Penulis: Dzanh Nguyen
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
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
Principal repayment can call for:
Total principal repaid at maturity or
Principal repaid over life of bond
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)
Credit spread risk
Exchange Rate 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]
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
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]
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
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 = 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]
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
Graph of yield of bonds with same credit rating but different maturities
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?
Pure expectations Theory
No systematic factors other than expected future short term rates affects forward rates
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
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?
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
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.
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
Portfolio is constructed so that the maturity of the securities in the portfolio are highly concentrated at one point on the yield curve
The maturity of the portfolio securities are concentrated on two extreme maturities
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
Capital gains at maturity
Interest income from reinvestment
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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