**Judul: BondsPenulis: Dzanh Nguyen**

Introduction

What are the fundamental features of a bond? How do these features influence the expected cash flows, risk, and return of the bond?

Nature of issuer

Federal government

Municipal Governments

Corporations

Term to Maturity

Principal and Coupon Rates

Floating rate bonds – coupon rates reset periodically

Coupon Reset Formula = reference rate + quoted margin

Ex. 30 day LIBOR + 150 BPs

Linkers – bonds with inflation tied interest rates

Inverse Floating Rate Bonds – moves opposite of interest rates

Amortization Feature

Principal repayment can call for:

Total principal repaid at maturity or

Principal repaid over life of bond

Embedded Options

Call Provision – issuer right to retire debt fully or partially before maturity

Put Option – Holder right to sell back at par value on set dates

Convertible Bond – can exchange bond for comm stock

Exchangeable Bond – can exchange bond for specified # of shares of a corporation different from the issuing corporation

What are the various types of risk faced by investors in fixed-income securities?

Interest Rate Risk/Market Risk

Reinvestment Risk (pg.8)

Call Risk

Credit Risk

Default risk

Credit spread risk

Downgrade risk

Inflation Risk

Exchange Rate Risk

Liquidity Risk

Volatility Risk

Risk RiskPricing of Bonds

Be able to estimate the price of a bond [Refer to the assigned problems at the end of the chapter]

Pg. 32

Explain the relationship between price, coupon, and required yield? How would you characterize the 'shape' of this relationship?

Coupon and Price move together

Price and Yield move inversely

Price of the bond is PV of cash flows

Price Yield has a "bowed relationship"

When yield>coupon rate => price<par value (selling at discount)

Bond price will move towards par as it reaches maturity

Explain why bond prices change?

Δ Required yield owing to Δ credit quality of issuer

Δ Required yield owing to Δ yield of comparable bonds

Δ price of bond selling at premium or discount w/o Δ in required yield, simply because bond is maturing

Measuring Yields

Tax Stuff

After Tax Yield = Pretax Yield x (1 - marginal tax rate)

Equivalent Taxable Yield=tax-exempt yield1-marginal tax rateBe able to estimate the current yield, YTM, YTC, YTP, and cash flow yield of a bond [Refer to the assigned problems at the end of the chapter]

Pg. 55

YTM

Be able to calculate yield for a portfolio [Refer to the assigned problems at the end of the chapter]

CF of a portfolio discounted by the interest rate that will make them equal to the market value of the portfolio

Explain the limitations of the conventional measure of yield in the context of the reinvestment risk. Be able to calculate total return for a bond and explain the strength of this measure.

Other sources of Dollar Return:

Coupon payments from issuer

Capital gain when bond matures, is called, or sold

Interest income generated from reinvestment of CF

Current Yield only considers coupon payments

YTM, YTC, and CF Yield all take into account these 3 components

Bond Price Volatility

In the context of the shape of the price-yield relationship, explain how the characteristics of the bond affect its price volatility.

↓Coupon Rate ↑Volatility

↑TTM ↑Volatility

Be able to calculate the following measures of bond price volatility:

Price value of a basis point

ΔPrice resulting in a 1BP ΔRequired Yield

Yield value of a price change

Estimate bond's YTM if price ↓ by X dollars

Initial Yield – New Yield = Yield value of X dollar change

Modified Duration

Macaulay Duration:

Modified = Macaulay duration1+y Portfolio Duration

Weighted average of the bond durations in portfolio

Explain how duration and price sensitivity (such as percentage price change or dollar price change) are related?

% Change in Price

∆PP= -modified duration × ∆yDollar Price Change

∆P∆y= -modified duration × P% Change in Price due to Convexity

∆PP=12convexity measure∆y2Dollar Convexity=∆P∆Y2convexity measure in years=convexity measure in m period year per yearm2What are the limitations of using duration to estimate bond price sensitivity? Explain how convexity measures are better.

Duration does not account for large changes in yield

approximate duration=P--P+2(P0)(Δy)Convexity captures the ends of the Price-Yield curve

approximate convexity measure=P++P--2P0P0∆y2Estimate the convexity measure of a bond using the approximate formula [Refer to the assigned problems at the end of the chapter]

Pg. 90

Using the duration and convexity measures, estimate the percentage price change for a bond for a given change in required yield. [Refer to the assigned problems at the end of the chapter]

Factors affecting Bond Yields and Term Structure of Interest Rates

Explain why yields on US treasury securities are used as benchmark rates.

US Treasuries have no credit risk

What are relative yields and what factors influence them?

