Bond Valuation and Features

• Capital markets involve equity and debt instruments with original issue maturities exceeding one year.
• Bonds represent long-term debt obligations issued by corporations and government entities.
• Bond markets facilitate the issuance and trading of bonds, including Treasury notes (T-notes), Treasury bonds (T-bonds), municipal bonds (Munis), and corporate bonds.
• Bond instruments outstanding went from $6.2 trillion in 1994 to $30.4 trillion in 2018.

Bond Valuation

• A bond is a debt contract, or interest-only loan.
• The borrower only pays interest each period.
• The principal is paid back at the end of the term.

Bond Features

• Par Value/Face Value: The principal amount repaid at the end of the term, typically assumed to be $1,000.
• Coupon Payment: The stated interest payment made on a bond, expressed in dollar terms.
• Coupon Rate: The annual coupon payment divided by the face value of the bond, expressed as a percentage.
• Maturity: The specified date on which the principal amount of a bond will be repaid, expressed in years.
• Yield-to-Maturity (YTM): The interest rate required in the market on a bond, also referred to as "yield," and quoted as an APR.

Yield-to-Maturity

• YTM represents the rate of return the market demands for bonds with similar risk and maturity.
• On day 1, YTM is usually equal to the coupon rate.
• Changes in interest rates affect bond prices which affects YTM.
• YTM also serves as the discount rate for bond valuation, and is quoted as an APR.

Bond Cash Flows

• A 10-year bond that pays annual interest with an 8% coupon with a face value of $1000 will pay out $80 ($1000 * 0.08) per year for 10 years, and then pay $1000 at the end of year 10.

Present Value Formulas

• Present Value of an Annuity (PVAnnuity) = C * [1 - (1 / (1+r)^t)] / r
• Present value of a cash flow.
• r = Interest rate per period.
• t = Number of periods.
• C = Cash amount per period.
• Present Value of a Lump Sum (PVLump Sum) = FV / (1 + r)^t
• FV = Future Value
• PV = Present Value
• r = Interest Rate
• t = # of periods

Present Value Formulas for Bonds.

• C = Coupon payment
• r = Yield-to-maturity (YTM)
• FV = Face value of bond (F)
• t = Time to maturity (t)

Bond-Pricing Equation

• Bond Value = Present Value of the Coupons + Present Value of the Face Value
• Present Value of an Annuity = C * [1 - (1 / (1+YTM)^t)] / YTM
• Present Value of a Lump Sum = F / (1 + YTM)^t
• For example, a bond with an 8% coupon rate, YTM of 8%, and a face value of $1000 with a maturity can use the bond pricing equation to have a bond price of $1000.

Bond Pricing Question

• Bond prices do not remain constant at $1,000 due to fluctuating interest rates.
• Interest rates change based on economic conditions, monetary policy, and inflation.

Semi-Annual Bonds

• Most bonds pay interest semi-annually (every 6 months).
• Variables must be adjusted to be on a semi-annual basis
• The cash/coupon payment (C), interest rate (YTM), and number of periods (t) must be adjusted.

Bond Pricing with Semi-Annual Coupons

• Annual cash flow from interest = (Coupon rate / 2) * Face Value
• Discount rate= YTM/2
• Periods to maturity = (Years to Maturity)*2

Bond-Pricing Equation Adjusted for Semi-Annual Coupons

• Bond Value = (C/2) * [1 - (1 / (1+YTM/2)^(2t))] / (YTM/2) + F / (1+YTM/2)^(2t)
• C/2 equals the semi-annual coupon.
• YTM/2 equals the semi-annual YTM.
• 2t equals the number of 6-month periods to maturity.
• For example, a bond with a 14% coupon rate, 16% YTM (APR), and 7 years to maturity, is expected to get a bond value of $917.56.

Treasury Notes and Bonds

• Treasury notes and bonds (T-notes and T-bonds) are issued by the U.S. Treasury to finance the national debt and government expenditures.
• The annual federal deficit is the difference between annual expenditures (G) and taxes (T) received.
• The National Debt is the sum of historical deficits.

Treasury Notes and Bonds Risk

• Backed by the full faith and credit of the U.S. government.
• Reflect lower default risk.
• They experience wider price fluctuations compared to money market securities when interest rates change.
• Older issues trade less frequently than newly issued ones.
• T-notes mature in 1-10 years, while T-bonds mature in over 10 years.
• They can be fixed principal or adjusted for inflation.
• Inflation-indexed bonds are called Treasury Inflation Protection Securities (TIPS). The principal value of TIPS is adjusted according to the Consumer Price Index (CPI) every six months.

