CHAP09

Fin4360: Investment AnalysisSpring, 2006Dragon Tang: 

Fin4360: Investment Analysis Spring, 2006 Dragon Tang Lectures 6&7 Bond Prices and Yields February 6, 2006 Readings: Chapter 9 Practice Problem Sets: 1-17,22,24,25,26,29,30,31,33,35,36

“Conventional Wisdom” Predictors: 

“Conventional Wisdom” Predictors Super Bowl: Rule for the Seahawks! Hemline: Short skirts help our market Presidential election: Democrats beat republicans by 5% Halloween effect: Sell in May and go away. SAD effect: We love sunshine! Lunar phase: Full Moon is depressing …

Homework 1: 

Homework 1 Financial markets vs banking system Risk vs return Municipal bond: Current yield = coupon/price Market indexes

Bond Prices and Yields: 

Bond Prices and Yields Objectives: Analyze the relationship between bond prices and and bond yields. Calculate how bond prices will change over time for a given interest-rate projection. Identify the determinants of bond safety and rating. Analyze how callable, convertible, and sinking fund provisions will affect a bond's equilibrium yield to maturity. Define the yield curve and study its properties

Coupon Bonds: 

Coupon Bonds Coupon bonds pay regular, constant interest usually semiannually (at the 15 or 30 of the month). The actual purchase price of the bond is the price of the bond plus accrued interest.

Coupon Bonds: 

Coupon Bonds Example: A $10,000 face value U.S. Treasury note with a coupon rate of 7¼% has an ask quote of 118:22. The bond made a coupon payment 95 days ago and the next coupon payment will be made in 88 days. If you purchased the today, how much would you pay?

Corporate Bonds: 

Corporate Bonds Trade in 1/8ths (explicit fractions, e.g. 1021/4), price in percentage Trade in units of $1,000 Current Yield=Annual coupon/price Corporate bond market is very thin compared to Treasury market Usually registered bonds Corporate bonds are subject to default risk Often callable and convertible

Convertible Bonds: 

Convertible Bonds Allow the holder to exchange bonds for a specified number of shares of stocks in the firm Conversion ratio = #of shares per bond. Market conversion value= is the current value of the shares for which the bond may be exchanged. Conversion premium= Bond price – Mkt conversion value

Convertible Bonds: 

Convertible Bonds Example: Suppose the price of XYZ bond is $1,000, convertible in 40 shares of XYZ. The price of XYZ is currently $20. Is it worth to convert? What if the price of XYZ is $30?

Bond Securities: 

Bond Securities Callable bonds: issuer can buy it back at pre-specified price Puttable bonds: bondholders can extend or retire the bond Floating rate bonds: coupon rate is linked to market interest rate Preferred stocks: pay dividends but not voting rights International bonds Bond innovations

Bond Ratings: 

Bond Ratings Moody’s S&P Aaa(1,2,3) AAA Aa AA A A Baa BBB Ba BB B B Caa CCC Ca CC C C D D Investment grade Speculative grade (junk bonds)

Junk Bonds: 

Junk Bonds Rating less than Baa by Moody’s or BBB by S&P Were fallen angels before 1977 Original-issue junk bonds started in 1977 Michael Milken and others felt that the default rates did not justify the wide yield spreads which prevailed

Yield Spreads: 

Yield Spreads Spread between corporate bond yield and “equivalent” Treasury yield Yield spreads widen when the economy is in recession During uncertain times, a flight to quality occurs when investors move their funds to safer bonds

Determinants of Bond Safety: 

Determinants of Bond Safety Coverage ratios Times-interest earned (EBIT / Interest) Fixed-charge coverage (EBIT / fixed cash obligations) Leverage ratios Liquidity ratios Current ratio (current asset / current liabilities) Quick ratio (current assets w/out inventories / current liab.) Profitability ratios Return on assets (EBIT / total assets) Cash flow to debt ratio

Bond Indentures: 

Bond Indentures The bond indenture is a contract between the bond issuer and the bondholder. Protective covenants place restrictions on the issuers activities. Sinking fund Subordination of further debt Dividend restrictions Collateral Debentures: un-collateralized bonds.

Holding Period Return (HPR): 

Holding Period Return (HPR) Ingredients: Beginning Price Dividend/Interest Income Ending Price HPR=Rate of return over a given investment period

Slide17: 

Stocks: Bonds: Houses:

Annual Rate Approximation (APR): 

Annual Rate Approximation (APR) Example: If you earn 10% over a 3-month period, an approximation for the annual rate would be: APR= HPR x (#of periods in one year)

Slide19: 

Example: If you earn 10% over a 3-month period, the quarterly-compounded annual rate would be: Where n = #of period in a year

Slide20: 

Holding period greater than one year Example: If you earn 50% over a 2-year holding period, then an approximation for the annual rate would be:

Slide21: 

Holding period greater than one year Example: If you earn 50% over a 2-year holding period, then the annual compounded rate would be:

Relationship APR--EAR: 

Relationship APR--EAR Let n be the number of compounding periods in a year As n becomes larger (I.e. we compound more often) Continuous Compounding

Continuous Compounding: 

Continuous Compounding Effective Annual Rates for an APR of 6 percent Compounding Frequency n EAR(%) Annually 1 6.00 Semiannually 2 6.09 Quarterly 4 6.13636 Monthly 12 6.16778 Weekly 52 6.17998 Daily 365 6.18313 Continuously 6.18365

Present Value: 

Present Value Value today of an amount to be received in the future FVn = payment received at time n n = number of periods r = interest rate per period PVn = Present value

Present Value. Example: 

Present Value. Example Example: What is the present value of $1 to be received (or paid) in 10 years if the annual interest rate is 5%?

Bond Pricing: 

Bond Pricing Bond value =Present value of coupons + present value of par value

Bond Pricing: 

Bond Pricing Example: Find the value (price) of a 30-year semiannual $1,000 par bond with coupon rate of 8% when similar bonds are also paying 8%. Using formula or PRICE function in Excel.

Bond Pricing: 

Bond Pricing Example: Find the value (price) of a 30-year semiannual $1,000 par bond with coupon rate of 8% when similar bonds are also paying 10% (I.e., 5% semi-annually).

Bond Pricing: 

Bond Pricing Market interest rates rise Þ bond prices fall

Bond Pricing: 

Bond Pricing Example: Find the value (price) of a 30-year semiannual $1,000 par bond with coupon rate of 8% when similar bonds are also paying 6% (I.e., 3% semi-annually).

Bond Pricing: 

Bond Pricing Market interest rates fall Þ bond prices rise

Bond Pricing and Market Interest Rates: 

Bond Pricing and Market Interest Rates Market Maturity Coupon Interest Bond Value Rate Rate Price $ 1,000 8% 8% $1,000.00 $ 1,000 8% 10% $ 810.71 $ 1,000 8% 6% $1,276.75

Bond Pricing: Convexity: 

Bond Pricing: Convexity Convexity - An increase in the interest rate results in a price decline that is smaller than the price gain that results from a decrease of equal magnitude in the interest rate. Flatter Bond Price Market Interest Rate

Bond Pricing: Maturity and Coupon: 

Bond Pricing: Maturity and Coupon The longer the time to maturity/lower coupon rate of a bond, the greater the sensitivity of price fluctuations to the interest rate. Price of a 8% Coupon Bond when Mkt Interest Rate is Maturity 4% 6% 8% 10% 12% 1yr $1,038 $1,019 $1,000 $981 $963 10yrs 1,327 1,148 1,000 875 770 20yrs 1,547 1,231 1,000 828 699 30yrs 1,695 1,276 1,000 810 676

Yield to Maturity: 

Yield to Maturity Yield to maturity is a measure of the average rate of return that will be earned if the bond is held to maturity. YTM assumes reinvestment of the coupons at the yield to maturity. YTM is the solution (IRR) of :

Yield to Maturity: 

Yield to Maturity Example: Find the YTM of a semiannual bond with a price = $1,276.76, 30 years left to maturity, and a coupon rate of 8%. (Use trial and error method. In Excel: use Solver or YIELD function).

Bond Yields: 

Bond Yields Yield To Maturity (YTM). Bond Equivalent Yield. Annualized YTM using Simple interest (APR) Effective Yield. Annualized YTM using Compound Interest Current Yield. Annual Coupon / Bond Price Coupon Rate. Annual Coupon / Face Value

Bond Yields Relationships: 

Bond Yields Relationships If a bond sells at a Discount (capital gain embedded): Coupon Rate < Current yield <Effective yield If a bond sells at a Premium (capital losses embedded): Coupon Rate > Current yield > Effective Yield

Callable Bonds: 

Callable Bonds Refunding - the firm retires debt and issues new bonds at a lower coupon rate. Yield to Call – Computed as YTM with two differences Maturity is the First Callable Date Call Price Replace the Par value *Assumes the premium bond is called at Par.

Callable Bonds: 

Callable Bonds Bond Price Interest Rate Call Price Straight Bond Callable Bond

Yield to Call (YTC). If Call=Par: 

Yield to Call (YTC). If Call=Par Discount bonds: not likely to be called Call would enhance yield YTC > YTM Premium Bonds: likely to be called Call reduces price appreciation YTC < YTM WSJ quotes: -YTC for premium (callable) Bonds -YTM for discount (callable) bonds

Corporate Bonds: 

Corporate Bonds Promised versus Expected Yield The promised or stated yield is the maximum possible return if held to maturity. The expected yield weights the promised yield by the probability of future default. The default premium is the differential in promised yield between a corporate bond and a government bond.

Realized Compounded Yield (RCY): 

Realized Compounded Yield (RCY) Annualized return from reinvestment of all the Proceeds from the bond. Total return = Where T = number of years

RCY. Example I.: 

RCY. Example I. Consider a 2-yr bond selling at par and paying a 10% coupon once a year. The coupon is reinvested at 10%. Time 0 1 2 Actual Cash Flows 0 $100 $1,100 FV of reinvestment $ 110 Total $1,210 Total Return: 1,210/1,000=1.21 RCY= (1.21)0.5-1=10%

RCY. Example II.: 

RCY. Example II. Consider a 2-yr bond selling at par and paying a 10% coupon once a year. The coupon is reinvested at 15%. Time 0 1 2 Actual Cash Flows 0 $100 $1,100 FV of reinvestment $ 115 Total $1,215 Total Return: 1,215/1,000=1.215 RCY= (1.215)0.5-1=10.23%

YTM versus RCY: 

YTM versus RCY If the reinvestment rate >YTM, then RCY>YTM If the reinvestment rate <YTM, then RCY<YTM If the reinvestment rate =YTM, then RCY=YTM

Realized Compounded Yield Example: 

Realized Compounded Yield Example Example: A $1,000 20-year 10% semiannual coupon bond purchased at face value (I.e., YTM=10%) Assumed Total Realized Reinvestment Future Compound Rate (%) PMT x FA(rr/2,2T) Dollars Return (%) 0 $2,000 $3,000 5.57 5 3,370 4,370 7.51 8 4,751 5,751 8.94 9 5,352 6,352 9.46 10 6,040 7,040 10.00 11 6,830 7,830 10.56 12 7,738 8,738 11.14

Holding Period Return: 

Holding Period Return Where Bt = Bond Price at time t Bt+1= Bond Price at time t+1

Bond Prices over Time: 

Bond Prices over Time Coupon bonds Premium bonds move towards par as they approach maturity Discount bonds move towards par as they approach maturity

In well-functioning Bond Markets: 

In well-functioning Bond Markets Bond Sell at Par if Coupon rate = Market Rate Bond Sell at Premium if Coupon rate > Market Rate Bond Sell at Discount if Coupon rate < Market Rate (Examples: Zero-coupon bonds,STRIPS) However, in Equilibrium, HPR=Market Rate!

Yield Curve: 

Yield Curve 3 6 1 2 3 5 10 30 Mos. Years 7.00% 6.50% 6.00% 5.50% 5.00% Source: Federal Reserve statistical release H.15 Treasury Security Yield Curve August 1, 1997 August 1, 1996

Yield Curve Theories: 

Yield Curve Theories Term structure of interest rates: Expectations Theory Liquidity Preference Theory Combination (Synthesis)

The Expectation Hypothesis: 

The Expectation Hypothesis Example: Suppose that 2-year bonds offer yields to maturity of 6%, and 3-year bonds have yields of 7%. What is the expected one-period rate for the third year?

Wall Street Interview Question: 

Wall Street Interview Question From the term structure of interest rates, you see that the five-year spot rate is 10% per annum and the 10-year spot rate is 15% per annum. What is the implied forward rate from year 5 to year 10?

Yield Curve. Combination of Theories: 

Yield Curve. Combination of Theories Example: Suppose the liquidity preference theory predicted a 4% rate for 1-year securities and a 6% rate for 2-year securities. However, investors expected the interest rate in year 2 fall by 2%. 6% 4% Liquidity Preference Yield Curve Combined Yield Curve Maturity Yield 1 2

Summary: 

Summary Inverse relationship between bond prices and bond yields Premium and discount bonds Corporate bonds and default risk Ratio analysis and bond safety Role of the Bond indenture Term structure of interest rates Expectations theory Liquidity preference theory Next Class: Managing Bond Portfolios