Measure of risk premium by taking ratio of yield spread to yield level

Realtive Yield Spread=yield bond A-yield bond Byield bond BSpreads interact with economy

Spreads tighten when economy is growing

Spreads widen when economy is slowing

Financial crisis – ultimate flight to safety

Yield Curve

Graph of yield of bonds with same credit rating but different maturities

Pg. 115

What are Spot Rates and how do we estimate them? Why are these the best rates to use in valuing bonds?

Rates that apply from today until some future date. Zero Coupon: Yield of a zero coupon treasury with the same maturity. Best rates because you use the unique interest rate to discount the CF when you receive it rather than one discount rate for all CFs

Given coupon bonds and their required yields, how can we estimate theoretical spot rates?

How is the theoretical spot rate used in pricing bonds?

P=CF11+S121+CF21+S222+CF3+M1+S323Expectations Theory:

Pure expectations Theory

No systematic factors other than expected future short term rates affects forward rates

Liquidity Theory

Forward rates AREN'T an unbiased estimate of market expectations for future interest rates because they embody a liquidity premium

Preferred Habitat Theory

Also adopts the view that term structure reflects the expectation of the future path of interest rate as well as a risk premium

Risk premium does NOT rise uniformly with maturity

Market Segmentation Theory

Investors have preferred habitats dictated by the nature of their liabilities

Investors and borrowers aren't willing to shift from one maturity sector to another

Explain the relation between spot rates and forward rates.

fn=1+Sn+1n+11+Snn-1Treasury and Federal Agency Securities

What are the various types of securities issued by the U.S. Department of Treasury?

3 month, 6 month, 1 year Bills

zero coupon

2, 5,and 10 year Notes

30 year Bonds

How are the features of TIPS different from the regular treasury securities? What are the pros and cons for the issuer and the investor?

TIPS

Adjusts the principal of a bond semiannually

Describe the Auction process used to issue treasury securities.

Sealed bidding process that are competitive or noncompetitive

Noncompetitive – bid that is willing to purchase the auctioned security at the yield that is determined by the auction process

Competitive – specifies the quantity sought and the yield at which the bidder is willing to purchase the auctioned security

Estimate the yield on a bank discount basis? Are there any problems with this estimate of yield? [Refer to the assigned problems at the end of the chapter]

Yd=(DF)(360t)Y = annualized yield on bank discount basis (decimal)

D = dollar discount (face value – price)

F = Face Value

t = number of days remaining to maturity

Given a price quote for a treasury coupon security, estimate the dollar price. [Refer to the assigned problems at the end of the chapter]

Rearrange above equation and solve for D

Explain how the stripped treasury securities are created.

Separating the interest on a bond from the underlying coupon

Done to create zero coupon instruments with no credit risk

Repo Market

Explain the basic structure of a bilateral repo transaction, identifying the parties involved.

Sale of security with a commitment by the seller to buy the same security back from the purchaser at a specified price (repurchase price) and date (repurchase date).

Like a collateralized loan where the collateral is the security sold and subsequently repurchased

The interest rate is called the repo rate. One-day loan is called overnight repo. More than one day is called term repo.

Ex. Government security dealer purchased $10MM of a particular Treasry security. The dealer uses the security as collateral to obtain financing from an entity (a municipality that just collected taxes) that has $10MM in excess cash. Suppose the dealer seeks an overnight repo with a rate of 6.5%. The dealer would sell the $10MM for $9,998,195 (the $1,805 difference is (6.5%/360)). The dealer would then pay back the full $10MM to get their securities back.

Trading Strategies

Be able to explain the structure of the trading strategies discussed in class (Long/Short)

Yield Curve Strategies such as bullet/barbell, Steepeners/Flatteners

Flattening of the Yield Curve

The yield spread between the yield on a long term and a short term treasury has decreased

Sell bonds with lower maturities

Buy bonds with higher maturities

Steepening of the yield curve

The yield spread between the yield on a long term and a short term treasury has increased

Buy bonds with lower maturities

Sell bonds with higher maturities

Bullet Strategy

Portfolio is constructed so that the maturity of the securities in the portfolio are highly concentrated at one point on the yield curve

Barbell Strategy

The maturity of the portfolio securities are concentrated on two extreme maturities

Maturity Importance

Gives time period of the life of the bond and coupon payments

Yield depends on maturity (yield curve shape)

Price volatility moves with maturity (↑Maturity ↑Volatility)

Potential Sources of Dollar Return

Coupon payments

Capital gains at maturity

Interest income from reinvestment

Duration Limitations

Only accounts for small yield changes (no convexity)

Assumes all cash flows discounted at same rate (flat yield curve)May not apply to bonds with embedded options (unpredictable cash flows)

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