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Com 4FJ3

Fixed Income Analysis

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Plain Vanilla Bond

• Issuer

• Maturity Date

• Face Value ($1,000)

• Coupon Rate (paid 1/2 every six months)

• Financial engineering has made things much more complicated

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US Bond Market Segments

• Treasury

• Agency (smallest sector)

• Municipal (tax exempt)

• Corporate, including Yankee bonds

• Asset backed securities

• Mortgage securities;– residential or commercial

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The Indenture

• Legal document that spells out all details of the particular issue.

• Maturity, face value, coupon rate

• Special features

• Redemption provisions

• Collateral & Covenants

• Embedded options

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Term to Maturity

• Different types of markets– Money market; less than 1 year– Short term; 1 - 5 years– Intermediate term; 5 - 12 years– Long term; greater than 12 years

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Importance of Maturity

• Time period for promised cash flows

• Influences the required yield on the bond based on the yield curve

• Price volatility; all else being equal, the longer the term to maturity, the greater the price volatility

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Principal & Coupons

• Principal: aka; redemption value, par value, face value, maturity value– Amount to be paid at maturity

• Coupon Rate: aka; nominal rate– stated annual rate– principal x coupon rate paid every year– typically 1/2 of that paid every 6 months– some European markets pay annually

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Odd Coupons

• Zero coupon or pure discount bonds

• Floating rate bonds– reference rate + quoted margin– usually an interest rate, but not always

• Inverse floating rate bonds

• Deferred coupon bonds; deferred, step-up or payment in kind. Usually junk bonds.

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Amortization

• Principal paid off over the life of the bond, not just at maturity

• Amortization schedule is the required payments of principal

• Mortgage and asset backed securities

• Term to maturity is much less meaningful– weighted average life or average life

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Embedded Options

• Call; issuer can buy back bond at a predetermined price.

• Put; buyer can sell bond back to issuer• Convertible; buyer can trade bond for a

fixed number of common shares of issuer• Exchangeable; trade for other securities• Currency; coupon payments in different

currencies, issuer or buyer chooses

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Risk

• Bonds are considered lower risk than equity

• Even treasury bonds have risk

• Nine types of risk identified

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Interest Rate Risk

• When interest rates change, market prices of bonds change

• Called interest rate risk or market risk

• Amount of risk dependent on;– term to maturity– coupon rate– embedded options

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Reinvestment Risk

• How much will an investment be worth in 5 years?

• Highly dependent on interest-on-interest

• Reinvestment risk increases as coupon rate increases

• Zero coupon = no reinvestment risk, but much more interest rate risk

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Call Risk

• Three problems for buyer;– cash flow pattern not certain– if called for refinancing, high reinvestment risk– capital appreciation limited

• Callable bonds are priced to give a higher yield than non-callable bonds

• Spread dependant on call parameters

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Credit Risk

• Possibility of default

• Credit spread risk– risk premium over treasury– change in credit rating can affect prices– upgrade reduces spread, increases prices– downgrade increases spread, decreases prices

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Inflation Risk

• Also known as purchasing power risk

• Interest rates include a provision for expected inflation

• Unexpected changes in inflation could mean that the proceeds of the investment is not sufficient for the planned use of funds

• Floating rate bonds somewhat protected

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Exchange Rate Risk

• Also called currency risk

• Affects any bond with cash flows denominated in foreign currency

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Liquidity Risk

• How easy is it to sell your bond?

• High bid/ask spread for bonds with low liquidity

• Important to institutional investors since they need to “mark to market” periodically, so the bond must trade with some frequency to determine a market price

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Volatility Risk

• Important for bonds with embedded options

• Option prices increase with an increase in the volatility of the underlying asset

• If interest rates become more volatile, the value of the embedded option will increase

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Risk Risk

• Not knowing what the risk of a security is.

• Many new types of securities lead to some misunderstanding of the risk/return characteristics of securities

• Complex securities can offer opportunities and return enhancement

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Financial Innovation

• Economic Council of Canada classifications– market broadening instruments; increase the

liquidity of the market– risk management instruments– arbitrage instruments and processes; take

advantage of differences between markets including; risk perception, information, taxation, and regulation

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Financial Innovation

• Bank for International Settlements – Price-risk-transferring instruments– Credit-risk-transferring instruments– Liquidity-generating innovations– Credit-generating innovations– Equity-generating innovations

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Pricing a Bond

• Consider the following bond;• $1,000 face value 6% coupon rate

• 10 years to maturity 7% required return

• Coupons are an ordinary annuity.• PVIFA(0.035, 20)

• Face value returned at year 10 (t = 20)

• FV = PV x (1 + r)t

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$928.94 57.502 426.37

)20,035(.000,120,035.30

PVIFPVIFA

PVPVPrice facecoupons

Pricing a Bond

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• Price = $928.94

• The bond trades at a discount because the coupon rate is below required return.

• Return = coupons + capital gain.

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A Premium Bond

• Consider the following bond;• $1,000 face value 12% coupon rate

• 7 years to maturity 7% required return

• Coupons are an ordinary annuity.• PVIFA(0.035, 14) = $655.23

• Face value returned at year 7 (t = 14)

• FV = PV x (1 + r)t = $617.78

• Price = $1,273.01, a premium of over 27%.

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In General

• If the YTM of a bond is equal to the coupon rate, the bond sells at par.

• If the yield exceeds the coupon rate the bond sells at a discount.

• If the coupon rate is greater than the required rate of return, the bond will trade at a premium.

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Price/Yield RelationshipFor a 10% Coupon Bond

$500

$750

$1,000

$1,250

$1,500

$1,750

$2,000

0% 5% 10% 15% 20%

YTM

Pri

ce

1-year bond 10-year bond par

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Price/Time RelationshipPrice vs. Maturity

$0

$200

$400

$600

$800

$1,000

$1,200

$1,400

$1,600

$1,800

0 5 10 15 20

Time to maturity

Bo

nd

pri

ce

YTM 5% YTM 10% YTM 15%

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Reasons for Price Changes

• Change in credit quality of issuer causes required return to change

• non-Par bond, yield doesn’t change, but time passes

• Market interest rates change causing required return to change

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Closer Payments

• What is the price of bond if the next coupon payment date is less than 6 months away?

• Value as 6 months away and future value the price for the extra days at the required return

• e.g. if purchased 22 days after previous coupon payment multiply by (1+r)^(22/181)

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Other Complications

• Cash flows uncertain: for bonds with an embedded option or mortgage backed.

• Single discount rate for all cash flows:– could view bond as package of pure discount

payments and price that way

• Price of floater; near par unless credit spread has changed or it has a cap or floor

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Quotes and Accrued Interest

• Prices are typically quoted as a percent of face value; a price of 107.5 would mean a $5,000 face value bond sells for $5,375

• If the bond is not in default, the buyer must also pay the seller the interest that has accrued since the last coupon payment, this total price is called the dirty price or full price, the quoted price is the clean price