Bond prices and yields
This presentation is the property of its rightful owner.
Sponsored Links
1 / 115

Bond Prices and Yields PowerPoint PPT Presentation


  • 170 Views
  • Uploaded on
  • Presentation posted in: General

Bond Prices and Yields. CHAPTER 14. Bond Characteristics. Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture. Different Issuers of Bonds. U.S. Treasury Notes and Bonds Corporations Municipalities

Download Presentation

Bond Prices and Yields

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Bond prices and yields

Bond Prices and Yields

CHAPTER 14


Bond characteristics

Bond Characteristics

  • Face or par value

  • Coupon rate

    • Zero coupon bond

  • Compounding and payments

    • Accrued Interest

  • Indenture

Bahattin Buyuksahin, Derivatives Pricing


Different issuers of bonds

Different Issuers of Bonds

  • U.S. Treasury

    • Notes and Bonds

  • Corporations

  • Municipalities

  • International Governments and Corporations

  • Innovative Bonds

    • Floaters and Inverse Floaters

    • Asset-Backed

    • Catastrophe

Bahattin Buyuksahin, Derivatives Pricing


Figure 14 1 listing of treasury issues

Figure 14.1 Listing of Treasury Issues

Bahattin Buyuksahin, Derivatives Pricing


Figure 14 2 listing of corporate bonds

Figure 14.2 Listing of Corporate Bonds

Bahattin Buyuksahin, Derivatives Pricing


Provisions of bonds

Provisions of Bonds

  • Secured or unsecured

  • Call provision

  • Convertible provision

  • Put provision (putable bonds)

  • Floating rate bonds

  • Preferred Stock

Bahattin Buyuksahin, Derivatives Pricing


Convertible bonds

Convertible Bonds

  • Give bondholders an option to exchange each bond for a specified nb of shares of common stock

  • Conversion ratio

    • = number of shares per convertible bond

  • Market conversion value

    • = conversion ratio * current market value per share

  • Conversion premium

    • = bond value - conversion value

    • intuitively: extra amount to pay so as to become a shareholder

  • Bahattin Buyuksahin, Derivatives Pricing


    Conversion example

    Conversion Example

    Bahattin Buyuksahin, Derivatives Pricing


    Conversion example1

    Conversion Example

    Bahattin Buyuksahin, Derivatives Pricing


    Innovation in the bond market

    Innovation in the Bond Market

    • Inverse Floaters

    • Asset-Backed Bonds

    • Catastrophe Bonds

    • Indexed Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Table 14 1 principal and interest payments for a treasury inflation protected security

    Table 14.1 Principal and Interest Payments for a Treasury Inflation Protected Security

    Bahattin Buyuksahin, Derivatives Pricing


    Bond prices and yields1

    Bond Prices and Yields

    • Time value of money and bond pricing

    • Time to maturity and risk

    • Yield to maturity

      • vs. yield to call

      • vs. realized compound yield

  • Determinants of YTM

    • risk, maturity, holding period, etc.

  • Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing

    PB=Price of the bond

    Ct = interest or coupon payments

    T = number of periods to maturity

    y = semi-annual discount rate or the semi-annual yield to maturity

    Bond Pricing

    Bahattin Buyuksahin, Derivatives Pricing


    Price 10 yr 8 coupon face 1 000

    Price: 10-yr, 8% Coupon, Face = $1,000

    Ct= 40 (SA)

    P= 1000

    T= 20 periods

    r= 3% (SA)

    Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing1

    Bond Pricing

    • Equation:

      • P = PV(annuity) + PV(final payment)

      • =

  • Example: Ct = $40; Par = $1,000; disc. rate = 4%; T=60

  • Bahattin Buyuksahin, Derivatives Pricing


    Bond prices and yields2

    Bond Prices and Yields

    • Prices and Yields (required rates of return) have an inverse relationship

    • When yields get very high the value of the bond will be very low

    • When yields approach zero, the value of the bond approaches the sum of the cash flows

    Bahattin Buyuksahin, Derivatives Pricing


    Prices vs yields

    Prices vs. Yields

    • P   yield 

      • intuition

  • convexity

    • Fig 14.3

    • intuition: yield   P   price impact 

  • Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 3 the inverse relationship between bond prices and yields

