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CHAPTER 5
Interest Yields, Interest Rate Risk,
and Derivative Securities
CHAPTER OVERVIEW
Chapter 5 begins by drawing an analogy between the concept of exchange rate risk, as studied in the previous
chapter, and interest rate risk, which is the subject of this chapter. Before studying the various potential sources
of interest rate risk and the instruments that are designed to hedge against these risks, the chapter begins with a
presentation of the concept of discounted present value and how it relates the market price of a bond to its yield.
This section also introduces the term structure of interest rates, and the representation of the yield curve. The
section then proceeds with a discussion of various theories of the term structure, and the extent to which they
are able to explain regular features of the yield curve, such as its upward slope. The theories discussed are (1)
the segmented markets theory, (2) the expectations theory and (3) the preferred habitat theory. Finally, the
section ends with an elaboration of the various sources of interest rate risk, and other reasons for interest rate
differentials between instruments with similar maturities. These include (1) differences in the degree of default
risk, (2) differences in the degree of liquidity and (3) differences in tax obligations.
The next section discusses ways in which investors can hedge against interest rate risk using derivatives. The
section points out that forward exchange contracts are simply one example of a derivative security. Just as
investors use forward exchange rate markets to hedge against exchange risk, investors can use derivative
securities that are based on forward interest rates to hedge against interest rate risk. The chapter then describes
some of the most common forms of available derivatives, such as interest rate futures, stock index futures, and
currency futures. The use of options and swaps in each of these markets is also discussed. The chapter ends with
a brief discussion of the types of risks associated with derivatives.
OUTLINE
I.
Interest Rates
A. Instrument Yields and Financial Instrument Prices
1. Alternative Measures of Interest Yields
a. Nominal Yield
b. Coupon Return
c. Current Yield
d. Yield to Maturity
2. Discounted Present Value
3. Price of a Bond
4. Term to Maturity
5. Interest Rate Risk
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Instructor’s Manual — International Monetary and Financial Economics
B. Term Structure of Interest Rates
1. Yield Curves
2. Segmented Markets Theory
3. Expectations Theory
4. Preferred Habitat Theory
C. Risk Structure of Interest Rates
1. Default Risk
2. Liquidity
3. Tax Differentials
II. Hedging, Speculation, and Derivative Securities
A. Responses to Interest Rate Risk
1. Strategies for Limiting Interest Rate Risk
2. Hedging
B. Derivative Securities
1. Forward Contracts
2. Speculation
III. Common Derivative Securities and Associated Risks
A. Forward Contracts
1. Non-Standardized
2. Long Position
3. Short Position
B. Futures
1. Standardized Contracts
2. Interest Rate Futures
3. Stock Index Futures
4. Currency Futures
C. Options
1. Stock Options and Futures Options
2. Currency Options
a. Out of the Money
b. At the Money
c. In the Money
D. Swaps
1. Interest Rate Swaps
2. Currency Swaps
E. Derivatives Risks and Regulations
1. Measuring Risks
2. Types of Risks
a. Credit Risk
b. Market Risk
c. Operating Risk
IV. Summary
Chapter Five
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FUNDAMENTAL ISSUES
1.
How are interest yields, financial instrument prices, and interest rate risk interrelated?
2.
Why do market interest yields vary with differences in financial instruments’ terms to maturity?
3.
How does risk cause market interest yields to differ?
4.
What are derivative securities?
5.
What are the most commonly traded derivative securities?
CHAPTER FEATURES
1.
Policy Notebook: “Risk for Sale!”
This notebook considers the case of the Export-Import Bank, which allows private investors to purchase shares
of risk to which the bank was exposed in making loans to support U.S. exports. This allows the export-import
bank to reduce its exposure to risk, and helped provide the bank with an external judgement of the risks
involved with various loan-support subsidies.
For Critical Analysis: Private investors may be interested in making bids for shares o the bank’s risk if they feel
that the risk is overstated. If this were the case, the risk premium would be relatively high. Assuming default
does not take place, the purchaser of this risk will earn a market premium.
2.
Management Notebook: “Just How Widespread Is the Use of Derivatives by U.S. Businesses?”
