Bonds

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Bonds

• Lakehead Shad Valley

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Bond Features

• Fixed coupon rate expressed as a of the par or
  face value
• face value 1,000
• known term to maturity
• required rate of return is the rate the market
  demands on such an investment YTM
• coupon payments are usually made semi-annually

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Bond Concepts

• Note the difference between Canada Bonds and
  Canada Savings Bonds (CSBs)
• CSBs are not negotiable.if you want to liquidate
  such an investment you redeem them through a
  financial institution like a Bank.

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Bond Terminology

• Par value face value
• coupon rate
• term to maturity
• zero-coupon bonds
• call provision
• convertible bonds
• retractable and extendible bonds
• floating-rate bonds

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Quoted Bond Prices

• Quoted bond prices do not include the accrued
  interest that accrues between coupon payment
  dates.

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Bond Quality

• determinants of bond safety
• coverage ratios
• leverage ratio
• liquidity ratio
• profitability ratio
• cashflow to debt ratio
• bond ratings focus on the foregoing factors

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Bond Indentures

• Contract between the issuer and bondholder
• protective covenants
• sinking funds (two systems)
• subordination of further debt
• dividend restrictions
• collateral

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Bond Pricing

• Present value of all expected future cashflows
• Yield to maturity
• ex ante calculation
• underlying assumptions
• Yield to call
• Realized Compound Yield (ex post) versus Yield to
  Maturity (ex ante)
• Yield to Maturity versus Holding Period Return
• current yield

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After-Tax Returns

• OID - original issue discount - example
  zero-coupon bonds
• OIDs result in an implicit interest payment to
  the holder of the security.
• Revenue Canada requires tax on imputed interest
  each year.

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Strip Bonds

• A derivative security
• a product created by an investment dealer
  decomposing a government bond and selling
  individual claims to the different parts of the
  bond to different investors

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Stripped Bond

• Is a claim on the face value of a coupon-bearing
  bond.
• The types of bonds that are stripped are often
• government of Canada
• provincial bonds
• Ontario Hydro, Hydro Quebec

K. Hartviksen
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Stripped Bonds

• Why are they called a derivative security?

New Market Price
New Market Price
Market Price
Stripped bond
K. Hartviksen
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What is the appeal of a Stripped Bond for
investors?

• You avoid the problems associated with
  reinvestment of the annual coupons.
• A yield-to-maturity (YTM) calculation assumes
  that all coupon interest that will be received is
  reinvested at the ex ante YTM.
• Because there are no intermediate cash flows
  (coupon interest) involved in a stripped bondthe
  ex ante YTM must equal the ex post YTM. This
  allows the investor to lock in a rate of return
  on their stripped bond investment for the term
  remaining to maturity (as much as 30 years!

K. Hartviksen
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Stripped bond example

• What price would you pay for a stripped bond if
  it has 30 years to maturity, 20,000 face value
  and offers a 12 yield-to-maturity?
• P0 20,000(PVIFn30, k 12)
• 20,000 (.0334)
• 668.00
• Many people who are planning for retirement use
  such securities to lock in a given rate of return
  in their RRSPs.
• Parents can use them to save for their childs
  education through an RESP.

K. Hartviksen
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Disadvantages of Stripped bonds

• You lock in a given rate of returnif interest
  rates rise, the market value of the investment
  will drop very rapidly.
• As a derivative product, the investment is
  illiquid (ie. No secondary market for this
  exists). Your ability to liquidate your
  investment will depend on the underwriters
  willingness to reverse the transaction. Hence
  this is not a good vehicle to use to make
  speculative returns when trying to take advantage
  of interest rate forecasts.
• Held outside of an RRSP or RESP, the imputed
  interest earned each year is subject to tax
  despite the fact that you did not receive a cash
  return.

K. Hartviksen
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Interest Rate Price Sensitivity

• Because there are no coupon payments, stripped
  bonds have a duration equal to their term to
  maturity.
• Because of the distant cashflow involved, the
  current price (present value of that distant cash
  flow) is highly sensitive to changes in interest
  rates.

