Economics 173A and Management 183

Financial Markets

Fixed Income Securities: Bonds

Bonds

• Debt Security – corporate or government borrowing • Also called a Security • Covenants or Indenture define the contract (this can be complex) • 2 types of Payments: principal • Interest payments are the • Principal payment is the Face 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 Residual Claim High Priority on cash flows Lowest Priority on cash flows Tax Deductible Not Tax Deductible Fixed Infinite life No Management Control Management Control

Bonds Hybrids (Combinations Common Stock of debt and equity) Bond Analysis • Characteristics – – Types: mortgage, callable, convertible, senior or subordinated, floating rate, zero coupon . – Denomination () 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

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 1 • Prices quoted in points (of face) + /32 • No default / credit risk

US Treasury Bonds Rates

Maturity 7-6-90 9-11-01 4-9-14 7-6-15 3 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 % 148.5 bps 10 Year 4.84 % 8.51 % 2.71 % 219.8 bps 30 Year 5.43 % 8.51 % 3.56 % 308.0 bps

http://www.treasury.gov/resource-center/data-chart-center/interest- rates/Pages/TextView.aspx?data=yield

Corporate Bonds Maturity 4/9/2014 2015 2016 2yr AA 0.50 2yr A 0.70 5yr AAA 1.80 5yr AA 2.05 5yr A 2.18 10yr AAA 3.10 10yr AA 3.33 10yr A 3.59 20yr AAA 3.99 20yr AA 4.32 20yr A 4.64 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. 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.

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)

Example

We invest $100. 1 year later we have $130 and, a year later, we have $150. Calculate the following:

Total Return HPR Annualized HPR CAGR APR APY Bond Pricing

• DCF Technique

T T B = C t + Face P ∑ t T t=1 (1+r ) (1+r )

PB = Price of the bond

Ct = interest or coupon payments T = number of periods to maturity r = discount rate Bond Pricing an 8% 10 year bond at 6%.

Ct = 80 (A), F = 1000, T = 10 periods, r = 6% (A)

10 P = 80 + 1 B Σ t 1000 10 t =1 (1+.06) (1+.06)

PB = $1,147.20

Three Bonds in a 10 percent world …

Insert Figure 4-6 here. Bond Pricing

• Zero Coupon Bonds par value current bond price = PV(principal) = (1+ r) n

• Consols – Zero Face Bonds ∞ cash flow at time t = current bond price ∑ t t=1 (1+ r) cash flow at time t = r this is “capitalizing” a cash flow Bond Yields

• : 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. 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 Price

Yield Bond Risks

• Price Risks – Default risk – Interest rate risk

• Convenience Risks – Call risk – Reinvestment rate risk – Marketability risk 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

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

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. • = bond price + accrued interest • = bond price – By convention, accrued interest is calculated using a 360-day year. 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?

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. 5 30 1,000 = + = p0 ∑ t 5 913.39 t=1 (1+ 0.10/ 2) (1+ 0.10/ 2)

Step Two: The $30 coupon is added to $913.39. The sum is $943.19. Step Three: The value $943.19 is discounted back 4 months to the purchase date. 943.39 p0 = = 913.16 (1+ 0.10 / 2)4/ 6 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 $923.16. Forward Rates

term years rat year

2 11 (1+=++2r 0 ) (1 10 rr ) (1 11 ) 21 1 (1+2rr 0 ) / (1 +=+ 10 ) (1 11 r )

One-year rate one year from now

3 21 (1+=++30r ) (1 20 rr ) (1 12 ) 32 1 (1+30rr ) / (1 +=+ 20 ) (1 12 r )

One-year rate two years from now