Topic

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Topic 4 Financial Instruments in the Market I
Bonds

• Dr. J. D. Han
• Kings College
• University of Western Ontario

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Objective

• Calculate the Rate of Returns on Bonds
• 2) Use the Term Structure of various Bonds for
  forecast of the economy

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1. What are Bonds?

• Definition Fixed Income Securities consist of
  bonds(debts secured with collaterals) and
  debentures(unsecured debts).
• Examples
• 1) Government Bonds All Levels
• Treasury Bills
• Short-term, Medium Term, and Long-term Bonds
• 2) Corporate Bonds
• Commercial Papers
• Mortgage Backed Securities

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2. Returns on BondsCoupon, and YieldFixed
Income may be a misnomerWhat you see is not
what you get

• 1) Definition
• Effective Annual Rate of Returns
• Yield to Maturity (YTM)
• Nominal annual Interest Rate
• Annual Capital Gains as percentage of Average
  Price of Bonds

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2) Approximation Formula for Yield to Maturity

• where Average Price (Purchase Price 100)/2
• And Annual Changes in Prices (Face Value
  Purchase Price) / Maturity Period

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Example

• suppose that newspaper on March 1, 2004
• Issue Coupon Rate Maturity Date Bid/Ask
  Yield
• ABC Co. 10 1 March 08/09 92 ?
• Yield to Maturity (10 8/4) / 96 x 100
  11.46
• /09 means that the bonds are extendable for a
  year.

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3) Formal Formula 1 Annual Payment of Coupons

• Market Price B, Face Value F, Coupon Rate I,
  Maturity Periods, and n years.
• Annual Yield to Maturity r is obtained from

Proof can be found in My Handout.
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Formal Formula 2 Semiannual Payment of Coupons

• Market Price B, Face Value F, Semiannual Coupon
  Rate I/2, Maturity periods 2n half years.
• Annual Yield to Maturity r is obtained from

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3) Discount or Premium?

• A bond could be sold in the financial market at
  the price higher than the Face Value.
• - Market Price gt Face Value Premium
• - yield to maturity lt coupon rate
• Eg) Face Value 1000 Coupon Rate 10 Market
  Price 1050
• Yield to Maturity ?
• Otherwise, Market Price lt Face Value Discount
• - Yield to Maturity gt Coupon Rate
• Eg) Face value 1000 Coupon rate 2 Market
  Price 950
• Yield to Maturity ?

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Bonds always at Discount Zeros (Zero Coupon
Bonds)

• Bonds which are stripped of coupons, which are
  sold separately.
• Zeros are all sold in the market below the face
  value, at a discount
• YTM (Face value market price) / of maturity
  periods

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Different Rates of Returns on Different Bonds

• Yield R Risk Premium
• The higher is the Risk, the higher the Yield
  should be
• Default/Credit Risk measured with Bond Ratings
• (Financial) Market Risk measured with
• (1) the Standard Deviation of Yields over time
• -Mean Variance Theorem or alternatively
• (2) with Beta Capital Asset Pricing Model
• SD measures the entirety of the fluctuations
  of the rates of returns, and Beta measures only
  the non-diversifiable portion of the fluctuation.
• Liquidity Risk and Inflation(Monetary Policy)
  Risk Term Structure Theory

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3. A Variety of YTMs1) Equalization of YTM for
bonds with the same risk characteristics

• Competition in the financial market leads to the
  equalization of YTM of various bonds and other
  financial assets as long as have the same risk
  characteristics.

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2) Different Rates of Returns on Different Bonds

• Differences in YTM for Different Bonds
• Compensation for differences in Risk
• Differences in Risk Premium

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3) Different YTMs of Bonds issued by the same
borrower for a variety of Terms to Maturity Term
Structure of Interest Rates

• Same Government Bonds with Different Maturity
  Dates
• Ontario Government Bonds which will mature and be
  repaid in six months
• Ontario Government Bonds which will mature and be
  repaid in one year
• Ontario Government Bonds which will mature and be
  repaid in two years
• Their annual actual interest rates (annual
  yields, annual rate of returns) differ from each
  other

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4) What risk?

