Bond Portfolio Management Strategies: Basics

1
Bond Portfolio Management Strategies Basics

• 02/16/09

2
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?

3
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?

4
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
5
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)

6
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.

7
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
8
Nominal Yield

• Measures the coupon rate that a bond investor
  receives as a percent of the bonds 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

10
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.

11
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.

12
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.

13
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
14
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.

15
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.

16
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.

17
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
18
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

19
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

20
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)

21
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.

22
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

23
Readings

• RB 18 (up to page 698)