Treasury Bond Quotes

• Maturity (mo/yr): The bond matures November 15, 2045.
• Coupon: The coupon rate is 3%, or $30.00 annually, paid semi-annually on a $1,000 face value.
• Bid: Closing price per $100 of par that the dealer pays for the bond; the seller receives 107.6563% of $1,000, or $1,076.56.
• Asked: The closing price per $100 of par the dealer requires to sell the bond; the buyer pays 107.6865% of $1,000, or $1,076.87.
• Chg: The change from the prior closing ASKED price.
• Asked Yld = Promised compound yield rate if purchased at the Asked price. In this case, the yield is 2.624%

Treasury STRIPS

• Separate Trading of Registered Interest and Principal Securities (STRIPS) is a Treasury security with separate interest and principal payments.
• One is interest payments.
• Another is the final principal payment.
• STRIPS can be used to protect against interest rate risk.

Citigroup STRIPS Example

• Citigroup creates a 5-year Treasury STRIP with a 5-year T-note with a par value of $10,000.
• It has an 8% coupon with semiannual compounding and a YTM of 7.9%.
• Citigroup can then sell 11 different securities: 10 securities associated with each of the semiannual coupon payments of $400 and one that pays $10,000 (the face or principal value) in five years to outside investors.

Zero Coupon Bonds

• Pure discount bonds do not make interest payments and have a 0% coupon rate.
• These are purchased at a value less than $1000, with the purchaser receiving $1000 at maturity.
• The entire YTM comes from the difference between the purchase price and par value ($1000).

Treasury Note and Bond Yields

• calculated from the following formula is the price (referred to as the clean price) quoted in the financial press: V♭ = INT MN 1 Σ mt=1 + M rb rb1+1+ m TmN mN] [1 INT + M rbrb (1+)mNmNm m where V₁ = Present value of the bond M = Par or face value of the bond INT = Annual interest (or coupon) payment on the bond equals the par value times the coupon rate N = Number of years until the bond matures m = Number of times per year interest is paid rb = Interest rate used to discount cash flows on the bond

Accrued Interest

• This is the coupon payment portion accruing between the last coupon payment and the settlement day.
• A bond buyer must pay accrued interest if the T-note or T-bond is purchased between interest payment dates.
• Accrued interest on a T-note or T-bond is based on the actual number of days the bond was held by the seller since the last coupon payment:
• Accrued interest = (INT / 2) * (Actual number of days since last coupon payment / Actual number of days in coupon period)

T-Notes and T-Bonds

• U.S. Treasury sells T-notes and T-bonds through competitive and noncompetitive Treasury auctions.
• Auction is a single-price auction. all bidders pay the same price, which is the price associated with the highest of the competitive yields bid
• At each auction, noncompetitive bids are filled first
• Next, competitive bids are ranked from the lowest to highest yield, indicating a bidder's willingness to accept the lowest yield to pay the highest price.
• The coupon rate of the auctioned notes or bonds is the stop-out yield rounded down to the nearest 1/8 percent.
• Most secondary trading occurs directly through broker and dealer trades.

Municipal Bonds

• These are securities issued by state and local governments, repaid with tax receipts or revenues from a project.
• Funds are raised to address imbalances between expenditures and receipts.
• Funds are raised to finance long-term capital outlays.
• They are attractive to household investors because interest is exempt from federal and most local income taxes.
• General obligation (GO) bonds are backed by the full faith and credit of the issuer.
• Revenue bonds are sold to finance specific revenue-generating projects and are backed by the cash flows from that project.
• Convert municipal interest rates to tax equivalent rates, and compare to corporate bonds with the following formulas.
• ra = r(1-t) ra = after-tax yield on a taxable corporate bond r₁ = before-tax yield on a taxable bond rm = yield on a municipal bond t= marginal total income tax rate of the bond holder

Examples

• For a 28% tax bracket, the equivalent after-tax rate of a 6% corporate yield is 4.32%.
• For a 28% tax bracket, the corporate taxable yield equivalent to a 4.5% municipal bond yield is 6.25%.

Municipal bonds

• Primary markets have firm commitment underwriting: A public offering of Munis through an investment bank, guaranteeing a price by buying and reselling.
• best efforts offering: Public offering without investment bank guaranteeing a price.
• private placement: bonds are sold on a semi-private basis to qualified investors (generally FIs)
• Secondary markets: These have infrequent trading due to limited information on bond issuers.

Corporate Bonds

• These are long-term obligations issued by corporations, with coupon-paying bonds generally paying interest semiannually.
• A bond indenture legally defines rights/obligations of issuer/holders.
• This contains covenants and the rules/restrictions placed on the bond issuer and bond holders.
• Mortgage bonds finance projects pledged as collateral.
• Debentures are unsecured bonds.
• Subordinated debentures are junior to mortgage bonds.
• Convertible bonds can be exchanged for other securities at the holder's discretion.
• Callable bonds allow the issuer to repurchase the bond, with the call premium being the excess over par value.
• The sinking fund provision requires the issuer to retire a portion annually.
• Primary sales mirror municipals, and may happen through a sale or private placement.

Corporate Bonds - Secondary Markets & Ratings

• Secondary markets: The exchange (NYSE Bonds) and over-the-counter (OTC) markets exist.
• Bond ratings are preformed by Moody's, Standard & Poor's (S&P), and Fitch.
• Ratings are rated by perceived default risk
• Bonds may be either investment or speculative (junk) grade.