• a) Default/Credit Risk The lower the Bond
  Rating, the higher the risk of default The
  higher the risk premium The higher the YTM
  should be in order to induce the people to hold
  the bonds of more risk
• -gt Bond Rating show the level of this risk
• b) Liquidity Risk
• c) Inflation Risk
• d) (Financial) Market Risk
• (1) Mean Variance Theorem The higher the
  SD (variance) of the price and returns over
  time, the higher the rate of return should be
• (2) Capital Asset Pricing Model The higher the
  Correlation of the rate of return of a bond with
  the overall Market Index, the higher the rate of
  return should be.
• e) Idiosyncratic Risk specific to one particular
  bond

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4. Credit Risk and Bond RatingBond Rating
Services in the world

• Moodys
• Aaa (best quality)
• Aa (high quality)
• A (uppper-medium-grade)
• Baa (medium grade)
• _____________
• Ba (Speculative)
• B
• Caa
• Ca
• C

• Standard Poors
• AAA (extremely strong)
• AA (very strong)
• A (strong)
• BBB (adequate or fair)
• _________
• BB(uncertain or speculative)
• B
• CC (extremely vulnerable)

Canadian Bond Rating Services Combined with S
Ps
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Junk Bonds?

• Bonds are generally classified into two groups -
  "investment grade" bonds and "junk" bonds.
  Investment grade bonds include either Standard
  Poor's (AAA, AA, A, BBB) or Moody's (Aaa, Aa, A,
  Baa).
• The term "junk" is reserved for all bonds with
  Standard Poor's ratings below BBB and/or
  Moody's ratings below Baa.
• Investment grade bonds are generally legal for
  purchase by banks junk bonds are not.

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Some Canadian ExamplesSourcehttp//www.stand
ardandpoors.com/RatingsActions/RatingsLists/Canadi
anIssuers/index.html

• Ontario Government AA
• Quebec Government A
• York Municipality AAA
• Rogers Cable systems BB
• Xerox Canada BBB
• New Foundland A
• Nova Scotia A
• New Brunswick AA
• Nortel Network A
• Pacific Northern Gas BB
• Air Canada BB
• Alberta Government AAA or AA
• Canadian Government AAA

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5. Liquidity Risk, Inflation Risk, and Term
Structure and Yield Curve

• Go back to previous example.
• 1) Liquidity Risk Premium Theory
• -gt Simply, the longer the term, the higher the
  liquidity risk and thus the higher the risk
  premium and the YTM
• 2) Inflation Expectation Theory
• -gt (Future) Monetary/ Economic Conditions change.

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1) Liquidity Risk

• The longer the term to maturity, the longer the
  commitment and thus the higher the risk premium
  should be.
• Otherwise, no one will hold the long-term bonds.
• Long-term bonds YTM should be always higher than
  Short-bonds YTM

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Some argues against Liquidity Premium Theory

• Preferred Habitat Theory (Market Segmentation)
• -gt Risk Premium is not necessarily larger for
  long-term maturity
• -gt The risk premium depends on what you consider
  to be risky
• For instance, the pension fund manager prefer the
  long-term investment to short-term investment.
  Unless the short-term investment carries a higher
  YTM, he would not invest on it.
• But the PHT is not necessarily true at the
  Aggregate Level, on Average or In General.

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2) Expectations Theory

• The long-run interest rate is the average of the
  current actual interest rate and the expected
  future short-run interest rates, which reflect
  the contemporary monetary conditions.
• Long-term bonds YTM could be either higher or
  lower than Short-term bonds YTM

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6. Expectations Theory of Term Structure

• 1) L.T. YMT reflects the present and future S.T.
  YTMs.
• 2) Formula
• Rn YTM of bond with n years to maturity date
• R1 current YTM of bond with 1 year to maturity
  date
• E n-1 1 expected YTM on a 1-year bond for one
  year starting n-1 years from today.

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Example I Expectations Hypothesis
Simplifying Assumptions no credit risk
difference no liquidity risk premium difference

• We assume the same risk for the short-term and
  the long-term bonds- Ignore liquidity risk.
• Suppose that the current and the expected yields
  on a 1-year short-term bonds are as follows.

