Bond Valuation and Zero-Coupon Bonds
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Questions and Answers

What does the yield curve primarily represent?

  • The performance of real estate investments.
  • The fluctuations of a currency against another.
  • The prices of various stocks over time.
  • The relationship between interest rates and the maturity of debt. (correct)

Which bond does NOT include default risk in its pricing?

  • Zero-coupon bonds (correct)
  • Municipal bonds
  • Treasury bonds (correct)
  • Corporate bonds

How can the price of a coupon bond be determined according to the Law of One Price?

  • By summing the face values of similar bonds.
  • By reconstructing its cash flows using zero-coupon bonds. (correct)
  • By applying market trends to its projected sales.
  • By averaging its past sale prices.

What is a key feature of default-free zero-coupon bonds?

<p>They do not pay any interest until maturity. (D)</p> Signup and view all the answers

What does it indicate if a bond is trading at a price that differs from the calculated price using the Law of One Price?

<p>The bond is experiencing arbitrage opportunities. (B)</p> Signup and view all the answers

What is the primary benefit of using zero-coupon bonds for replicating coupon bond cash flows?

<p>They match specific cash flow timings effectively. (C)</p> Signup and view all the answers

What should an investor consider regarding the internal rate of return when evaluating different bonds?

<p>It represents the projected growth rate of the investment. (A)</p> Signup and view all the answers

What is the primary purpose of using zero-coupon bond yields in relation to coupon bonds?

<p>To derive the price of the coupon bond. (B)</p> Signup and view all the answers

What is the primary plot of coupon-paying yield curves based on?

<p>Yields of coupon bonds with different maturities (A)</p> Signup and view all the answers

What happens if the price of the coupon bond is higher than expected?

<p>Arbitrage profit can be earned by selling the coupon bond. (C)</p> Signup and view all the answers

What do practitioners generally refer to when they mention 'the yield curve'?

<p>The coupon-paying Treasury yield curve (C)</p> Signup and view all the answers

How is the price of a coupon bond calculated using zero-coupon bond yields?

<p>By using the present value of future cash flows discounted at market interest rates. (A)</p> Signup and view all the answers

Why might two coupon bonds with the same maturity have different yields?

<p>Due to differences in credit ratings or issuer risk (D)</p> Signup and view all the answers

What does 'YTM' stand for in the context of zero-coupon bonds?

<p>Yield to maturity. (D)</p> Signup and view all the answers

What occurs when the coupon bond's price is lower than expected?

<p>Arbitrage profit can be made by buying the coupon bond and short selling zero-coupon bonds. (B)</p> Signup and view all the answers

How can zero-coupon bond yields be determined from the coupon-paying yield curve?

<p>Via the Law of One Price (D)</p> Signup and view all the answers

What is implied when a bond has a high credit risk?

<p>Its cash flows are uncertain and may not return the full promised amount (B)</p> Signup and view all the answers

Which of the following factors is included in the present value calculation of a coupon bond?

<p>Future coupon payments and eventual face value. (C)</p> Signup and view all the answers

What characterizes a default-free zero-coupon bond?

<p>The payout at maturity is known with certainty (D)</p> Signup and view all the answers

What can be inferred if a coupon bond has a higher quality rating than a zero-coupon bond?

<p>The coupon bond will offer lower returns. (D)</p> Signup and view all the answers

Which of the following best describes a coupon bond?

<p>A bond that makes periodic interest payments until maturity (A)</p> Signup and view all the answers

Which statement best describes arbitrage in the context of coupon bonds and zero-coupon bonds?

<p>Arbitrage involves taking a long position in one bond and shorting the other. (C)</p> Signup and view all the answers

How does the presence of arbitrage affect the pricing of bonds with different ratings?

<p>It can lead to mispricing if not corrected (C)</p> Signup and view all the answers

Flashcards

Yield Curve

The relationship between yields of bonds with different maturities at a given point in time.

Replicating a Coupon Bond

The process of using zero-coupon bonds to replicate the cash flows of a coupon bond.

Zero-Coupon Bond

Default-free bonds that pay only one payment at maturity, the face value.

Law of One Price

The principle that two assets with identical cash flows should have the same price.

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Spot Interest Rate

The yield of a zero-coupon bond with a maturity equal to the time to the next coupon payment.

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Yield to Maturity (YTM)

The implied yield of a coupon bond calculated based on the prices of zero-coupon bonds with matching maturities.

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Bond Arbitrage

A strategy that exploits differences in the prices of bonds to generate a risk-free profit.

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Why is the Yield Curve Important?

The yield curve provides sufficient information to determine the price and yield of any other default-free bond because we can replicate the cash flows of any coupon bond using zero-coupon bonds.

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Coupon-Paying Yield Curve

The plot of yields of coupon bonds with different maturities.

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U.S. Treasury Yield Curve

The yield curve for U.S. Treasury bonds, where U.S. bond traders often refer to 'the yield curve'.

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On-The-Run Bonds

The most recently issued bonds, typically used in creating a yield curve.

