Bond Portfolio Management Strategies: Basics 02/16/09.

Bond Portfolio Management Strategies: Basics

02/16/09

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The Analysis and Valuation of Bonds

Questions to be answered:• How do you determine the value of a

bond based on the present value formula?

• What are the alternative bond yields that are important to investors?

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The Analysis and Valuation of Bonds

• How do you compute the following yields on bonds: current yield, yield to maturity, yield to call, and realized (horizon) yield?

• What are spot rates and how do we use these rates to estimate bond price?

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The Fundamentals of Bond Valuation

• The value of a bond is the present value of its cash flows.

n

tn

p

tt

m i

P

i

CP

2

12)21()21(

2

Where:Pm=the current market price of the bondn = the number of years to maturityCi = the annual coupon payment for bond ii = the prevailing yield to maturity for this bond issuePp=the par value of the bond

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The Fundamentals of Bond Valuation

• If yield < coupon rate, bond will be priced at a premium to its par value

• If yield > coupon rate, bond will be priced at a discount to its par value

• Price-yield relationship is convex (not a straight line)

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The Yield Model• Investors often price bonds in terms of yields

– the promised rate of return under certain assumptions.

• This yield can be computed if you know the bond’s current market price.

• We can approach the bond investment decision by comparing the bond’s promised yield to your required rate of return.

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Bond Yields

Yield Measure PurposeNominal 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.

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Nominal Yield

• Measures the coupon rate that a bond investor receives as a percent of the bond’s par value.

9

Current Yield

• The current yield is similar to dividend yield for stocks and is important for income-oriented investors.

• It is calculated as:

CY = Ci/Pm

where: CY = the current yield on a bond

Ci = the annual coupon payment of bond i

Pm = the current market price of the bond

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Nominal yield and current yield

• Both these measures are primarily descriptive in nature and contribute little to the investment decision making, especially if the investor is concerned about total return.

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Promised Yield to Maturity

• The promised yield to maturity (or simply YTM) is the rate of return that an investor will achieve if the following two assumptions hold:• Investor holds bond to maturity• All the bond’s cash flows are reinvested at the computed

yield to maturity

• The promised YTM = realized yield if the above two assumptions hold.

• Yield illusion – investors incorrectly stating that they are “locking-in” high yields during periods of high interest rates.

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Promised Yield to Call

• When the bond is callable by the issuing firm, investors need to consider the bond’s promised yield to call (YTC).

• This represents the return that an investor would earn if they hold the bond until the call date and can reinvest coupons at the YTC.

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Computing YTC

• Calculating the YTC is similar to calculating the YTM:

nc

tnc

ct

tm YTC

P

YTC

CP

2

12)21()21(

2

Where:Pm=the current market price of the bondnc= the number of years to first call dateCi = the annual coupon payment for bond iPc=the call price of the bond

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Using the YTC

• Premium bonds are evaluated in terms of “minimum yield”. This will be the smaller of the YTM and the YTC. When the bond is selling at a premium, and the price is greater or equal to the call price, investors should consider valuing the bond using the YTC instead of the YTM.

• The price, below which the YTM provides the minimum yield and above which the YTC provides the minimum yield, is known as the crossover price. At this price, the YTM = YTC and the yield is referred to as the crossover yield.

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Using the YTC

• When a bond has multiple call dates and prices, the bond should be priced using the lowest yield, or the yield to worst.

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Realized (Horizon) Yield

• The realized or horizon yield estimates the return you expect to generate on a bond that you plan to sell prior to maturity.

• This return can be used to estimate returns from various trading strategies.

• This measure requires additional estimates of future selling price and coupon reinvestment rates.

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Computing Realized Yield

• Computing realized yield:

• Note: This formulation assumes that you reinvest coupons at the realized yield. We will relax this assumption.

hp

thp

f

tt

m i

P

i

CP

2

12)21()21(

2

Where:Pm=the current market price of the bondhp= holding periodCi = the annual coupon payment for bond iPf= future selling price

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Calculating Future Bond Prices

• To compute a realized yield, we need an estimate for the future bond price at the time when we expect to sell the bond.

where:Pf = estimated future price of the bondCi = annual coupon paymentn = number of years to maturityhp = holding period of the bond in yearsi = expected semiannual rate at the end of the holding period

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phpn

tt

tf i

P

i

CP

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Incorporating Differential Reinvestment Rates

• The following steps can be used to calculate realized yield using differential reinvestment rates:• Calculate the future value at the horizon date of all coupon

rates reinvested at estimated rates.• Calculate the expected sales price at the horizon date

based on estimated YTM at that date.• The above two values added up represent the total ending-

wealth value.• Realized yield (per period) is:

1 valuebeginning

lue wealth vaending 2

1

n

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Yield Adjustments for Tax-Exempt Bonds• The interest income received from government and agencies

bond issues are fully or partially tax-exempt.

• To compare these issues with taxable bonds, , we need to compute the fully taxable equivalent yield (FTEY)

Where i = the promised yield on the tax exempt bondT = the amount and type of tax exemption (i.e., the investor’s

marginal tax rate)

T-1

iFTEY

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Spot Rates

• The yield curve is rarely flat, and is usually upward sloping, which means that investors require different rates of return for cash flows at different times.

• Therefore, it is inappropriate to discount all flows at a single rate and all cash flows should be discounted at spot rates consistent with the timing of the cash flows.

• Spot rates are the relevant rate of return for specific maturities.

• For Government issues, these rates are the yields for U.S. Treasury Strips.

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Bond Valuation Using Spot Rates

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tt

t

t

m i

CP

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1 )21(

• We can estimate the bond price accounting for different spot rates in the following way:

where: Pm = the market price of the bond

Ct = the cash flow at time tn = the number of yearsit = the spot rate for Treasury securities plus appropriate spread at maturity t

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Readings

• RB 18 (up to page 698)