Bond Pricing and Yield Fundamentals

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Questions and Answers

What is the main purpose of calculating bond prices?

To assess the real estate market conditions

To determine the stock market trends

To evaluate the relationship between bonds and yields (correct)

To find out the intrinsic value of company shares

Which of the following components is NOT used to calculate the price of a bond?

Future dividends from stocks (correct)

Future cash flows of the bond

Present value of the bond's face value

Present value of coupon payments

What does the yield to maturity (YTM) of a bond represent?

The rate of return on a bond if held until maturity (correct)

The constant coupon payments over the bond’s life

The average interest rate of the market

The current bond price as compared to face value

Which bond features allow for flexibility in management?

Putable bonds Signup and view all the answers

How is the coupon rate of a bond calculated?

Annual coupon divided by par value Signup and view all the answers

Which of the following statements about bond yields is true?

Current yield is based on the bond's price not the face value Signup and view all the answers

Why is interest rate risk significant for bond investors?

It can cause fluctuations in bond prices due to changes in interest rates Signup and view all the answers

What would a bond's price be if its yield to maturity is lower than its coupon rate?

It would increase above its face value Signup and view all the answers

What is true about premium bonds?

Coupon rate is greater than the YTM. Signup and view all the answers

If a bond is sold at a discount, which of the following must be true?

Coupon rate is less than YTM. Signup and view all the answers

What indicates a par bond?

Coupon rate equals the YTM. Signup and view all the answers

Which statement is correct about the relationship between term to maturity and bond price?

Longer maturity generally increases the premium for premium bonds. Signup and view all the answers

How is the current yield of a bond calculated?

Annual payment divided by current market price. Signup and view all the answers

Which of the following correctly describes the relationship among yield measures for discount bonds?

Coupon rate < current yield < YTM. Signup and view all the answers

When calculating yield to maturity (YTM), which aspect is considered?

The current price of the bond. Signup and view all the answers

What can be inferred about longer-term discount bonds?

They have a greater discount from par value. Signup and view all the answers

What does Macaulay’s Duration indicate for a bond?

The bond's effective maturity in years Signup and view all the answers

For a zero-coupon bond, how does the duration compare to its maturity?

Duration equals maturity Signup and view all the answers

What happens to the duration of a bond as its maturity increases, all else being equal?

Duration increases at a decreasing rate Signup and view all the answers

If a bond has a higher coupon rate, what is the expected effect on its duration?

Duration decreases Signup and view all the answers

What is the formula for calculating Macaulay’s Duration for a bond with constant semiannual coupons?

Duration = $rac{C}{YTM} imes rac{(1 - (1 + YTM)^{-M})}{YTM}$ Signup and view all the answers

What does the Dollar Value of an 01 measure in bond analysis?

The change in bond price due to a one basis point change in yield Signup and view all the answers

What type of bond selling at par would have a duration of less than its maturity?

A high coupon rate bond Signup and view all the answers

How does an increase in yield to maturity affect a bond's duration, holding all else constant?

Duration decreases Signup and view all the answers

How does the change in a bond's price relate to its term to maturity for a given change in yield to maturity (YTM)?

The price change increases at a diminishing rate. Signup and view all the answers

What is the relationship between the percentage change in bond price and the bond's coupon rate?

Inversely related; higher coupon rates lead to lower price changes. Signup and view all the answers

For a given absolute change in a bond’s yield to maturity (YTM), how does the price change compare between a decrease and an increase in yield?

The decrease in yield causes a greater price increase than the increase in yield causes a price decrease. Signup and view all the answers

What does Macaulay Duration measure in relation to bond prices?

The average time until cash flows are received. Signup and view all the answers

What is the primary benefit of dynamic immunization for a bond portfolio?

It reduces reinvestment risk caused by fluctuating bond yields. Signup and view all the answers

How does Modified Duration differ from Macaulay Duration?

It accounts for changes in yield to maturity in its formula. Signup and view all the answers

What is the formula to estimate the percentage change in bond price for a given change in YTM?

Pct.Change in Bond Price = - Duration × (Change in YTM / (1 + YTM)^2) Signup and view all the answers

What is a potential drawback of implementing dynamic immunization?

Accumulation of management and transaction costs. Signup and view all the answers

When comparing two bonds with the same duration, what is expected regarding their price sensitivity to yield changes?

They will have equal price sensitivity to yield changes. Signup and view all the answers

What does duration matching in a dedicated portfolio aim to achieve?

Offset the effects of interest rate changes on portfolio value. Signup and view all the answers

Which of the following is NOT a component of Malkiel’s Theorems?

Price risk in dedicated portfolios. Signup and view all the answers

If a bond has a Macaulay Duration of 10 years and a YTM of 7%, what will happen if the YTM increases to 7.5%?

The percentage change in price will be estimated as negative. Signup and view all the answers

What is the primary focus of a dedicated portfolio?