    Figure 14.3 The Inverse Relationship Between Bond Prices and Yields

    Bahattin Buyuksahin, Derivatives Pricing


    Table 14 2 bond prices at different interest rates 8 coupon bond coupons paid semiannually

    Table 14.2 Bond Prices at Different Interest Rates (8% Coupon Bond, Coupons Paid Semiannually)

    Bahattin Buyuksahin, Derivatives Pricing


    Yield to maturity

    Yield to Maturity

    • Interest rate that makes the present value of the bond’s payments equal to its price

      Solve the bond formula for r

    Bahattin Buyuksahin, Derivatives Pricing


    Yield to maturity example

    Yield to Maturity Example

    10 yr MaturityCoupon Rate = 7%

    Price = $950

    Solve for r = semiannual rate

    r = 3.8635%

    Bahattin Buyuksahin, Derivatives Pricing


    Yield measures

    Yield Measures

    Bond Equivalent Yield

    7.72% = 3.86% x 2

    Effective Annual Yield

    (1.0386)2 - 1 = 7.88%

    Current Yield

    Annual Interest / Market Price

    $70 / $950 = 7.37 %

    Yield to Call

    Bahattin Buyuksahin, Derivatives Pricing


    Pure discount bonds zero coupon bonds

    Pure Discount Bonds (Zero-Coupon Bonds)

    A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T

    • Discount bonds, also called zero-coupon bonds, are securities which “make a single payment at a date in the future known as maturity date. The size of this payment is the face value of the bond. The length of time to the maturity date is the maturity of the bond” (Campbell, Lo, MacKinley (1996)).

    Bahattin Buyuksahin, Derivatives Pricing


    Pure discount bond

    Pure Discount Bond

    • The promised cash payment on a pure discount bond is called its face value or par value. Yield (interest rate) on a pure discount bond is the annualized rate of return to investors who buy it and hold it until it matures.

    Bahattin Buyuksahin, Derivatives Pricing


    Example

    Example

    Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing2

    Bond Pricing

    • To calculate the cash price of a bond we discount each cash flow at the appropriate zero rate

    • The theoretical price of a two-year bond providing a 6% coupon semiannually is

    Bahattin Buyuksahin, Derivatives Pricing


    Bond yield

    Bond Yield

    • The bond yield is the discount rate that makes the present value of the cash flows on the bond equal to the market price of the bond

    • Suppose that the market price of the bond in our example equals its theoretical price of 98.39

    • The bond yield is given by solving

      to get y = 0.0676 or 6.76%.

    Bahattin Buyuksahin, Derivatives Pricing


    Par yield

    Par Yield

    • The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value.

    • In our example we solve

    Bahattin Buyuksahin, Derivatives Pricing


    Par yield continued

    Par Yield (continued)

    In general if m is the number of coupon payments per year, d is the present value of $1 received at maturity and A is the present value of an annuity of $1 on each coupon date

    Bahattin Buyuksahin, Derivatives Pricing


    Bootstrap method to calculate discount factor

    Bootstrap Method to calculate discount factor

    • A discount function is a set of discount factors, where each discount factor is just a present value multiplier. For example, d(1.0) is the present value of $1 dollar received in one year. The key idea is that each d(x) can be solved as one variable under one equation because we already solved for shorter-term discount factors.

    • The most popular approach is to use bootstrap method

    Bahattin Buyuksahin, Derivatives Pricing


    Bootstrap example

    Bootstrap : Example

    Bahattin Buyuksahin, Derivatives Pricing


    Discount factor

    Discount Factor

    Bahattin Buyuksahin, Derivatives Pricing


    Determining treasury zero rates

    Determining Treasury Zero Rates

    Bahattin Buyuksahin, Derivatives Pricing


    Treasury zero rate curve

    Treasury Zero Rate Curve

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 4 bond prices callable and straight debt

    Figure 14.4 Bond Prices: Callable and Straight Debt

    Bahattin Buyuksahin, Derivatives Pricing


    Example 14 4 yield to call

    Example 14.4 Yield to Call

    Bahattin Buyuksahin, Derivatives Pricing


    Realized yield versus ytm

    Realized Yield versus YTM

    • Reinvestment Assumptions

    • Holding Period Return

      • Changes in rates affect returns

      • Reinvestment of coupon payments

      • Change in price of the bond

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 5 growth of invested funds

    Figure 14.5 Growth of Invested Funds

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 6 prices over time of 30 year maturity 6 5 coupon bonds