This management notebook examines the use of various derivative instruments by U.S. businesses of varying
size. The evidence suggested by a cited study states that the proportion of larger firms that use derivatives is
greater than the proportion of smaller firms that use derivatives. It also cites evidence that the
most commonly used derivatives are forward and futures contracts.
For Critical Analysis and Group Discussion: The evidence cited is consistent with the notion that there are
economies of scale associated with the use of derivatives. A larger fraction of large companies are cited to use
derivatives than small companies. This may be the case because larger firms benefit from additional
specialization given their size, which in turn can create economies of scale. It may be further motivated by the
currency requirements necessary to purchase derivative contracts.
ANSWERS TO END OF CHAPTER QUESTIONS
1.
The coupon yield is equal to the bond’s coupon return divided by its market price, which equals
¥600 / ¥9,000 = 0.067, or 6.7 percent. The bond’s nominal yield is equal to the coupon return divided by
the face value of the bond, which equals ¥600/ ¥10,000 = 0.06, or 6.0 percent.
2.
The current yield is equal to £ 800 / £ 10,000 = 0.08, or 8.0 percent.
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3.
Given that: PB = C/(1+r) + C/(1+r)2 + C/(1+r)3 + C/(1+r)4 +…
multiply each side by (1+r): PB (1+r) = C + C/(1+r) + C/(1+r)2 +…
subtract PB from each side: PB (1+r) – PB = [C + C/(1+r) + C/(1+r)2 +…] – [C/(1+r) + C/(1+r)2 +…]
simplifying: PB * r = C
Therefore, PB = C/r
4.
In this situation, annual yields decline as the term to maturity increases, which means that the yield curve
slopes downward. According to the expectations theory of the term structure of interest rates, this situation
arises because bond-market traders anticipates that short-term interest rates will fall sharply. Thus, an
average of current and future short-term rates, which, when added to any term premium applicable to a
longer maturity, is lower than the current short-term rate.
5.
The longer that it takes for the owner of a bond to receive interest and principal payments, the greater is the
owner’s exposure to interest rate risk. This is true for two reasons. First, bonds with longer terms to
maturity expose the owner to risk of capital losses stemming from unexpected interest-rate increases over a
longer interval. Second, an owner of bonds with less frequent interest payments earns returns at a slower
rate, which also exposes the owner to greater risk of capital loss in the faces of unanticipated interest-rate
increases. Hence, as the duration of a bond, or the average time during which the owner of a bond received
payments of principal and interest, increases, the owner’s exposures to interest-rate risk rises.
6.
In contrast to forward currency contracts, currency futures require delivery of standard quantities of
currencies. In addition, holders of currency futures experience profits of losses on the contracts during the
entire period before the contracts expire, whereas profits or losses occur only at the expiration date of a
forward currency contract.
7.
A currency future already is a derivative, because its value varies with the exchange rate. The value of a
currency futures option, in turn, depends on the underlying value of a currency futures contract, so its value
is derived from the futures derivative. In this way, a currency futures option is a “derivative of a
derivative.”
8.
a.
b.
c.
The company owes 500,000 Sf and is concerned about the future spot exchange value of the U.S.
dollar-Swiss franc. It can therefore purchase future contracts to set a limit to its potential exchange
rate losses.
The Sf is purchased in 125,000 franc increments. Therefore, the firm would want to purchase
500,000/125,000 = 4 futures contracts.
Given the initial margin on a franc contract, the total initial margin the firm establishes is:
4($1,688) = $6,752.
Daily margin changes:
First: (0.6252 – 0.6251)(125,000)(4) = +$50. Therefore its margin equals $6,802.
Second: (0.6127 – 0.6252)(125,000)(4) = –$6250. Therefore the margin would fall to $552.
However, the maintenance margin is equal to $1,250. Thus, the margin will equal $1,250.
Third: (0.6115 – 0.6127)(125,000)(4) = –$600. Again, the margin must remain at $1,250.
Fourth: (0.6806 – 0.6115)(125,000)(4) = –$1450. Again, this daily change would fall beneath the
maintenance margin. Thus, it remains at $1,250.
As the dollar continues to appreciate relative to the Swiss franc, the value of the futures contract falls.
