FINC3019 FIXED INCOME SECURITIES

FINC3019 FIXED INCOME SECURITIES WEEK 1 BONDS o Debt instrument requiring the issuer to repay the lender the amount borrowed + interest over specified time period o Plain vanilla (typical) bond:! Fixed date when principal is due (maturity date/term/maturity) AND! Contractual amount of interest (typically semi-annually)! Face value/redemption value/maturity value/par value/face value o Assuming issuer does not default/redeem issue prior to maturity date assured a known cash flow pattern o Australian Government Bond Yields! Increase as maturity date increases (i.e. higher yield if 10 yrs vs. 5 yrs until maturity) HIGHER yield " LOWER price KEY CONSIDERATIONS o Issued amount o Market price currently trading price in bond market o Market yield IRR that makes security price = PV of future cash flows o Contractual features callable, convertible, puttable, sinking fund provisions o Credit-rating investment vs. non-investment grade Cash-Flow Rights o Debt > Equity (residual claims) o Debt contracts specify bankruptcy events and how bondholders will be compensated DEBT MARKET PARTICIPANTS o Key Sectors! 1. Agency sector Federally related institutions and government-sponsored enterprises! 2. Municipal sector State and local governments and their authorities raise funds o 1. Tax-backed bonds 2. Revenue bonds! 3. Corporate sector Securities issued by US-corporations/non-US corporations (but still in US)! 4. Asset-backed securities sector Corporations pool loans/receivables and use asset pool as collateral for security issuance MORTGAGE o Residential mortgage sector o Commercial mortgage sector E.g. agency mortgage-backed securities, agency mortgage passthrough security, collateralized mortgage obligations, stripped mortgage backed securities, sub-prime mortgage backed securities o 1. Issuers issue debt securities to raise capital! Governments, corporations (e.g. to finance budget deficit), banks, specialpurpose vehicles (SPVs), foreign institutions! Purpose/Roles

Maximize capital raised Liquid secondary market for repurchasing/financing Minimize funding costs o 2. Investors Invest savings by purchasing debt securities (Buy side)! Sovereign wealth funds, pension funds (invest in debt markets on behalf of households note: actual investments depend on policy/mandate), insurance companies, managed funds, commercial banks, asset management companies, households (obtain debt from banks/financial institutions; invest through superannuation/pension funds or managed investments)! Purpose/Roles Obtain diversification Buy securities at fair market price Receive capital market expertise Alter previous investment decision at lower cost (flexibility) o 3. Intermediaries assist buyers and sellers by making markets (Sell side)! Investment banks (short-term and long-term securities/lend + borrow in interbank market), commercial banks, dealers, credit-rating agencies (e.g. Federal National Mortgage Association Fannie Mae, helps direct credit to housing sector) Assist in auctions, tenders, underwriting in primary markets! Purpose/Roles Earn bid-ask spread by making a secondary market Provide risk management services/earn fees Types of US debt securities o 1.Treasury (debt to US govt) o 2. Municipal bonds (debt to state/local governments) o 3. Agency bonds (issued by federally related institutions/government sponsored e.g. Fannie Mae) o 4. Corporate (issued by US/foreign corporations) o 5. Money market (short-term debt - < 13 months) o 6. Mortgage related (securities backed by mortgage loans) o 7. Asset backed (securities backed by a pool of assets) Note: Pre-GFC, mortgage related bonds were most common but now treasury bonds are most common Australian Bond Market (non-government bonds are majority of issues) o Bonds issued by Australian government, financial institutions, corporates o Asset-backed bonds issued by Australian-domiciled vehicles o Australian dollar bonds issued in Australia by non-residents (Kangaroo bonds) BOND RISK o Interest rate risk (incl. reinvestment) (*most important)! INCREASE in int. rates = DECREASE in bond prices (investors make capital LOSS from price decrease) Risk of changes to interest rate affecting bond price Coupon reinvestment affected o Credit risk (assessed by credit rating agencies)! Risk that issuer NOT able to make contractual payments to bondholders Treasury securities have NO credit risk o Reinvestment risk! Additional income from investment (interest-on-interest) Variability in reinvestment rate = risk

