Bus 315 Week 2 Ch' 11 Fixed Income Instruments Ch'12 Term Structure of Interest Rates

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Bus 315 Week 2Ch. 11 Fixed Income Instruments
Ch.12 Term Structure of Interest Rates
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Bond Characteristics

• Face or par value
• Coupon rate
• Zero coupon bond
• Compounding and payments
• Accrued Interest and dirty price
• Example find the price plus accrued interest for
  a 10 bond paying coupon 01.01 annually if the
  todays (03.01) price for this bond is 115 CAD.
• Answer

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Provisions of Bonds

• Secured or unsecured
• Registered or bearer bonds (Canada)
• Call provision
• Convertible provision
• Retractable and extendible (putable) bonds
• Floating rate bond
• Sinking funds

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Bond Pricing

• PB price of the bond
• Ct interest or coupon payments
• T number of periods to maturity
• r the appropriate discount rate

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Bond pricing (example)

• A 7 coupon bond that pays interest annually has
  a par value of CAD 1,000, matures in 5 years, and
  has a yield to maturity of 10. Calculate the
  bond price.
• Answer 886.28
• What if bond pays coupon semiannually?
• Answer

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Bond Prices and Interest Rates

• Prices and yields (required rates of return) have
  an inverse relationship
• When yields get very high the value of the bond
  will be very low
• When yields approach zero, the value of the bond
  approaches the sum of the cash flows

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Prices and Interest Rates
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Yield to Maturity

• Interest rate that makes the present value of the
  bonds payments equal to its price
• Solve the bond price formula for r
• Calculate YTM of a 7 coupon bond that pays
  interest annually has a par value of CAD 1,000,
  matures in 5 years and sells at CAD 886.28
• Answer

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Bond Pricing (2)
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Bond pricing (2) example

• A 7 coupon bond that pays interest annually has
  a par value of CAD 1,000, matures in 5 years, and
  has a yield to maturity of 10. Calculate the
  bond price.
• Answer 886.28

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Yield Measures

• Current Yield (Annual Interest/Market Price)
• Yield to Maturity
• Effective Annual Yield
• Yield to Call
• Realized Compound Yield
• Holding Period Return

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Effective Annual Yield

• Used to compare bonds of different maturities
• Calculated as
• Example find and compare EAY for
• A) 3-month T-bill sold at 980
• B) 6-month T-bill sold at 920

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Holding-Period Return

• where
• C coupon payment
• P1 price at the end of the period
• P0 beginning of the period price

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HPR example

• Suppose you buy today a 10 bond paying coupon
  annually with 5 years to maturity, YTM5. You
  sell it in one year when the YTM increases to
  10. Find HPR?
• Solution

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Realized Compound Yield vs. YTM

• Requires actual calculation of reinvestment
  income
• Solve for the Internal Rate of Return using the
  following
• Future Value sale price future value of
  coupons
• Investment purchase price

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Realized Compound Yield (Example)

• Two-year bond selling at par, 10 coupon paid
  once a year. First coupon is reinvested at 8.
  Find RCY

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Price Paths of Coupon Bonds
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Default Risk and Ratings

• Rating companies
• Moodys Investor Service
• Standard Poors
• Fitch IBCA
• Dominion BRS (Canada)
• Rating Categories
• Investment grade (BBB or above)
• Speculative grade (junk bonds)
• fallen angels
• original-issue junk

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Credit ratings by agencies

• SP (and Fitch) AAA, AA, AA, AA-, A, A, A-D
• Moodys Aaa, Aa1, Aa2, Aa3, A1, A2,
  A3Baa1Ba1.. B1C

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Factors Used by Rating Companies

• Coverage ratios
• Leverage ratio
• Liquidity ratios
• Profitability ratios
• Cash flow to debt

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Financial Ratios by Rating Class
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Protection Against Default

• Sinking funds
• Subordination of future debt
• Dividend restrictions
• Collateral

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Default Risk and Yield

• Risk structure of interest rates
• Default premiums
• Yields compared to ratings
• Yield spreads over business cycles
• Flight to quality

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Bond Pricing with Non-Constant Rates
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Zeros Prices and Yields
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Yield Curve
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Short rates VS Spot rates

• Short rates are rates prevalent in some future
  period (e.g. year 2)
• Spot interest rates are rates over period (e.g.
  2-year spot rate is an average rate for a 2-year
  period)
• Spot rates are equivalent to YTM for zero bonds
  of corresponding maturities

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Pricing of coupon bonds

• Coupon bond is similar to combination of zero
  bonds (some with the face value and maturities
  equal to those of coupons)
• Given interest rates structure mentioned, what is
  the price of an 8 bond with 3 years to maturity?
• Answer

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Holding Period Returns

• Should be similar to the rate over the period
• Verify with the previous example with zero bonds
  

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Forward Rates

• In real life investors dont know future short
  rates
• Only know bond prices and yields
• Still, we can predict the rates (forward rates)
• Example

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Forward Rates Calculation
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Liquidity Premium

• If investors have preference for short-term
  investments -gt positive liquidity premium
• Liquidity Premiumfn-E(rn)
• Suppose, there are two bonds. 1-year and 2-year
  zeros
• r18, E(r2)10
• Invest either in 1-year bond or in 2-year bond
  for 1 year

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Theories of term structure

• Yield curve may be
• Upward sloping (normal)
• Downward sloping
• Hump-shaped
• How we can explain that?

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Expectation Theory

• Yield curve is upward sloping if the short rates
  are expected to be higher in future
• fnE(rn)
• Forward rate give expected short rates

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Liquidity Preference Theory

• Short-term investors dominate the market
• To induce them invest in longer term instruments
  there should be a positive liquidity premium
• Suppose r110, E(r2)10, E(r3)10
• LP is positive, therefore y2gt10