    Figure 14.6 Prices over Time of 30-Year Maturity, 6.5% Coupon Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Holding period return single period

    Holding-Period Return: Single Period

    HPR = [ I + ( P0 - P1 )] / P0

    where

    I = interest payment

    P1= price in one period

    P0 = purchase price

    Bahattin Buyuksahin, Derivatives Pricing


    Holding period return example

    Holding-Period Return Example

    CR = 8% YTM = 8%N=10 years

    Semiannual CompoundingP0 = $1000

    In six months the rate falls to 7%

    P1 = $1068.55

    HPR = [40 + ( 1068.55 - 1000)] / 1000

    HPR = 10.85% (semiannual)

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 7 the price of a 30 year zero coupon bond over time at a yield to maturity of 10

    Figure 14.7 The Price of a 30-Year Zero-Coupon Bond over Time at a Yield to Maturity of 10%

    Bahattin Buyuksahin, Derivatives Pricing


    Default risk and ratings

    Default Risk and Ratings

    • Rating companies

      • Moody’s Investor Service

      • Standard & Poor’s

      • Fitch

    • Rating Categories

      • Investment grade

      • Speculative grade/Junk Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 8 definitions of each bond rating class

    Figure 14.8 Definitions of Each Bond Rating Class

    Bahattin Buyuksahin, Derivatives Pricing


    Factors used by rating companies

    Factors Used by Rating Companies

    • Coverage ratios

    • Leverage ratios

    • Liquidity ratios

    • Profitability ratios

    • Cash flow to debt

    Bahattin Buyuksahin, Derivatives Pricing


    Table 14 3 financial ratios and default risk by rating class long term debt

    Table 14.3 Financial Ratios and Default Risk by Rating Class, Long-Term Debt

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 9 discriminant analysis

    Figure 14.9 Discriminant Analysis

    Bahattin Buyuksahin, Derivatives Pricing


    Protection against default

    Protection Against Default

    • Sinking funds

    • Subordination of future debt

    • Dividend restrictions

    • Collateral

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 10 callable bond issued by mobil

    Figure 14.10 Callable Bond Issued by Mobil

    Bahattin Buyuksahin, Derivatives Pricing


    Default risk and yield

    Default Risk and Yield

    • Risk structure of interest rates

    • Default premiums

      • Yields compared to ratings

      • Yield spreads over business cycles

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 11 yields on long term bonds 1954 2006

    Figure 14.11 Yields on Long-Term Bonds, 1954 – 2006

    Bahattin Buyuksahin, Derivatives Pricing


    Credit risk and collateralized debt obligations cdos

    Credit Risk and Collateralized Debt Obligations (CDOs)

    • Major mechanism to reallocate credit risk in the fixed-income markets

      • Structured Investment Vehicle (SIV) often used to create the CDO

      • Mortgage-backed CDOs were an investment disaster in 2007

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 14 12 collateralized debt obligations

    Figure 14.12 Collateralized Debt Obligations

    Bahattin Buyuksahin, Derivatives Pricing


    Chapter 15

    CHAPTER 15

    • The Term Structure of Interest Rates

    Bahattin Buyuksahin, Derivatives Pricing


    Overview of term structure

    Overview of Term Structure

    • Information on expected future short term rates can be implied from the yield curve

    • The yield curve is a graph that displays the relationship between yield and maturity

    • Three major theories are proposed to explain the observed yield curve

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 1 treasury yield curves

    Figure 15.1 Treasury Yield Curves

    Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing3

    Bond Pricing

    • Yields on different maturity bonds are not all equal

      • Need to consider each bond cash flow as a stand-alone zero-coupon bond when valuing coupon bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Table 15 1 yields and prices to maturities on zero coupon bonds 1 000 face value

    Table 15.1 Yields and Prices to Maturities on Zero-Coupon Bonds ($1,000 Face Value)

    Bahattin Buyuksahin, Derivatives Pricing


    Yield curve under certainty

    Yield Curve Under Certainty

    • An upward sloping yield curve is evidence that short-term rates are going to be higher next year

    • When next year’s short rate is greater than this year’s short rate, the average of the two rates is higher than today’s rate

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 2 two 2 year investment programs

    Figure 15.2 Two 2-Year Investment Programs

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 3 short rates versus spot rates

    Figure 15.3 Short Rates versus Spot Rates

    Bahattin Buyuksahin, Derivatives Pricing


    Forward rates from observed rates

    Forward Rates from Observed Rates

    fn = one-year forward rate for period n

    yn = yield for a security with a maturity of n

    Bahattin Buyuksahin, Derivatives Pricing


    Example 15 4 forward rates

    Example 15.4 Forward Rates

    4 yr = 8.00%3yr = 7.00%fn = ?