Risk that prevailing market rate at which the interim (coupon) cash flows reinvested will fall Note: Interest rate risk (risk of interest rate rises) and reinvestment risk (risk of interest rate falls) have offsetting effects o Once you have the bond you want price to increase (capital gain); but if you are reinvesting you want higher rates than the prevailing one used in the bond to make some gains (from lower prices of the new bonds)! FACTORS 1. Maturity of the bond longer maturity = higher likelihood that interest rates will lower 2. Interest rate on bond - higher interest rate, the bigger the coupon payments to be reinvested o Call risk! Issuer has right to call-back bond; effects on investor: 1. Cash flow pattern of callable bond is unknown with certainty 2. Issuer will call bonds when interest rates dropped, investor exposed to reinvestment risk (reinvest at lower rates) 3. Capital appreciation potential of bond reduced since price may not risk much above price issuer will call the bond o Liquidity risk! Ability to trade large size quickly, at low cost, whenever you want to trade o Contractual risk (call risk)! If int. rates decline, issuers with callable bonds more likely to call.: Refinance at a cheaper rate; callable bonds should have lower price + higher yield than similar non-call bond instruments o Inflation risk! Uncertainty over the future real value (after inflation) of investment (affect on purchasing power) Note: Fixed coupon securities incorporate compensation for expected inflation at the time of issuance! Affects nearly all fixed income securities since interest set for life (greater effect for longer maturity) o Event risk! Risk of adverse price changes if company restructures/mergers o Tax risk o Foreign exchange risk! Risk posed by exposure to unanticipated changes in exchange rate between 2 currencies o Model risk! Incorrect pricing models (more relevant for interest rate derivatives rather than plain vanilla bonds) In recent times, Australian equities and Australian bonds both outperform global bonds/equities ORGANISATION OF FIXED INCOME MARKETS PRIMARY MARKETS o Markets where borrowers issue debt securities o Investors provide capital to borrowers

o Debt securities obtained by dealers using auctions, underwriting procedures or tenders o Dealers need to:! Assess demand for issue, price issue, hedge positions, distribute securities to investors (e.g. Barclays Capital, Deutsche Bank, JP Morgan, UBS) SECONDARY MARKETS o Markets where previously issued securities are traded! Generally over the counter (OTC) structure o Dealers provide bid-ask quotes o Investors buy/sell in secondary market o Different from trading stocks on exchanges WEEK 2 PV Calculations o Annual compounding: o Semi-annual compounding: Annuity Perpetuity OPTION-FREE BOND PRICING o Requires estimate of:! 1. Expected cash flows! 2. Appropriate required yield Reflects appropriate/comparable risk of alternative/substitute investments o Cash flows consist of : 1. Coupon payments 2. Principal at maturity E.g. for $100 face value bond with annual coupons: o Note: For semi-annual coupons PRICING AUSTRALIAN COMMONWEALTH GOVERNMENT SECURITIES CGS pay interest semi-annually on the 15 th day of that month Bond trades typically settled in 3 business days (t + 3) Pricing is from the settlement date (SD) not the transaction date (when order made) o Settlement price (P 0 ) is paid to seller on settlement date If investor purchases bond BETWEEN the set coupon payments o Investor must compensate bond seller for coupon interest earned (accrued interest)

PRICING SCENARIOS 1. Pricing with an integer period to maturity (i.e. buy bond when it is comfortably before the maturity date) o METHOD 2. Pricing with non-integer period to maturity o Irregular date of purchase (not a comfortable 6 months)! Must adjust the accrued interest between sellers and buyers! METHOD (calculating the settlement price that must be paid) 1. Determine previous coupon payment date (PCD) and next coupon payment date (NCD): PCD < SD < NCD o Determine the bond price (P ) HAD settlement occurred on the next-coupon date! Exclude coupon paid on that date (purchaser not entitled to it) (i.e. the first coupon after the SD unfair) Use normal bond pricing formula calculation 2a) Determine fraction of period (f) between SD and NCD to discount P back to SD (no. of days) 2b) Determine if cum-interest OR ex-interest (and then discount to PV accordingly) o Purchaser receives coupon if bond is cum-interest! I.e. CI = if > 7 days between SD and NCD! If CI the coupon payment on the NCD MUST BE INCLUDED o Purchaser DOES NOT receive coupon if bond is ex-interest! I.e. XI = if 7 or < 7 days between SD and NCD Still discount accordingly Dirty bond price gradually rises until interest payment (coupon) date then bond price falls rapidly Accrued Interest P 0 is the invoice/settlement/dirty price (includes any interest accrued since the last date of coupon payment)

