Fixed Income Securities

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1 3st lecture IES, UK October 7, 2015

2 Outline Bond Characteristics 1 Bond Characteristics 2

3 Bond Characteristics Government bond listing Rate Maturity mo/yr Bid Asked Chg Ask yld July :22 108: Feb 13 99:10 99: Corporate bond listing Issuer name Symbol Coupon Maturity Rating High Low Last Change Yield % Gener. Electr. GE.HG 3.0% Dec 11 Aaa Gold. Sachs GS.HR 1.7% Mar 11 Aaa Investment-grade bonds - bonds with ratings above BBB Speculative-grade bonds (junk bonds) - bonds with rating below BBB

4 Bond Pricing Bond Characteristics Bond value = Present value of coupon + Present value of par value = T Coupon Par value = + (1 + r) t (1 + r) T t=1 In listings, we have the flat price adjust for the accrued dividends pricing the bond Invoice price = Flat price + Accrued interest Accrued interest = Coupon payment Days since last coupon payment Days separating coupon payments

5 Bond Pricing Bond Characteristics What is the relation between bond prices and market interest rate? that is the economic intuition behind? prices fall when market interest rises, since the outside opportunity brings higher returns How bond price will fluctuate with interest rate fluctuation depending on the maturity? why? with longer maturity the price sensitivity to interest rate fluctuation rises since your money locked for longer time incurs higher losses

6 Bond Pricing Bond Characteristics What is the relation between bond prices and market interest rate? that is the economic intuition behind? prices fall when market interest rises, since the outside opportunity brings higher returns How bond price will fluctuate with interest rate fluctuation depending on the maturity? why? with longer maturity the price sensitivity to interest rate fluctuation rises since your money locked for longer time incurs higher losses

7 Bond Pricing Bond Characteristics What is the relation between bond prices and market interest rate? that is the economic intuition behind? prices fall when market interest rises, since the outside opportunity brings higher returns How bond price will fluctuate with interest rate fluctuation depending on the maturity? why? with longer maturity the price sensitivity to interest rate fluctuation rises since your money locked for longer time incurs higher losses

8 Zero Coupon Pricing

9 Bond Yields Bond Characteristics Yields to maturity - you can think of it as or the interest rate that makes the present value of a bond s payments equal to its price; the average rate of return which will be earned if bought now and held until maturity. Distinguish yields to maturity from current yields: Current yields = Bond s annual coupon payment Bond price

10 Bond Pricing Yield to call Bond Characteristics Yield to call is calculated as yield to maturity, we only change: time to maturity for time to call; par value for call price

11 Realized Compound Returns vs Yields to maturity Realized compound return is calculated by formula: V o (1 + r) t = V t When we talk about yields to maturity, we implicitly assume that the coupon is reinvested at the same rate. if the reinvestment rate stays the same, realized compound return equals yields to maturity if the reinvestment rate, how does the relation between realized compound returns and yields to maturity changes? realized compound returns > yields to maturity which measure of return is better? realized compound return is useful, but its attraction is lower due to the fact that you need to forecast future price and future reinvestment rates

12 Realized Compound Returns vs Yields to maturity Realized compound return is calculated by formula: V o (1 + r) t = V t When we talk about yields to maturity, we implicitly assume that the coupon is reinvested at the same rate. if the reinvestment rate stays the same, realized compound return equals yields to maturity if the reinvestment rate, how does the relation between realized compound returns and yields to maturity changes? realized compound returns > yields to maturity which measure of return is better? realized compound return is useful, but its attraction is lower due to the fact that you need to forecast future price and future reinvestment rates

13 Yields to maturity vs holding-period return Holding period return Holding period return = Coupon + (Price t Price t 1 ) Price t 1 Comparison Yield to maturity depends on bond s coupon current price par value Holding period return depends on coupon market prices at the begining and at the end of holding period

14 Default Risk and Bond Pricing Determinants of bond safety: Company earnings 1 Coverage ratio = Fixed costs - falling ratio indicates possible cash flow difficulties 2 Leverage ratio = Debt Equity - high level indicates excessive indebtedness Current assets Current liabilities or Current assets excluding inventories Current liabilities 3 Liquidity ratios: Current ratio = Quick ratio = measure the firm s ability to pay bills with its most liquid assets 4 Profitability ratios measure the rates of return on assets and Earnings before interests and taxes equity: Return on assets = Total assets, Return on equity = Net income Equity 5 Cash flow to debt ratio = Total cash flow Outstanding debt

15 Bond Indenture Bond Characteristics Indenture - bond contract terms Protective measures for bondholder: sinking fund - put aside money to retire indebtedness serial bond issue - bonds with staggered maturity dates subordination clauses restrict the amount of additional borrowing dividend restriction collateral credit default swaps - insurance policy

16 Yields and Future Interest Rates Term structure refers to the interest rates for various terms to maturity embodied in the prices of zero-coupon bonds Yields on zero coupon bond are the following Maturity, years Yields to maturity, % Price 1 5 $952.38=$1000/ $890=$1000/ $816=$1000/1.07 3

17 Yields and Future Interest Rates Short rates versus spot rates Spot rate - yield to maturity on zero-coupon bonds; the rate which prevails today for a time period corresponding to the zero s maturity Short rate - the interest rate for the interval available at different points in time Spot rate on long-term Iuliia bond Brushko reflects Fixed the Income path Securities of short rates

18 Yields and Future Interest Rates Consider 2 investments programs: No arbitrage opportunity implies that the returns should be equal on both alternatives = (1 + y 2 ) 2 = (1 + r 1 )(1 + r 2 )

19 Forward Rates Bond Characteristics Generalizing the formula (1 + y 2 ) 2 = (1 + r 1 )(1 + r 2 ) to n periods, or (1 + y n ) n = (1 + y n 1 ) n 1 (1 + r n ) = (1 + y n 1 ) n 1 (1 + f n ) (1 + y n ) n = (1 + y n 1 ) n 1 (1 + r n ) = (1 + y n 1 ) n 1 (1 + E(r n )), where f n - forward rate for period n (1 + y n ) n - total growth factor of an investment in an n-year zero held until maturity (1 + y n 1 ) n 1 - growth factor of an investment in an (n 1)-year zero But if we take into account uncertainty, forward rate f n maybe different from expected short rate E(r n )

20 Theories of Term Structure Expectation hypothesis: f n = E(r n ) Liquidity preference theory: short-term investors require f n > E(r n ) long-term investors require E(r n ) > f n

21 Why to Care about Term Structure at all Yield curve - plot yields to maturities as a function of time to maturity But we also know that yield is a function of short rates, i.e. (1 + y 2 ) = [(1 + r 1 )(1 + r 2 )] 1/2 so if y 2 > r 1 = r 2 > r 1 - yield curse slopes upwards It is difficult to predict future short rates with the yields due to liquidity premium, but steep yields curves predict expansion comparing the market expectation of interest rates with your own, whether you are relatively bullish or bearish on interest rates

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