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Bond Portfolio Management Strategies Basics

- 02/16/09

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?

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?

The Fundamentals of Bond Valuation

- The value of a bond is the present value of its

cash flows.

Where Pmthe current market price of the bond n

the number of years to maturity Ci the annual

coupon payment for bond i i the prevailing

yield to maturity for this bond issue Ppthe par

value of the bond

The Fundamentals of Bond Valuation

- If yield lt coupon rate, bond will be priced at a

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

discount to its par value - Price-yield relationship is convex (not a

straight line)

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 bonds

current market price. - We can approach the bond investment decision by

comparing the bonds promised yield to your

required rate of return.

Bond Yields

- Yield Measure Purpose

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

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.

Realized (horizon) yield

Nominal Yield

- Measures the coupon rate that a bond investor

receives as a percent of the bonds par value.

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

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.

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 bonds 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.

Promised Yield to Call

- When the bond is callable by the issuing firm,

investors need to consider the bonds 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.

Computing YTC

- Calculating the YTC is similar to calculating the

YTM

Where Pmthe current market price of the

bond nc the number of years to first call

date Ci the annual coupon payment for bond

i Pcthe call price of the bond

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.

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.

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.

Computing Realized Yield

- Computing realized yield
- Note This formulation assumes that you reinvest

coupons at the realized yield. We will relax this

assumption.

Where Pmthe current market price of the

bond hp holding period Ci the annual coupon

payment for bond i Pf future selling price

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 bond
- Ci annual coupon payment
- n number of years to maturity
- hp holding period of the bond in years
- i expected semiannual rate at the end of the

holding period

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

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 bond
- T the amount and type of tax exemption (i.e.,

the investors marginal tax rate)

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.

Bond Valuation Using Spot Rates

- 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 t
- n the number of years
- it the spot rate for Treasury securities

plus appropriate spread at maturity t

Readings

- RB 18 (up to page 698)

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