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Chapter 6: Problem 9

It is May 5,2008 . The quoted price of a government bond with a \(12 \%\) coupon that matures on July 27, 2011, is \(110-17\). What is the cash price?

Short Answer

Expert verified
The cash price of the bond is approximately 113.53.

Step by step solution

01

Understand Quoted Price Format

The quoted price format of a bond like \(110-17\) is a shorthand commonly used in bond markets. Here, \(110\) represents the full percentage, and \(17\) after the dash indicates the fraction in 32nds. Thus, the quoted price in decimal form is \(110 + \frac{17}{32}\).
02

Convert Fraction to Decimal

Convert the fraction to a decimal by dividing the numerator by the denominator: \(\frac{17}{32} = 0.53125\).
03

Calculate Decimal Quoted Price

Add this fraction as a decimal to the whole part of the price: \(110 + 0.53125 = 110.53125\). This is the decimal quoted price of the bond.
04

Determine Accrued Interest

Since the coupon rate is \(12\%\) per annum, and the bond pays interest semi-annually, the coupon payment per period is \(\frac{12}{2} = 6\%\) of the face value per half-year. The bond was issued 12 months ago, with 3 months having passed since the last interest payment on February 15. The interest for these 3 months needs to be calculated as: \(100 \times \frac{12}{100} \times \frac{3}{12} = 3\).
05

Calculate Cash Price

The cash price is the sum of the quoted price and the accrued interest: \(110.53125 + 3 = 113.53125\). Therefore, the cash price of the bond is \(113.53\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quoted Price Format
In the bond market, the quoted price format is a commonly used method to express the price of bonds. The price is presented in a two-part format, such as "110-17." In this notation:
  • The number before the dash, here "110," represents the whole dollar value of the bond as a percentage of its face value. So, this indicates 110% of face value.
  • The number after the dash, "17," represents the fractional part of the percentage, expressed in thirty-seconds. So, "17/32" is equivalent to 0.53125 in decimal form.
By converting the fraction to a decimal and adding it to the whole dollar portion, investors can determine the bond's price in decimal form. This method ensures clarity and precision in pricing, which is crucial for effective trading in bond markets.
Accrued Interest
Accrued interest is the interest that accumulates on a bond between its coupon payment dates. It is important for buyers and sellers to understand this concept because it affects the cost and sale price of bonds.
  • Bonds typically pay interest at regular intervals, such as annually or semi-annually.
  • When a bond is sold, the buyer owes the seller the interest that has accrued since the last payment.
  • This interest is calculated based on the coupon rate, the principal amount, and the fraction of the period that has elapsed since the last payment.
For instance, if a bond has a 12% annual coupon rate and pays interest semi-annually, every six months, an investor needs to calculate how much interest has accrued if they buy the bond off-schedule. This is done to ensure fairness in transactions.
Coupon Rate
The coupon rate of a bond is a crucial concept for understanding how much an investor will earn from that bond. It is the annual interest rate paid on the bond's face value.
  • The coupon rate is expressed as a percentage. For example, a 12% coupon rate means the bond will pay 12% of its face value in interest annually.
  • These payments are typically made in equal installments, which can be annually, semi-annually, or even more frequently, depending on the bond's terms.
  • Investors use the coupon rate to assess the income they can expect from their investment before market influences, such as price changes or interest rate shifts.
Understanding the coupon rate helps investors make informed decisions about the potential profitability of owning a particular bond, as this figure directly relates to the cash flow they will receive over time.
Bond Market
The bond market is where investors go to buy and sell bonds. This marketplace is integral for raising capital and diversifying investment portfolios. Bonds are considered a safer investment compared to stocks, although they come with lower returns.
  • The bond market includes various types of bonds, such as government, municipal, and corporate bonds.
  • Investors in this market focus on factors like credit risk, interest rate risk, and the bond's term to maturity.
  • Trading bonds involves understanding terms like quoted price, accrued interest, and current market conditions which affect bond valuations.
For investors and institutions, the bond market provides opportunities to secure predictable income streams while balancing risks through carefully selecting bonds with favorable terms.

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Most popular questions from this chapter

It is July 30, 2009. The cheapest-to-deliver bond in a September 2009 Treasury bond futures contract is a \(13 \%\) coupon bond, and delivery is expected to be made on September 30,2009 . Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is \(12 \%\) per annum. The conversion factor for the bond is 1.5. The current quoted bond price is \(\$ 110\). Calculate the quoted futures price for the contract.

The 350 -day LIBOR rate is \(3 \%\) with continuous compounding and the forward rate calculated from a Eurodollar futures contract that matures in 350 days is \(3.2 \%\) with continuous compounding. Estimate the 440 -day zero rate.

Suppose that a Eurodollar futures quote is 88 for a contract maturing in 60 days. What is the LIBOR forward rate for the \(60-\) to 150 -day period? Ignore the difference between futures and forwards for the purposes of this question.

Suppose that a bobd portoulo with a duration of 12 years is hedged using a futures contract in which the underlying asset has a duration of 4 years. What is likely to be the impact on the hedge of the fact that the 12 -year rate is less volatile than the 4 -year rate?

Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 90 -day rate is \(10 \%\) per annum, and the 180 -day rate is \(10.2 \%\) per annum, both expressed with continuous compounding and actual/actual day count. The Eurodollar futures price for a contract maturing in 91 days is quoted as \(89.5 .\) What arbitrage opportunities are open to the bank?
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