o Price paid by traders P adj quoted/flat/clean price (easier to look at/preferable) o Adjusts the dirty price for the accrued interest! Note: Theoretically interest earned every day between coupon payment dates o USE! Can be used to examine changes in price caused by: Change in credit quality of issuer Changes in market yield (rate) Change in time as maturity date approaches CLEANING THE DIRTY PRICE o Dirty Price = Clean Price + Accrued interest o Cum-interest (accrued interest between PCD and SD must be deducted) Already going to get coupon payment so subtract the addition! P adj = P 0 C(1-f) o Ex-interest (accrued interest between PCD and SD must be added back) Since not getting coupon payment, add back! P adj = P 0 + C(f) o Note: Settlement and quoted price are equal on coupon payment date Note: Most clean prices quoted in US bond market; dirty prices quoted in European bond market o Most of the time we look at US bond markets, so clean price provided Relationship between Bond Price and Time PAR VALUE BONDS: Coupon rate = YTM o As bond moves closer to maturity, bond = sell at par o Price constant as bond moves towards maturity date PREMIUM/DISCOUNT BONDS (Coupon rate > or < YTM) (different) o Discount bond = increases in price as it approaches maturity (assuming YTM doesn t change) o Premium bond = decreases in price as it approaches maturity (assuming YTM doesn t change)! Price = Par value at Maturity date Bond price changes with time Reason for Price Changes 1. Change in required yield due to changes in issuer s credit rating (credit risk) 2. Change in price of bond selling at premium or discount (without change in yield) since bond moving towards maturity 3. Change in required yield due to change in yield of comparable bonds (i.e. change in yield required by market)

OTHER BONDS ZERO-COUPON BONDS Properties o No coupons o Issued at discount to face value o Interest paid at maturity o Value of interest = difference between face value and purchase price Prices and Yields of US T-bills US Treasury bills are Zero-coupon bonds Market Convention quote on discount yield basis o Annualised and show capital gains Discount Yield o Measure of bond s % returns (used to calculate yield on short-term bonds and T-bills sold at discount) Where d = discount yield per $100 face value n = no. of days between settlement and maturity I.e. Discount yield = [(par value purchase price)/par value] x [360/days to maturity] Day Count Convention (30 day month, 360 day years) o For a T coupon security accrued interest based on actual no. of days held o For other types of bonds accrued interest based on 360 day year Pricing Problems 1. Pricing formula uses 360 rather 365 2. Dollar gain divided by 100 rather than P (initial outlay) BOND EQUIVALENT YIELD Allows comparisons between fixed-income securities whose payments are NOT annual to those that ARE Corrects for identified problems o Reflects the return an investor will make if buy T- bill and hold until maturity! BEY > discount yield (easier/quicker to compute) Note: Australian Treasury notes priced using BEY FLOATING RATE BONDS Floating Rate Bond ( Floater ) o Floater price: reference rate + quoted margin! USE 1. Note: Quoted margin spread to compensate for risk o Additional amount issuer agrees to pay above reference rate 2. Restrictions imposed on resetting coupon rate

o Maximum coupon rate: CAP o Minimum coupon rate: FLOOR! E.g. 1 month LIBOR (reference rate) + 150 basis points (1.5%) o Price of floater usually traders close to par value! As long as spread unchanged; NEITHER cap NOR floor reached! If market requires a larger (smaller) spread, the price of a floater will trade below (above) par value Inverse-Floating-rate Bond ( Inverse floater ) o Inverse floater price: Collateral s price floater s price! Found by determining the price of the collateral and the price of the floater! Created from collateral: fixed-rate security 1. Total coupon interest paid to two bonds in each period collateral s coupon interest in each period 2. Total par value of two bonds collateral s total par value o The floors and ceilings act to stop the coupon rate from being negative! Floor (on inverse) set at 0 (so coupon interest paid to the two bonds does not exceed collateral s coupon interest)! Cap (on floater) stop it from going to high o Note: Changes in interest rate affect price of collateral, reference rate only important that it restricts the coupon rate of floater Combination o Weighted average gives a fixed-rate bond calculation o Collateral s price = floater s price + inverse price YIELD Without computer/financial calculator requires TRIAL AND ERROR o Note: Yield is for that particular period (i.e. semi-annual or annual etc.) To compute simple annual interest rate yield for period is multiplied by no. of periods in year Effective Annual yield o Effective annual yield = (1 + periodic interest rate) m - 1! Where m is the frequency of payments per year Periodic Interest Rate o Periodic interest rate = (1 + effective annual yield) 1/m - 1 YTM o IRR of bond cash flows! Considers: timing of cash flows, coupon income, capital gain/loss if bond held until maturity (assumes that coupons reinvested at prevailing interest rate) o So if interest rate changes then YTM is inaccurate Note: For semi-annual double periodic rate to give YTM (annualized) Current Yield o Annual coupon interest (C) (as % of price (P): o Annual income (interest or dividends) divided by the current price of security! Looks at current price of bond (instead of face value) and return investor would expect if bond purchased and held for year o Problems (inaccurate)! Ignored capital gain/loss! Does not consider time value of money