However, the cost of 500,000 franc payment is becoming cheaper on terms of the U.S. dollar.
Chapter Five
9.
a.
b.
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The call option is currently out of the money.
(0.0188)(62,500) = $1,175
($1,175)(8 contracts) = $9,400
Net Profit
10,600
0.960
0.980
0.9988
1.02
0
Break Even
9,400
Out of the Money
In the Money
At the Money
Net Loss
c.
d.
e.
At S = $0.96/ € the option is not exercised and the firm is out $9,400
At S = $1.02/ € the option is exercised. The firm earns $10,600
At S = $0.9657/€, the firm does not exercise the option and is out $9,400
Break even: $0.9988/€
See Diagram given in part (b).
10. The pros and cons of forward contracts and swaps lie within how each works. A forward contract can be
arranged between a purchaser and a seller, and is dependent upon each participant’s beliefs of what will
happen in the future. Sometimes it can be difficult to match counterparties to such contracts. Swaps, on the
other hand, directly match traders who require flows of currencies held by one another. Swaps may also
allow borrowers to receive better loan rates by issuing debt in their home currency rather than in a foreign
currency; thereby potentially avoiding a risk premium. Considerations of the reason for the long position
on a currency and which currency is at issue will influence the decision of which derivative to use.
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48
MULTIPLE CHOICE EXAM QUESTIONS
1.
The amount of credit extended via the purchase of a financial instrument is the
A.
B.
C.
D.
front load.
present discounted value.
principal.
sum of the coupons.
Answer: C
2.
The coupon yield divides the coupon value by the ________ whereas the coupon value divides the
coupon by the ________.
A.
B.
C.
D.
bond’s face value; price of the bond
price of the bond; bond’s face value
nominal interest rate; real interest rate
sum of the coupons; sum of the coupons and principal
Answer: A
3.
The rate of return that the owner of and instrument would earn by holding the instrument until maturity is
called the
A.
B.
C.
D.
coupon yield.
coupon value.
nominal rate of return.
yield to maturity.
Answer: D
4.
To calculate the price of an instrument one must find the
A.
B.
C.
D.
present discounted value of the stream of coupon payments and principal.
sum of the coupons divided by the principal.
sum of the coupons plus the principal.
principal plus the present discounted value of the coupons.
Answer: A
5.
A bond with no fixed maturity date is called a
A.
B.
C.
D.
treasury bill.
callable bond.
perpetuity.
discount bond.
Answer: C
Chapter Five
6.
A bond with an infinite payment life will have a price
A.
B.
C.
D.
that is arbitrarily high, as it will produce coupon payments forever.
of the present discounted value of its principal.
of the coupon amount divided by the interest rate.
of the coupon amount divided by one plus the interest rate.
Answer: C
7.
Suppose the price of a perpetuity is $1,000 and that the perpetuity pays $60 per year. The interest rate on
this bond is
A.
B.
C.
D.
0.06%
0.60%
6%
60%
Answer: C
8.
Suppose the interest rate on a perpetuity is 5% and its price is $1,500. The annual coupon must therefore
equal
A.
B.
C.
D.
$75.
$300.
$750.
$30,000.
Answer: A
9.
Suppose a perpetuity pays $100 per year and its interest rate is 8%. Its price is therefore
A.
B.
C.
D.
$80.
$125.
$800.
$1,250.
Answer: D
10. Zero-coupon bonds have the distinguishing feature that they
A.
B.
C.
D.
pay no coupons.
have an indefinite life.
are issued only by the Treasury.
pay only coupons that carry an interest rate equal to the real interest rate.
Answer: A
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11. A measure of the average time during which all payments of coupons and principal on a financial asset
are made is referred to as the
A.
B.
C.
D.
term to maturity.
duration.
extension.
average markup.
Answer: B
12. The yield curve displays the relationship among yields on bonds that differ only in their
A.
B.
C.
D.
default risk.
terms of maturity.
bond rating.
country of origin.
Answer: B
13. The segmented markets theory is grounded in the assumption that
A.
B.
C.
D.
bonds with different maturities are nonsubstitutable.
investors have identical preferences for all bond maturities.
inflation will be prevalent in only certain long-term bonds.
domestic investors prefer domestic bonds.
