Citibank: basic of corporate finance
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9-40 FIXED INCOME SECURITIES
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Please complete Practice Exercise 9.4, which will give your experience with calculating
the duration of a bond. When you have checked your answers, continue on to the Unit
Summary that follows.
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PRACTICE EXERCISE 9.4
Directions: Calculate the correct answer(s) for each question. Check your solutions
with the Answer Key on the next page.
12. A 2-year Treasury note with a coupon rate of 6.5% has a percentage issue price of
98.50. What is the duration of the instrument?
Duration = _____________ years
Use this table to help with your calculation.
Price: _________ BEY: _________
Coupon: _________ Discount Rate: _________
Maturity: _________
Time Cash Flow
Present
Value at Semi-
annual Rate
Present
Value /
Bond Price
Time-
weighted
Value
______________ _____________ ______________
TOTAL
13. What is the duration of the following portfolio?
Percentage
of Portfolio Security Duration
42.5% 2-year notes 1.8654
37.8% 5-year notes 4.7333
19.7% 10-year bonds 9.6655
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ANSWER KEY
12. A 2-year Treasury note with a coupon rate of 6.5% has a percentage issue price of
98.50. What is the duration of the instrument?
Duration = 1.9067 years
Use this table to help with your calculation.
Price: 98.50 BEY: 7.3199%
Coupon: 6.50% Discount Rate: 7.4538%
Maturity: 2 years
Make sure that you have calculated the correct discount rate.
Find the yield to maturity of the note using the bond features on your calculator.
That rate should be 7.3199%.
Convert this to an equivalent semi-annual discount rate.
Divide 0.073199 by 2, add 1, square this result, and subtract 1.
You should get 0.074538.
Use this rate to discount the cash flows and your table should look like this.
Time Cash Flow
Present
Value at Semi-
annual Rate
Present
Value /
Bond Price
Time-
weighted
Value
0.5 3.25 3.1353 0.0318 0.0159
1.0 3.25 3.0246 0.0307 0.0307
1.5 3.25 2.9178 0.0296 0.0444
2.0 103.25 89.4224 0.9078 1.8157
TOTAL 98.5001 0.9999 1.9067
13. What is the duration of the following portfolio?
(0.425) (1.8654) + (0.378) (4.7333) + (0.197) (9.6655) = 4.4861 years
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FIXED INCOME SECURITIES 9-43
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UNIT SUMMARY
In this unit, we introduced the basic methodologies for pricing and
calculating yield on debt securities that trade in the secondary
markets. Specifically, we discussed U.S.Treasury bills, notes, bonds,
and Eurobonds.
Treasury bills are short-term, zero-coupon (non-interest bearing)
securities. The quoted price of a Treasury bill is discounted from the
face value at a discount rate that is often referred to as the yield to
maturity of the security. The discount rate is based on the face value
of the security; the rate of return to the investor or true yield of the
bill is based on the difference between the purchase price and the
sale price.
Treasury notes are bonds with maturities ranging from one to ten years
that make semi-annual interest payments. Since all Treasuries are
quoted in terms of annual discount rates and annual coupon payments,
the price of Treasury notes is adjusted for the semi-annual interest
payments. You learned how to calculate the price of a note and the
yield to maturity.
Treasury bonds are securities with maturities greater than ten years.
The most common maturities are 20 to 30 years. Since bonds make
semi-annual coupon payments to investors, the price and yield
calculations are the same as they are for Treasury notes.
A Eurobond is a debt instrument issued by a company in an
international market that is outside any domestic regulations. They
typically make annual coupon payments to the investor.
The true selling price of a security that makes periodic interest
payments includes an adjustment for accrued interest which is owed
to the seller by the buyer. The convention is to adjust the payment by
the number of days in the coupon period that the security is actually
held by the seller.
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Bond prices are affected by their sensitivity to market interest rates,
the maturity of the bond, and the effective life of the bond. Duration
is the measure we use to estimate the average maturity of a bond's
cash flows.
You have demonstrated your understanding of each of these key concepts in the four
practice exercises; therefore, this unit has no Progress Check. Please continue your study
of securities with Unit Ten: Derivative Securities, which follows.
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Unit 10
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UNIT 10: DERIVATIVE SECURITIES
INTRODUCTION
In Unit Two, we introduced the three general subsets of capital markets: bond (debt)
markets, equity markets, and derivative markets. In this unit we will focus on the
derivative markets.
There are three basic forms of derivative products: forwards, options, and swaps. These
instruments are often referred to as derivative securities because their values are derived
from the value of the underlying security. In this unit you will be introduced to some of
the derivative instruments that investors use to manage exposure to risk.
We will focus on the characteristics of options and swaps and how the payoffs are
calculated for both types of instruments.
UNIT OBJECTIVES
After you successfully complete this unit, you will be able to:
• Recognize terminology that is associated with options trading
• Recognize the payoff profiles for call options and put options
• Identify the characteristics of interest rate swaps and currency swaps
OPTIONS
An option contract between a buyer (holder) and a seller (writer)
describes the rights of the option holder and the obligations of the
option writer.
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The purchase price of an option is called the premium. This is the
compensation that the holder of the option pays to the writer for the
rights described in the option contract.
Calls and puts
There are two types of options: call options and put options.
Call options - give the holder the right to buy an asset for a
specified price on or before a given expiration
(maturity) date.
Put options - give the holder the right to sell an asset for a
specified price on or before a given expiration
(maturity) date.
The specific asset named in the option contract is called the
underlying asset. The price at which the underlying asset may be
bought is called the exercise or strike or contract price. Purchasing
(or selling) the underlying asset of an option contract is referred to
as exercising the option.
The key thing to remember is that the holder of the option has the
right (but not the obligation) to exercise the option.
In the money /
Out of the
money
An option is "in the money" when its exercise would produce profits
for its holder. An option is "out of the money" during the time when
its exercise would not be profitable for its holder. This means that a
call option on a stock is in the money when the exercise price is
below the market price of the stock; a put option is profitable when
the exercise price is above the market price of the stock.
American /
European
Options may be either American or European. American options give
the holder the right to exercise the option at any time up to the
expiration date. European options give the holder the right to
exercise the option only on the expiration date.
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Background and Markets
When options were first traded, contracts were arranged between pairs
of investors and customized to meet specific needs. These customized
contracts could vary according to exercise price, expiration date, and
underlying asset. Because of these infinite possibilities, it was nearly
impossible for a secondary options trading market to exist. Investors
would enter into customized agreements according to their investment
needs; if their needs changed, it was difficult to find another investor
to buy the option contract.
Secondary
markets
This lack of liquidity and standardization was one of the driving
forces behind the creation of the Chicago Board Options Exchange
(CBOE) in 1973. The CBOE enacted rules to standardize option
contracts in order to restrict the number of contract types that would
trade on the exchange. Soon, other option exchanges were created.
This led to a broader standardization of option contracts and was the
key to creating a secondary market for options and increasing the
liquidity of option contracts.
Customized option contracts are still available to investors — they
are traded in over-the-counter (OTC) markets. These customized
options are usually considerably more expensive than the standard
option contracts because of the lack of liquidity.
Standardized
contracts
The first standardized contracts were for the purchase or sale of
common stock. However, investors soon created demand for options
on a variety of financial and physical assets, including options on:
• Common stock
• Stock indices
• Debt instruments
• Interest rate futures
• Foreign currency futures
• Agricultural commodities
• Precious metals
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