! Only considers coupon interest as the only source of interest MEASURES OF YIELD Yield to call o The yield of bond/note if you were to buy/hold security until call date o If bond is callable by issuer (at certain call price according to a call schedule that determines the call date)! IRR sets PV of cash flows = price once considering call date and call price o Usually calculate yield to first call, yield to next call, yield to first par call, yield to refunding! Replace face value with call price Yield to put o Bondholder can force issuer to buy issue at specific price o Interest rate that makes PV of cash flows to assumed put date + put price on date = bond s price! Specific yield that makes it possible o If investors can put bonds back to issuer! IRR sets of PV of cash flows relative to put date and put price Yield to worst o Minimum of YTM : every YTC and every YTP the worst possible Cash flow yield o Include all possible cash flows (useful for amortizing securities)! E.g. coupon interest, scheduled principal repayment (e.g. fort mortgages) and prepayments! Yield that equates market price with the PV of projected cash flows Yield (IRR) for Portfolio Determining cash flows for the portfolio and determining interest rate that makes PV of cash flows = market value of portfolio o 1. Calculate market value of portfolio s cashflows o 2. Solve for YTM Yield to floating rate securities Coupon rate for floater changes periodically based on coupon reset formula (reference rate + quoted margin) o Since knowing what reference rate in future will be is unknown difficult to determine cash flows (.: YTM can not be calculated) o Other Measures! Spread of life (simple margin), adjusted simple margin, adjusted total margin, discount margin* Discount margin average margin over reference rate that investor can expect to earn over life of security! Price of floating rate security will trade close to par if risk of the issuer does not change METHOD o 1. Determine cash flows assuming reference rate not changed o 2. Select margin (spread) o 3. Discount cash flows from (1.) by current value of reference rate + margin from (2.)

o 4. Compare PV of cash flows to required, test, adjust (trial and error) Problem o Assumes reference rate will not change over life of the security Dollar Return v YTM Total Return o Measure of yield that incorporates an explicit assumption about the reinvestment rate YTM o Promised yield because at time of purchase an investor is promised iff:! 1. Bond held to maturity! 2. ALL coupon interest payments reinvested at YTM o Note: YTM is not a good, sole determinant of comparing good bond investments SOURCES OF BOND S DOLLAR RETURN o An investor who purchases a bond can expect to receive dollar return from 1 or more sources o 1. Periodic coupon payments o 2. Capital gain or loss (when bond matures/called/sold) o 3. Reinvestment of coupon payments (personally done)! Reinvestment income ( interest on interest component) Non-amortizing securities o Interest earned from reinvesting the coupon interest payments Amortizing securities o Calculated as interest income from reinvesting both coupon interest payments AND periodic principal repayments PROBLEMS! Note: Calculation of YTM assumes that coupons are reinvested at the YTM 1. HOWEVER reinvestment rate may change over time (inflation/market) (and risk of reinvesting at lower rate than original) o IF differs from YTM then investor WILL NOT receive YTM by holding it to maturity 2. Based on assumption that: o a) Bond held to maturity o b) Coupon interest payments reinvested at YTM rate (may be higher or lower in reality)! PRICING FORMULA (determining interest-on interest dollar return) Coupon interest + interest on interest = C[(1+r) n 1)/r] o Total coupon interest = nc o Interest ON interest = C[(1+r) n -1]/r] nc AS BELOW Value of coupons and reinvestment return: o H: no. of holding periods