Economics 173A and Management 183 Financial Markets

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1 Economics 173A and Management 183 Financial Markets Fixed Income Securities: Bonds

2 Bonds Debt Security corporate or government borrowing Also called a Fixed Income Security Covenants or Indenture define the contract (this can be complex) 2 types of Payments: interest principal Interest payments are the Coupon Principal payment is the Face

3 Bond Basics Fixed Income Securities: A security such as a bond that pays a specified cash flow over a specific period. Fixed Income Securities vs. Common Stock Fixed Claim High Priority on cash flows Tax Deductible Fixed Maturity No Management Control Residual Claim Lowest Priority on cash flows Not Tax Deductible Infinite life Management Control Bonds Hybrids (Combinations of debt and equity) Common Stock

4 Bond Analysis Characteristics Types: mortgage, callable, convertible, senior or subordinated, floating rate, zero coupon. Denomination (Par value) Face Coupon, Dates of Coupon Payments Sinking Funds? Credit Rating Pricing present value of future cash flows Yields: Coupon yield = C / Price YTM = the DR that makes the NPV of CF s = 0 RCYTM = Compound all CFs to Term and do CAGR Sensitivity to Time, i.e. maturity Sensitivity to changes in interest rates

5 Treasury Bills, Notes, & Bonds Bills 90 days to 6 months Notes 1 year up to 10 years Bonds to 30 years Bond & Note: Face (denomination) of $1,000; quotes in $100 s Bills: Face = $10,000. Discounted and quoted at Yield. Bond & Note: Coupon (rate) paid semi-annually Prices quoted in points (of face) + 1 / 32 No default / credit risk

7 US Treasury Bonds Rates Maturity Month 3.36 % 8.08 % 0.02 % 2 bps 6 Month 3.23 % 8.14 % 0.04 % 9 bps 2 Year 3.53 % 8.32 % 0.40 % 55.7 bps 3 Year 3.82 % 8.41 % 0.87 % 95 bps 5 Year 4.41 % 8.44 % 1.69 % bps 10 Year 4.84 % 8.51 % 2.71 % bps 30 Year 5.43 % 8.51 % 3.56 % bps

8 Corporate Bonds Maturity 4/9/ yr AA yr A yr AAA yr AA yr A yr AAA yr AA yr A yr AAA yr AA yr A 4.64

9 Bond Pricing As with all Financial Assets The price is a Present Value of the expected cash flows discounted at the appropriate (relative to risk) discount (interest) rate.

10 Coupon Payments Relative to other types of securities, bonds produce cash flows that an analyst can predict with a high degree of precision. Fixed rate Variable rate Zero coupons Consols consolidated annuities - perpetuities introduced in 1751.

11 Rates, Returns Total Return (TR) Holding Period Return (HPR) Compound Average Growth Rate (CAGR) Risk-adjusted Discount Rate (RADR) Annual Percentage Rate (APR) Annual Percentage Yield (APY)

13 Example We invest $ year later we have $130 and, a year later, we have $150. Calculate the following: Total Return HPR Annualized HPR CAGR APR APY

14 Bond Pricing DCF Technique P B T t= C t Face t (1 + r) 1 (1 + r) = + T T P B = Price of the bond C t = interest or coupon payments T = number of periods to maturity r = discount rate

15 Bond Pricing an 8% 10 year bond at 6%. C t = 80 (A), F = 1000, T = 10 periods, r = 6% (A) 10 Σ t =1 P = 80 + B (1+.06) t P B = $1, (1+.06) 10

16 Three Bonds in a 10 percent world Insert Figure 4-6 here.

17 Bond Pricing Zero Coupon Bonds current bond price = PV(principal) = par value ( 1+ r ) n Consols Zero Face Bonds cash flow at time current bond price = t t= 1 ( 1+ r) cash flow at time t = r this is capitalizing a cash flow t

18 Bond Yields Yield to Maturity: The discount rate that makes the present value of a bond s payments equal to its price, or NPV = 0 Internal rate of return from holding bond till maturity. Example 3 year bond with interest payment of $100, principal of $1,000 and current price of $900 Assume coupon proceeds are reinvested at the YTM.

19 Bond 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

20 Price Yield

21 Bond Risks Price Risks Default risk Interest rate risk Convenience Risks Call risk Reinvestment rate risk Marketability risk

22 Default Risk The income stream from bonds is not riskless unless the investor can be sure the issuer will not default on the obligation. Rating companies Moody s Investor Service Standard & Poor s Duff and Phelps Fitch Kroll

23 Default Risk Rating Categories Investment Grade Bonds Speculative Grade Bonds S&P Moody s Very High Quality AAA, AA Aaa, Aa High Quality A, BBB A, Baa Speculative BB, B Ba, B Very Poor CCC, CC, C, D Caa, Ca, C, D

24 Bond Yields Current or Annual Yield: Annual coupon divided by bond price. Different from YTM Accrued Interest Interest is earned for each day that a bond is held, although interest payments are generally made twice a year only. A bond buyer must pay the accrued interest to the seller of the bond. dirty price = bond price + accrued interest clean price = bond price By convention, accrued interest is calculated using a 360-day year.

25 Bond Pricing: Accrued Interest Example Consider a bond that is paying a six percent annual coupon rate in semiannual payments with a yield to maturity of 10 percent and two years and ten months until its maturity. What is the quoted price or clean price? What is the dirty price?

26 Bond Pricing: Accrued Interest What is the quoted price or clean price? Step One: Calculate the present value of a bond that has 2.5 years until it matures and pays semiannual interest coupons. p 30 1, = + = 5 t= 1 t ( / 2) ( / 2) Step Two: The $30 coupon is added to $ The sum is $ Step Three: The value $ is discounted back 4 months to the purchase date p0 = = / / 2 ( )

27 Bond Pricing: Accrued Interest What is the dirty price? Calculate the accrued interest for two months. There are 180 days between semiannual coupon payments and 30 days in a month. Therefore 60/180 is the fraction of the coupon payment earned by the seller. In other words the accrued interest is $10 and the dirty price is $

28 Forward Rates term years r at year (1 + r ) = (1 + r ) (1 + r ) (1 + r ) / (1 + r ) = (1 + r ) One-year rate one year from now (1 + r ) = (1 + r ) (1 + r ) (1 + r ) / (1 + r ) = (1 + r ) One-year rate two years from now

Fixed Income Securities: Bonds

Economics 173A and Management 183 Financial Markets Fixed Income Securities: Bonds Updated 4/24/17 Bonds Debt Security corporate or government borrowing Also called a Fixed Income Security Covenants or