    (1.08)4 = (1.07)3 (1+fn)

    (1.3605) / (1.2250) = (1+fn)

    fn = .1106 or 11.06%

    Bahattin Buyuksahin, Derivatives Pricing


    Downward sloping spot yield curve example

    Downward Sloping Spot Yield CurveExample

    Zero-Coupon RatesBond Maturity

    12%1

    11.75%2

    11.25%3

    10.00%4

    9.25%5

    Bahattin Buyuksahin, Derivatives Pricing


    Forward rates for downward sloping y c example

    Forward Rates for Downward Sloping Y C Example

    1yr Forward Rates

    1yr[(1.1175)2 / 1.12] - 1 =0.115006

    2yrs[(1.1125)3 / (1.1175)2] - 1 =0.102567

    3yrs[(1.1)4 / (1.1125)3] - 1 =0.063336

    4yrs[(1.0925)5 / (1.1)4] - 1 =0.063008

    Bahattin Buyuksahin, Derivatives Pricing


    Interest rate uncertainty

    Interest Rate Uncertainty

    • What can we say when future interest rates are not known today

    • Suppose that today’s rate is 5% and the expected short rate for the following year is E(r2) = 6% then:

    • The rate of return on the 2-year bond is risky for if next year’s interest rate turns out to be above expectations, the price will lower and vice versa

    Bahattin Buyuksahin, Derivatives Pricing


    Interest rate uncertainty continued

    Interest Rate Uncertainty Continued

    • Investors require a risk premium to hold a longer-term bond

    • This liquidity premium compensates short-term investors for the uncertainty about future prices

    Bahattin Buyuksahin, Derivatives Pricing


    Term structure of interest rates

    Term Structure of Interest Rates

    • The term structure of interest rates (or yield curve) is the relationship of the yield to maturity against bond term (maturity).

    • Typical shapes are: increasing (normal), decreasing, humped and flat.

    Yield

    Maturity

    Bahattin Buyuksahin, Derivatives Pricing


    Upward vs downward sloping yield curve

    Upward vs Downward SlopingYield Curve

    • For an upward sloping yield curve:

      Fwd Rate > Zero Rate > Par Yield

    • For a downward sloping yield curve

      Par Yield > Zero Rate > Fwd Rate

    Bahattin Buyuksahin, Derivatives Pricing


    Theories of the term structure

    Theories of the Term Structure

    • A number of theory have been proposed: Expectation Hypothesis, Liquidity Preference Theory, Preferred Habitats Theory, Segmentation Hypothesis.

    • Fabozzi (1998): PureExpectation Hypothesis, Liquidity Preference Theory, Preferred Habitats Theory are different forms of the expectation theory ==> two major theories: expectation theory and market segmentation theory.

    Bahattin Buyuksahin, Derivatives Pricing


    Theories of the term structure of interest rates 1

    Theories of the Term Structure of Interest Rates (1)

    • The Pure Expectation Hypothesis: Implied forward rates are unbiased expectations of future spot rates ==> a rising term structure indicate that market expects short-term rates to rise in the future; a flat term structure reflects expectations that the future short term structure will be constant; and so on; Hicks (1937). Problems: It neglects the risks inherent in investing in bonds: if forward rates were perfect predictors of future interest rates then the future prices of bonds will be known with certainty.

    • The Liquidity Preference Theory (Keynes): Given that there is uncertainty, long bonds should have higher returns than short bonds ==> we should expect a risk premium arising out from investors liquidity preferences. It is consistent with the empirical results that yield curves are upward sloping ==> positive risk premium.

    Bahattin Buyuksahin, Derivatives Pricing


    Theories of the term structure of interest rates 2

    Theories of the Term Structure of Interest Rates (2)

    • The Preferred Habitat Theory: It adopts the view that the term structure is composed by two components: Expectations plus risk premium (= liquidity preference theory). However, the risk premium might be negative as well as positive to induce market participants to shift out of their preferred habitat (Modigliani & Sutch (1966)).

