How do you calculate the value of the forward contract on an equity index that is continuously compounded?

***Critical Concept****

Answer 20

Question 21

What adjustment do we need to make to calculate the price of a forward contract on a fixed income security?

Answer 21

Similar to the adjustment we make for dividends in equity contracts, we must do the same for coupon payments by adusted be either:

1. PV of expected coupon payments (PVC)
2. Future value of coupon payments (FVC)

Question 22

How do you calculate the forward price of a fixed income security prior to expiration?

Include alternative

Answer 22

Question 23

How do you c_alculate the value of the forward contract_ of a fixed income security prior to expiration?

Answer 23

Question 24

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%.

Answer 24

Question 25

**_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%.......

Answer 25

Question 26

What is a Eurodollar deposit?

Answer 26

The term for deposits in large banks outside the United States denominated in US dollars.

Question 27

In a forward rate aggrement (FRA), is the long position the person the borrows the money or lends the money?

Answer 27

Borrows.

Question 28

A FRA with the notation 2 X 3 means what? \*\*\*Critical Concept\*\*\*\*

Answer 28

A 1 month loan 2 months from now

Question 29

What are the 3 important things to remember about FRAs when you are pricing or valuing them?

Answer 29

1. LIBOR rates are quoted on the 30/360 day basis 2. The long position in an FRA, in effect, is long the rate and wins when the rate increases 3. 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.

Question 30

_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\*\*\*

Answer 30

1 x 4 means a 90 days loan, 30 days from now

Question 31

What is the equation _to calculate the price_ of a currency forward contract? \*\*\*\*Critical Concept\*\*\*\*\*

Answer 31

Question 32

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......

Answer 32

Question 33

What is the equation _to value_ a currency forward contract at any time prior to maturity??????? \*\*\*\*Critical Concept\*\*\*\*\*

Answer 33

Question 34

**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.

Answer 34

Question 35

In a forward contract, which party is exposed to the credit risk?

Answer 35

Whichever party has the position with a positive value if the contract would be terminated today.

Question 36

It is customary in the forward market for the initial value to be set to zero. If V₀ =S_T-F(0,T) 0 If amount is positive, who pays up front? If amount is negative, who pays up front?

Answer 36

If positive: paid by the party going long the forward If negative: paid by the party going short the forward

Question 37

What is the name of a forward contract whose initial contract is intentionally set at a nonzero value?

Answer 37

an off-market FRA

Question 38

What are some reasons we may want to know the value of a forward contract?

Answer 38

1. It makes good business sense to know the monetary value of an obligation to do something at a later date 2. 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. 3. The market value can be used as a gauge of the credit exposure 4. The market value can be used to determine how much money one party can pay to the other to terminate the contract.

Question 39

Is the forward price a forecast of where the spot price is expected to go in the future?

Answer 39

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.

Question 40

What is **Interest Rate Parity**?

Answer 40

a formula that expresses the equivalence, of spot and forward exchange rates, after adjusting for the differences in interest rates.

Question 41

What is it called if the forward rate in the foreign exchange market does not equal the forward rate given by interest rate parity?

Answer 41

Covered Interest Arbitrage

Question 42

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. e^1.05

Answer 42

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.