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Price Sensitivity Example

• Take our previous example
• P0 20,000(PVIFn30, k 12)
• 20,000 (.0334)
• 668.00
• Assume now that interest rates fall by 16.7 from
  12 to 10. What is the percentage change in
  price of the bond?
• P0 20,000(PVIFn30, k 10)
• 20,000 (.0573)
• 1,146.00
• Percentage change in price (1,146 - 668) /
  668
• 71.6

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Price Elasticity of Stripped Bonds
30 year stripped bond price given different YTM.
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Bond Value

• Value C(PVIFAn,r) 1,000(PVIFn,r)
• involves an annuity stream of payments plus the
  return of the principal on the maturity date

Bond Price discounted value of all future cash
flows
1 2 3 4 5 6 M
60 60 60 60 60 60 60
1,000
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Yield to Maturity

• An ex ante calculation
• the discount rate that equates the market price
  of the bond with the discounted value of all
  future cash flows.
• Is the investors required return
• changes in response to
• changes in the general level of interest rates in
  the economy
• changes in the risk of the issuing firm
• changes in the risk of the bond itself

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Bond Price Behaviour

• Bond prices are affected by changes in interest
  rates.
• Bond prices are inversely related to interest
  rates
• Longer term bond prices are more sensitive to a
  given interest rate change
• low coupon rate bond prices are more sensitive to
  a given interest rate change

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Example of Bond Price

• The Canada 10.25 1 Feb 04 is quoted at 123.95
  yielding 5.27. This means that for a 1,000 par
  value bond, these bonds are trading a premium
  price of 1,239.50
• The figure represents bond prices as of June 17,
  1998.
• This bond has 5 years and 8 months
  (approximately) until maturity 5(8/12) 5.7
  years
• Bond Price 102.50(PVIFAn5.7 ,r5.27)
  1,000 / (1.0527)5.7
• 102.50(PVIFAr5.27, n 5.7) 746.21
• 102.50(4.8156653) 746.21
• 493.61 743.42 1,237.03
• Can you explain why the quoted price might differ
  from your answer?

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K. Hartviksen
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Sensitivity Analysis of Bonds
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Prices over time
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K. Hartviksen
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How a change in interest rates affects market
prices for bonds of varying lengths of maturity.
1,055.35
10 yield-to-maturity
Years to maturity
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Yield to Maturity
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Yield to Maturity ...
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Yield to Maturity ...
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Yield to Maturity ...
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Yield to Maturity ...
Now instead of earning 9.2 she will only earn
8.478 because of the poor reinvestment rate
opportunities.
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The Reinvestment Rate Assumption

• It is crucial to understand the reinvestment rate
  assumption that is built-in to the time value of
  money.
• Obviously, when we forecast, we must make
  assumptionshowever, if that assumption not
  realisticit is important that we take it into
  account.
• This reinvestment rate assumption in particular,
  is important in the yield-to-maturity
  calculations in bondsand in the Internal Rate of
  Return (IRR) calculation in capital budgeting.

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Bond Applications

• Bonds are typically purchased by life insurance
  companies.
• These firms plan to buy and hold the bonds until
  they mature.
• These firms require a given return in order to
  accumulate a terminal value 20, 25 or 30 years
  out into the future.however, they are acutely
  aware that the reinvestment of the coupon
  interest can dramatically affect their realized
  return (making it different than the
  yield-to-maturity.)\
• They have some alternativeschoose zero coupon
  bonds, or immunize themselves from interest rate
  fluctuations (using duration matching strategies)

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Yield to Maturity The Approximation Approach

• Shad Valley

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The Approximation Formula

• F Face Value Par Value 1,000
• P Bond Price
• C the semi annual coupon interest
• N number of semi-annual periods left to
  maturity

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Example

• Find the yield-to-maturity of a 5 year 6 coupon
  bond that is currently priced at 850. (Always
  assume the coupon interest is paid
  semi-annually.)
• Therefore there is coupon interest of 30 paid
  semi-annually
• There are 10 semi-annual periods left until
  maturity

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Example with solution

• Find the yield-to-maturity of a 5 year 6 coupon
  bond that is currently priced at 850. (Always
  assume the coupon interest is paid semi-annually.)

The actual answer is 9.87...so of course, the
approximation approach only gives us an
approximate answerbut that is just fine for
tests and exams.
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The logic of the equation

• The numerator simply represents the average
  semi-annual returns on the investmentit is made
  up of two components
• The first component is the average capital gain
  (if it is a discount bond) or capital loss (if it
  is a premium priced bond) per semi-annual period.
• The second component is the semi-annual coupon
  interest received.
• The denominator represents the average price of
  the bond.
• Therefore the formula is basically, average
  semi-annual return on average investment.
• Of course, we annualize the semi-annual return so
  that we can compare this return to other returns
  on other investments for comparison purposes.