R1 E11 E21 E31 E41 14 13
12.5 12 11.5

• What would be the actual rate of returns on the
  long-term bonds?

R2 ?
R3 ?
R4 ?
R5 ?
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The Answer to Example I

• R1 14 R2 13.5 R3 13.2
• R4 12.9 R5 12.6 Term Structure
• Note As E goes down, R goes down too.
• Yield Curve is a graphic representation of the
  Term Structure

0 1 2 3 yrs Terms to Maturity
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Example II Expectations Hypothesis

• The current annualized short-term interest rate
  or YTM is 10 for a one-year bond this year.
• The YTM for a two-year bond is 12.
• What is the short-term annual interest rate
  which the financial market expected for the next
  year?

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Answer to Example II
Competition in the financial market will ensure
the equality between Options I and II.
1. Option I Investing on a 2 yr bond
12 24
12
2. Option II Rolling over investment on 1 yr
bonds
10
X
3. Returns on Option I Returns Option II
Thus, X 14
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3) Monetarists view of Expectations Theory of
Term Structure

• expectations of interest rate
• expectation of nominal interest rate (R r
  pe )
• expectations of inflation rate ( pe because
  r is constant)
• expectations of the rate of growth of money
  (supply)

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• Fisher Equation R r pe
• Quantity Equation of Exchange
• - MV P y
• - D M D V D P D y , where D P p
• Combining the two we get
• RA rA pe A and R B rB pe
  B
• RA - R B (rA - rB ) (pe A - pe B )
• - A lower interest rate means a strict monetary
  policy
• - Either a lower inflation
• - Or a slower business

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Yield Curve Graph of Term Structure
Steep(er)

• YTM()

Typical(Normal)
Flat(tened)
Inverted
(Maturity Term Years)
0 1 2 3 4 5 6
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Historical Examples of Yield Curves in the U.S.
economy

• Living Yield Curve
• http//www.smartmoney.com/onebond/index.cfm?storyy
  ieldcurvenavLeftNav 

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6. Harvey Campbells Use of Term Structure of
YTM for Business Forecast

• 1) Term Structure tells strongly about the Future
  of Economy
• The difference between L.T. YTM(10 year bond) and
  S.T. YTM(one year bond, or shorter) is is the
  most certain leading indicator of business
  cycles.
• - when L.T YTM minus S.T. YTM is negative (L.T.
  YTM lt S.T. YTM), we would soon see Recession
• Inverted Yield Curve is observed just prior to
  Recession
• - When the difference between L.T. YTM and S.T.
  YTM grows (L.T. YTM gtgt S.T. YTM), then the
  business gets better, and the growth rate of Y
  rises.

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2) Empirical Evidence

• J. Haubrich and A. M. Dombrosky tested the
  predictive power of the spread between the
  long-term and short-term bond yields.
• - Regression Model
• DY a b (R10-year R3-month T-Bill)
• - Data 19611Q to 1995IIIQ of U.S.
• - Results
• Y 1.83 0.97 (R10-year R3-month T-Bill)
• hat is 0.97 with its t-value4.50, being very
  significant.
• The spread has a substantial predictive power.
• The yield curve emerges as the most accurate
  predictor of real economic growth (better than
  more sophisticated leading index of business
  cycles).

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3)Two Explanations for Harvey Campbells Inverted
Yield Curve

• Economics Theory
• Inflation Expectation Theory
• A lower long-term interest rate means that
  compared to the current interest rate, either a
  lower rate of inflation, a slower growth rate of
  money supply, or a slowing down of the economy is
  expected for the future.
• Finance Theory
• Portfolio Substitution Theory
• When people expect a recession (not permanent),
  people would like to shift their investment into
  a safe haven from short-term investment(bonds)
  to long-term investment (bonds)
• Demand for, and Price of Long-term bonds go up
• Yield of Long-term bonds falls Inverted Yield
  Curve

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• 4) New Empirical Evidence by Campbell
  Harvey(1989)
• - Use the term-structure interest rate spread
  (long-term interest rate short-term interest
  rate) and other known leading indicator for the
  regression forecasting the economic growth
• - Compared two predictors of the spreads and
  other Leading indicators by their R2
• - