Bonds

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

The Fundamentals of Bond Valuation ,[object Object],Where: P m =the current market price of the bond n = the number of years to maturity C i = the annual coupon payment for bond i i = the prevailing yield to maturity for this bond issue P p =the par value of the bond

The Present Value Model ,[object Object],where: P m = the current market price of the bond n = the number of years to maturity C i = the annual coupon payment for Bond I i = the prevailing yield to maturity for this bond issue P p = the par value of the bond

The Yield Model ,[object Object],where: i = the discount rate that will discount the cash flows to equal the current market price of the bond

Computing Bond Yields ,[object Object],Nominal Yield Measures the coupon rate Current yield Measures current income rate Promised yield to maturity Measures expected rate of return for bond held to maturity Promised yield to call Measures expected rate of return for bond held to first call date Realized (horizon) yield Measures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price. It can also measure the actual rate of return on a bond during some past period of time.

Nominal Yield ,[object Object]

Current Yield ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Promised Yield to Maturity ,[object Object],[object Object],[object Object],[object Object]

Computing the Promised Yield to Maturity ,[object Object]

Computing Promised Yield to Call ,[object Object],[object Object],[object Object],[object Object],[object Object]

Realized (Horizon) Yield Present-Value Method

Calculating Future Bond Prices ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

REALISED YIELD TO MATURITY FUTURE VALUE OF BENEFITS (1+ r* ) 5 = 2032 / 850 = 2.391 r* = 0.19 OR 19 PERCENT

Yield Adjustments for Tax-Exempt Bonds ,[object Object],[object Object],[object Object],[object Object]

Bond Valuation Using Spot Rates ,[object Object],[object Object],[object Object],[object Object],[object Object]

What Determines Interest Rates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What Determines Interest Rates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Spot Rates and Forward Rates ,[object Object],[object Object]

ILLUSTRATIVE DATA FOR GOVERNEMNT SECURITIES Face Value Interest Rate Maturity (years) Current Price Yield to maturity 100,000 0 1 88,968 12.40 100,000 12.75 2 99,367 13.13 100,000 13.50 3 100,352 13.35 100,000 13.50 4 99,706 13.60 100,000 13.75 5 99,484 13.90

FORWARD RATES 88968 100000 • ONE - YEAR TB RATE 100000 88968 = r 1 = 0.124 (1 + r 1 ) • 2 - YEAR GOVT. SECURITY 12750 112750 99367 = + + r 2 = 0.1289 (1.124) (1.124) (1 + r 2 ) • 3 - YEAR GOVT. SECURITY 13500 13500 113500 100352 = + + (1.124) (1.124) (1 .1289) (1.124) (1.1289) (1 + r 3 ) r 3 = 0.1512

Term Structure of Interest Rates ,[object Object],[object Object],[object Object],[object Object],[object Object]

Expectations Hypothesis ,[object Object]

Liquidity Preference Theory ,[object Object]

Segmented-Market Hypothesis ,[object Object]

Trading Implications of the Term Structure ,[object Object]

Yield Spreads ,[object Object],[object Object],[object Object],[object Object]

Yield Spreads ,[object Object]

What Determines the Price Volatility for Bonds ,[object Object],Where: EPB = the ending price of the bond BPB = the beginning price of the bond

What Determines the Price Volatility for Bonds ,[object Object],[object Object],[object Object],[object Object],[object Object]

What Determines the Price Volatility for Bonds ,[object Object],[object Object],[object Object],[object Object]

The Duration Measure ,[object Object],[object Object],[object Object],[object Object],[object Object]

Characteristics of Macaulay Duration ,[object Object],[object Object],[object Object],[object Object],[object Object]

Modified Duration and Bond Price Volatility ,[object Object],Where: m = number of payments a year YTM = nominal YTM

Modified Duration and Bond Price Volatility ,[object Object],[object Object],Where:  P = change in price for the bond P = beginning price for the bond D mod = the modified duration of the bond  i = yield change in basis points divided by 100

Bonds

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Bonds