    • The Segmentation Hypothesis (Culbertson (1957)): It also recognises that investors have preferred habitat (= preferred habitat theory) ==> individuals have strong maturity preferences ==> there need be no relationship between bonds with different maturities ==> bonds with different maturities are traded in different markets.

    Bahattin Buyuksahin, Derivatives Pricing


    Expectations theory

    Expectations Theory

    • Observed long-term rate is a function of today’s short-term rate and expected future short-term rates

    • Long-term and short-term securities are perfect substitutes

    • Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates

    Bahattin Buyuksahin, Derivatives Pricing


    Liquidity premium theory

    Liquidity Premium Theory

    • Long-term bonds are more risky

    • Investors will demand a premium for the risk associated with long-term bonds

    • The yield curve has an upward bias built into the long-term rates because of the risk premium

    • Forward rates contain a liquidity premium and are not equal to expected future short-term rates

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 4 yield curves

    Figure 15.4 Yield Curves

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 4 yield curves concluded

    Figure 15.4 Yield Curves (Concluded)

    Bahattin Buyuksahin, Derivatives Pricing


    Interpreting the term structure

    Interpreting the Term Structure

    • If the yield curve is to rise as one moves to longer maturities

      • A longer maturity results in the inclusion of a new forward rate that is higher than the average of the previously observed rates

      • Reason:

        • Higher expectations for forward rates or

        • Liquidity premium

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 5 price volatility of long term treasury bonds

    Figure 15.5 Price Volatility of Long-Term Treasury Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 6 term spread yields on 10 year versus 90 day treasury securities

    Figure 15.6 Term Spread: Yields on 10-Year Versus 90-Day Treasury Securities

    Bahattin Buyuksahin, Derivatives Pricing


    Forward rates as forward contracts

    Forward Rates as Forward Contracts

    • In general, forward rates will not equal the eventually realized short rate

      • Still an important consideration when trying to make decisions :

        • Locking in loan rates

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 15 7 engineering a synthetic forward loan

    Figure 15.7 Engineering a Synthetic Forward Loan

    Bahattin Buyuksahin, Derivatives Pricing


    Chapter 16

    CHAPTER 16

    • Managing Bond Portfolios

    Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing relationships

    Bond Pricing Relationships

    • Inverse relationship between price and yield

    • An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield

    • Long-term bonds tend to be more price sensitive than short-term bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 1 change in bond price as a function of change in yield to maturity

    Figure 16.1 Change in Bond Price as a Function of Change in Yield to Maturity

    Bahattin Buyuksahin, Derivatives Pricing


    Bond pricing relationships continued

    Bond Pricing Relationships Continued

    • As maturity increases, price sensitivity increases at a decreasing rate

    • Price sensitivity is inversely related to a bond’s coupon rate

    • Price sensitivity is inversely related to the yield to maturity at which the bond is selling

    Bahattin Buyuksahin, Derivatives Pricing


    Table 16 1 prices of 8 coupon bond coupons paid semiannually

    Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)

    Bahattin Buyuksahin, Derivatives Pricing


    Table 16 2 prices of zero coupon bond semiannually compounding

    Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)

    Bahattin Buyuksahin, Derivatives Pricing


    Duration

    Duration

    • A measure of the effective maturity of a bond

    • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment

    • Duration is shorter than maturity for all bonds except zero coupon bonds

    • Duration is equal to maturity for zero coupon bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Duration calculation

    Duration: Calculation

    Bahattin Buyuksahin, Derivatives Pricing


    Spreadsheet 16 1 calculating the duration of two bonds

    Spreadsheet 16.1 Calculating the Duration of Two Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Duration price relationship

    Duration/Price Relationship

    Price change is proportional to duration and not to maturity

    D*= modified duration

    Bahattin Buyuksahin, Derivatives Pricing


    Rules for duration

    Rules for Duration

    Rule 1 The duration of a zero-coupon bond equals its time to maturity

    Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower

    Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity

    Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower

    Rules 5 The duration of a level perpetuity is equal to: (1+y) / y

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 2 bond duration versus bond maturity

    Figure 16.2 Bond Duration versus Bond Maturity

    Bahattin Buyuksahin, Derivatives Pricing


    Table 16 3 bond durations yield to maturity 8 apr semiannual coupons

    Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)