Aligning cash flows to meet specific future obligations. Signup and view all the answers

What is the total value Safety First expects to have in five years from the coupons and face value combined?

$100,000,000 Signup and view all the answers

What is reinvestment rate risk primarily associated with?

The need to reinvest bond coupons Signup and view all the answers

Which of the following is indicated as a simple solution to mitigate reinvestment rate risk?

Purchasing zero coupon bonds Signup and view all the answers

How does an increase in interest rates affect a dedicated bond portfolio?

It decreases bond prices but increases future cash flows from reinvested coupons Signup and view all the answers

What is the current yield of the Treasury STRIPS mentioned in the content?

7.75 percent Signup and view all the answers

What is price risk in the context of dedicated portfolios?

Risk that bond prices will decrease Signup and view all the answers

What does immunization aim to achieve in bond portfolio management?

Minimize uncertainty surrounding the target date value Signup and view all the answers

What is the estimated cost of removing reinvestment risk using STRIPS compared to Safety First's necessity?

$817,370 Signup and view all the answers

Study Notes

Chapter 10: Bond Prices and Yields

Bonds are an important part of portfolios
Key learning objectives include calculating bond prices and yields, understanding yield to maturity, learning about interest rate risk and Malkiel's theorems, and measuring the impact of interest rate changes on bond prices.
Goal is to understand the relationship between bond prices and yields, and the fundamental tools fixed-income portfolio managers use to assess bond risk.

Bond Basics, I

A straight bond is an IOU obligating the issuer to pay a fixed sum of money (principal, par, or face value) at maturity, plus constant periodic interest payments (coupons) during the bond's life.
U.S. Treasury bonds are a type of straight bond
Special features like convertible, callable, and putable bonds can be added.

Bond Basics, II

Two basic yield measures are coupon rate and current yield.
Coupon rate = Annual coupon / Par value
Current yield = Annual coupon / Bond price

Straight Bond Prices and Yield to Maturity

Bond price is the sum of the present values of coupon payments and the face value.
Yield to maturity (YTM) is the discount rate that equates the present value of future cash flows to today's bond price.

The Bond Pricing Formula

Bond Price = C /2 (1 - 1/(1 + YTM/2)^2M ) + FV / (1 + YTM/2)^2M
- C = annual coupon payments
- FV = face value
- YTM = yield to maturity
- M = maturity of the bond

Example: Using the Bond Pricing Formula

Example calculation for a straight bond with given values (face value, coupon rate, YTM, maturity).

Example: Calculating the Price of this Straight Bond Using Excel

Excel function called PRICE calculates bond prices
Function uses arguments like settlement date, maturity date, coupon rate, YTM, par value, frequency and actual / 365 day count to generate the bond price.

Spreadsheet Analysis, I

Spreadsheet example using the PRICE function to calculate the price of a coupon bond.
Spreadsheet use semi-annual coupon and 365/year day count to determine pricing.

Premium, Par, and Discount Bonds, I

Bonds are categorized as premium, par, or discount based on the selling price vs. par value
Premium bond: Coupon rate > YTM; Price > Face
Discount bond : Coupon rate < YTM; Price < Face
Par bond: Coupon rate = YTM; Price = Face

Premium, Par, and Discount Bonds, II

Graph showing relationship between bond prices (% of par) and time to maturity for premium, par, and discount bonds.

Premium, Par, and Discount Bonds, III

When coupon rate and YTM are constant, the longer the term to maturity, the greater the premium (for premium bonds) or discount (for discount bonds) over par.

Relationships among Yield Measures

YTM > current yield > coupon rate for premium bonds
YTM < current yield < coupon rate for discount bonds
Current yield = Annual coupon payment / Current market price for par value bonds

Calculating Yield to Maturity, I

Process of finding YTM given current price, coupon rate, and time to maturity.
Methods include trial-and-error approach, financial calculators, and spreadsheets.

Calculating Yield to Maturity, II

Excel function YIELD calculates YTM

A Quick Note on Bond Quotations, I

Clean price : Bond price quoted without accrued interest.
Dirty price : Acutal price the buyer pays, including accrued interest (also called invoice price).

A Quick Note on Bond Quotations, II

Clean price = quoted price excluding accrued interest
Dirty price = Clean price + accrued interest = actual price paid

A Quick Note on Bond Quotations, III

Example calculation using clean price and accrued interest to find the dirty/invoice price for a bond.

Callable Bonds

Callable bond gives the issuer the option to buy back the bond before maturity at a specified call price.
Yield to call (YTC): Yield assuming the bond is called at its earliest possible call date. Formula for calculating callable bond price is provided.

Spreadsheet Analysis, III

Examples using Excel functions DURATION and MDURATION calculate Macaulay's duration and Modified duration of a callable bond.

Interest Rate Risk

Interest rate risk: possibility of losses due to interest rate changes.
Realized yield: Actual return earned on a bond; almost never equal to the YTM.