Answer: A
14. A swap is a contract where parties
A.
B.
C.
D.
agree to the future price of a currency exchange.
exchange flows of payments.
exchange future cash flows for past cash flows.
have the right to buy an underlying asset at a fixed price.
Answer: B
15. An investor using the expectations theory would buy a two-year bond at the present time only if its yield is
A. greater than or equal to the average of the one-year spot rate and the expected spot rate a year from
now.
B. greater than or equal to the expected spot rate a year from now.
C. less than the average of the one-year spot rate and the expected spot rate a year form now.
D. greater than or equal to the one year spot rate.
Answer: A
Chapter Five
16. The preferred habitat theory suggests that investors
A. have a preference for domestic over foreign bonds.
B. will only select bonds over a small range of terms to maturity.
C. have a preferred maturity length but are willing to move away from this if the interest rate
differential is high enough.
D. have a select group of firms whose bonds they prefer to hold all else being equal.
Answer: C
17. Because of the possibility of default and low liquidity, some bonds carry a
A.
B.
C.
D.
no callable clause.
risk premium.
margin account.
lower interest rate.
Answer: B
18. The primary reason that municipal bonds earn a lower interest rate than treasury bonds is that
A.
B.
C.
D.
municipal bonds have less risk.
treasury bonds are in greater supply.
municipal bonds are often serial type bonds.
the interest earned on municipal bonds is tax-exempt.
Answer: D
19. Reinvestment risk arises from a situation in which
A.
B.
C.
D.
long-term instruments prohibit taking advantage of increases in interest rates.
an investor cannot be guaranteed the same interest rate when rolling-over short-term instruments.
the investor suffers from an inability to liquidate short-term instruments at opportune times.
an instrument cannot be transferred back into the domestic currency immediately.
Answer: B
20. One way to lock-in a future interest rate is to buy
A.
B.
C.
D.
a series of short-term bonds.
a stock index option.
an interest rate forward contract.
a currency exchange forward contract.
Answer: C
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21. The largest loss on a derivative deal to date has been on the order of
A.
B.
C.
D.
$5 million.
$50 million.
$100 million.
$1500 million.
Answer: D
22. A long position is an obligation to ________ whereas a short position is an obligation to ________.
A.
B.
C.
D.
sell; purchase
purchase; sell
exercise a call; exercise a put
exercise a put; exercise a call
Answer: B
23. A major difference between a forward contract and a future contract is that only a future contract is
A.
B.
C.
D.
a standardized contract that is traded over an exchange.
available exclusively from commercial banks.
limited to large contracts.
available for any amount and maturity.
Answer: A
24. If an investor wants to speculate on the direction of the entire stock market, the most efficient method
would be to acquire
A.
B.
C.
D.
an exchange forward.
a stock index future.
a portfolio of stocks and bonds.
a portfolio containing stocks of all traded companies.
Answer: B
25. An option on a financial instrument gives the holder the
A.
B.
C.
D.
right to purchase or sell an underlying financial instrument at a given price.
obligation to purchase or sell an underlying financial instrument at a given price.
right to purchase or sell an underlying financial instrument at its future spot price.
obligation to purchase or sell an underlying financial instrument at its future spot price.
Answer: A
Chapter Five
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26. A call option gives the holder the right to ________an instrument whereas a put option gives the holder the
right to ________.
A.
B.
C.
D.
exercise; confiscate
sell; purchase
purchase; sell
transfer; sell
Answer: C
27. An investor can simultaneously be “in the money” yet have a negative not profit on the basis of
A.
B.
C.
D.
having to cover the initial cost of the option.
the absence of transaction costs.
a failure to exercise an option.
uncertainty in the price of the underlying instrument.
Answer: A
28. Selling a call differs from selling a put in that a
A.
B.
C.
D.
put has possibly unlimited losses.
call has possibly unlimited losses.
put will sell for a lower price.
call will sell for a lower price.
Answer: B
29. The process of combining separate risk exposures that a firm faces in its foreign currency
denominated payments and receipts into a single net risk exposure is referred to as
A.
B.
C.
D.
netting.
consolidating.
diversifying.
hedging.
Answer: A