    Bahattin Buyuksahin, Derivatives Pricing


    Convexity

    Convexity

    • The relationship between bond prices and yields is not linear

    • Duration rule is a good approximation for only small changes in bond yields

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 3 bond price convexity 30 year maturity 8 coupon initial yield to maturity 8

    Figure 16.3 Bond Price Convexity: 30-Year Maturity, 8% Coupon; Initial Yield to Maturity = 8%

    Bahattin Buyuksahin, Derivatives Pricing


    Correction for convexity

    Correction for Convexity

    Correction for Convexity:

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 4 convexity of two bonds

    Figure 16.4 Convexity of Two Bonds

    Bahattin Buyuksahin, Derivatives Pricing


    Callable bonds

    Callable Bonds

    • As rates fall, there is a ceiling on possible prices

      • The bond cannot be worth more than its call price

    • Negative convexity

    • Use effective duration:

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 5 price yield curve for a callable bond

    Figure 16.5 Price –Yield Curve for a Callable Bond

    Bahattin Buyuksahin, Derivatives Pricing


    Mortgage backed securities

    Mortgage-Backed Securities

    • Among the most successful examples of financial engineering

    • Subject to negative convexity

    • Often sell for more than their principal balance

      • Homeowners do not refinance their loans as soon as interest rates drop

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 6 price yield curve for a mortgage backed security

    Figure 16.6 Price -Yield Curve for a Mortgage-Backed Security

    Bahattin Buyuksahin, Derivatives Pricing


    Mortgage backed securities continued

    Mortgage-Backed Securities Continued

    • They have given rise to many derivatives including the CMO (collateralized mortgage obligation)

      • Use of tranches

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 7 panel a cash flows to whole mortgage pool panels b d cash flows to three tranches

    Figure 16.7 Panel A: Cash Flows to Whole Mortgage Pool; Panels B–D Cash Flows to Three Tranches

    Bahattin Buyuksahin, Derivatives Pricing


    Passive management

    Passive Management

    • Bond-Index Funds

    • Immunization of interest rate risk:

      • Net worth immunization

        Duration of assets = Duration of liabilities

      • Target date immunization

        Holding Period matches Duration

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 8 stratification of bonds into cells

    Figure 16.8 Stratification of Bonds into Cells

    Bahattin Buyuksahin, Derivatives Pricing


    Table 16 4 terminal value of a bond portfolio after 5 years all proceeds reinvested

    Table 16.4 Terminal value of a Bond Portfolio After 5 Years (All Proceeds Reinvested)

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 9 growth of invested funds

    Figure 16.9 Growth of Invested Funds

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 10 immunization

    Figure 16.10 Immunization

    Bahattin Buyuksahin, Derivatives Pricing


    Table 16 5 market value balance sheet

    Table 16.5 Market Value Balance Sheet

    Bahattin Buyuksahin, Derivatives Pricing


    Cash flow matching and dedication

    Cash Flow Matching and Dedication

    • Automatically immunize the portfolio from interest rate movement

      • Cash flow and obligation exactly offset each other

        • i.e. Zero-coupon bond

    • Not widely used because of constraints associated with bond choices

    • Sometimes it simply is not possible to do

    Bahattin Buyuksahin, Derivatives Pricing


    Active management swapping strategies

    Active Management: Swapping Strategies

    • Substitution swap

    • Intermarket swap

    • Rate anticipation swap

    • Pure yield pickup

    • Tax swap

    Bahattin Buyuksahin, Derivatives Pricing


    Horizon analysis

    Horizon Analysis

    • Select a particular holding period and predict the yield curve at end of period

    • Given a bond’s time to maturity at the end of the holding period

      • Its yield can be read from the predicted yield curve and the end-of-period price can be calculated

    Bahattin Buyuksahin, Derivatives Pricing


    Contingent immunization

    Contingent Immunization

    • A combination of active and passive management

    • The strategy involves active management with a floor rate of return

    • As long as the rate earned exceeds the floor, the portfolio is actively managed

    • Once the floor rate or trigger rate is reached, the portfolio is immunized

    Bahattin Buyuksahin, Derivatives Pricing


    Figure 16 11 contingent immunization

    Figure 16.11 Contingent Immunization

    Bahattin Buyuksahin, Derivatives Pricing


  • Login