Interest Rate Risk and Maturity

Graph showing how bond prices decrease as yields increase, with longer maturity bonds showing higher sensitivity.

Malkiel's Theorems, I

Bond prices and bond yields move in opposite directions.
Larger change in bond price with longer maturity bonds for a given YTM change.

Malkiel's Theorems, II

Size of price change decreases as maturity increases for a given YTM change.
Percentage change in price is inversely related to coupon rate.
Magnitude of price increase for a decrease is greater than magnitude of price decrease for an increase.

Bond Prices and Yields (numerical examples)

Duration

Macaulay Duration measures the sensitivity of bond price to yield changes.
Formula for duration is given; two bonds with same duration but not necessarily same maturity will have similar price sensitivity

Example: Using Duration

Modified Duration

Modified duration is a variation of Macaulay duration for measuring bond price sensitivity to yield changes.

Calculating Macaulay's Duration, I

Macaulay's Duration values are expressed in years.
Duration for zero-coupon bond equals its maturity
Duration for coupon bond is a weighted average of individual maturities of the bond's separate cash flows, weighted proportionately to their present values.

Calculating Macaulay's Duration for Par Bonds

Duration formula for par-value selling bond given. Example calculation provided for the given values.

Calculating Macaulay's Duration, II

General formula for Macaulay's duration with constant, semi-annual coupons.

Calculating Macaulay's Duration: Example

Steps to calculate duration and modified duration for a given bond.

Calculating Macaulay Duration and Modified Duration, using Excel

Using Excel functions DURATION and MDURATION to calculate Macaulay and Modified duration given bond data.

Calculating Duration Using Excel, Explanation

Using DURATION and MDURATION excel functions to calculate bond duration and modified duration.

Duration Properties

Longer maturity bond, longer duration
Duration increases at a decreasing rate as maturity lengthens.
Higher coupon rate, shorter duration.
Higher yield to maturity, shorter duration.

Properties of Duration (Graph)

Graph showing relationship between bond duration and maturity for differing coupon rates.

Bond Risk Measures Based on Duration, I

Dollar Value of an 01: Change in bond price due to a one-basis-point change in yield
Yield Value of a 32nd: Change in yield needed for a 1/32nd change in bond price. Bond prices are per $100 face value.

Bond Risk Measures Based on Duration, II

Example problem to calculate the 01and(1)/32ndyieldvaluegivenamodifiedduration.Bondpricesareper01 and (1)/32nd yield value given a modified duration. Bond prices are per 01and(1)/32ndyieldvaluegivenamodifiedduration.Bondpricesareper100 face value

Dedicated Portfolios

Dedicated portfolio tailored for a future cash outlay (e.g., pension fund), also known as a target date portfolio.

Dedicated Portfolios: Scenario

Example of a pension fund needing to estimate future payout (e.g., $100 million in five years).

Dedicated Portfolios: Example

Solving for the present value required to have an amount $100 million in the future.
Using a specific interest rate and time period in an example, in calculating the amount that will be needed in present value
Calculating investment amount to reach a future value given coupon rate, YTM, and time period

Dedicated Portfolios: How Does it Work?

Illustrating the calculation and investment needed to generate the correct targeted payout amount for a dedicated portfolio.

Reinvestment Risk

Risk of uncertainty regarding the future value of reinvesting bond coupon payments at unknown yields.

The Cost of Removing Reinvestment Risk Using STRIPS

Illustrates the calculation to determine the present value of zero coupon bonds to reach a set future value at an expected yield.

Price Risk

Risk that bond prices will decrease due to future uncertainty, which is an aspect of price risk in dedicated portfolios.

Price Risk versus Reinvestment Rate Risk

Interest rate increases decrease bond prices but increase future value of coupons, which are reinvested
Interest rate decreases increase bond prices but decrease future value of reinvested coupons.

Immunization

Making a bond portfolio minimizing future value uncertainty surrounding target date values

Immunization by Duration Matching, I

Duration matching strategy to immunize a portfolio, where its duration matches the portfolio's target date resulting in minimal price risk.

Immunization by Duration Matching, II

Graph illustrating how matching portfolio duration and target maturity date minimizes price risk resulting from fluctuations in interest/coupon rates.

Dynamic Immunization

Periodic rebalancing of a dedicated bond portfolio to maintain a duration that matches the target maturity date.

Chapter Review, I

Brief overview of bond basics, straight bond pricing, premium/discount bonds, yield measures

Chapter Review, II

More detail on yields, yield to call, interest rate risk, and Malkiel's theorems

Chapter Review, III

Summarization of duration, dedicated portfolios, reinvestment risk, immunization, price risk, and dynamic immunization.

Studying That Suits You

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Description

Test your understanding of bond pricing and yield concepts in this quiz. Questions cover key aspects such as yield to maturity, coupon rates, and various bond features. Perfect for finance students or anyone looking to brush up on their bond knowledge.