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Calculating Coupon Bond Price from Zero-Coupon Prices

Using the prices of zero-coupon bonds to find the price of a coupon bond.

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Calculating Coupon Bond Price from Zero-Coupon Yields

Using the yields of zero-coupon bonds to find the price of a coupon bond.

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Different Yields for Same Maturity Bonds

Two coupon bonds with the same maturity can have different yields due to factors such as coupon rates and timing of cash flows.

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Credit Risk

The risk that the issuer of a corporate bond might not repay the full amount owed.

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Default

The potential for a company to default on its bonds, leading to uncertainty in bond cash flows.

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Pricing Coupon Bonds with Zero-Coupon Yields

The price of a coupon bond should equal the present value of its coupon payments and face value discounted at the market interest rates implied by zero-coupon bonds.

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Zero-Coupon Bond Yield

The yield to maturity of a zero-coupon bond is the competitive market interest rate for a risk-free investment with a term equal to the term of the zero-coupon bond.

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Coupon Bond Arbitrage

A strategy involving buying or selling a coupon bond and a portfolio of zero-coupon bonds to exploit price differences and earn a risk-free profit.

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Arbitrage Profit from High Coupon Bond Price

If the price of the coupon bond is higher than the present value of its cash flows discounted using zero-coupon bond yields, you can earn a risk-free profit by selling the coupon bond and buying a portfolio of zero-coupon bonds.

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Arbitrage Profit from Low Coupon Bond Price

If the price of a coupon bond is lower than the present value of its cash flows discounted using zero-coupon bond yields, you can earn a risk-free profit by buying the coupon bond and short-selling zero-coupon bonds.

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Present Value of Coupon Bond Cash Flows

The present value of a coupon bond's cash flows is calculated by discounting each coupon payment and the face value using the corresponding zero-coupon bond yields.

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Zero-Coupon Yields as Interest Rates

The competitive market interest rates for risk-free investments with different maturities.

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Coupon Bond Price and Zero-Coupon Yields

The price of a coupon bond must be equal to the present value of its cash flows discounted at the zero-coupon yields.

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Study Notes

Bond Valuation

  • Bonds are securities issued by governments or corporations to raise funds, promising future payments.
  • Bond certificates detail payment amounts and dates, including a maturity date, the time until repayment.
  • Coupon payments are periodic interest payments, while the face value is the principal amount repaid at maturity.
  • Coupon rates, set by the issuer, determine the coupon payment size.
  • Zero-coupon bonds don't offer periodic interest, delivering only the face value at maturity.
  • Bond prices are inversely related to yields (interest rates); higher yields correlate with lower prices, and vice versa.
  • Yields to maturity (YTM) represent the discount rate that makes the present value of all future cash flows equal to the current bond price. This is the return investors will earn if they hold a bond until maturity.

Zero-Coupon Bonds

  • Zero-coupon bonds trade at discounts (prices lower than their face value).
  • The yield to maturity on a zero-coupon bond is the discount rate making the present value of the promised face value equal to the current price.
  • The formula for the yield to maturity calculation of an n-year zero-coupon bond is provided: YTM = (FV / P)^(1/n) - 1.
  • FV stands for future value or face value
  • P is the current price

Coupon Bonds

  • Coupon bonds make periodic coupon payments in addition to the face value at maturity.
  • Bond prices fluctuate around coupon payment dates.
  • A coupon bond trades at a discount if the yield to maturity exceeds the coupon rate.
  • A premium is when the coupon rate exceeds the yield to maturity
  • A coupon bond trades at par when its coupon rate and yield to maturity are equal.

Time and Bond Prices

  • Bond prices rise as the maturity date approaches, with all else being equal.
  • A bond's price declines when a coupon is paid.
  • Bond prices are sensitive to interest rate fluctuations.

Risk-Free Interest Rates

  • The yield to maturity of a risk-free bond (zero-coupon bond) approximates the risk-free interest rate for a specific maturity.
  • The yield curve, which plots the risk-free interest rates for various maturities, also reflects expectations about inflation and economic growth.

Corporate Bonds

  • Corporate bonds have credit risk (the potential for the issuer to default).
  • Investors demand higher yields for corporate bonds than for similar risk-free securities; there is risk involved.
  • Bond ratings, from agencies like Standard & Poor's, provide assessment of the credit risk of corporate bonds. High ratings indicate less likely default.
  • Credit risk and default will affect the cash flows that investors expect to see
  • The price they are willing to pay for a corporate bond will decrease if the likelihood of default increases
  • Credit spreads or default spreads are the difference in yields between corporate bonds and risk-free bonds

Sovereign Bonds

  • Sovereign bonds are issued by national governments.
  • Sovereign bonds can have default risk (the risk the national government will not repay its debts).
  • Sovereign bond yields reflect investors' expectations of inflation, currency, and default risks.

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Valuing Bonds Chapter 6 PDF

Description

Explore the fundamentals of bond valuation and the unique characteristics of zero-coupon bonds. Understand how coupon rates influence payments, the importance of yields to maturity, and the relationship between bond prices and interest rates. This quiz covers essential concepts for students and investors alike.

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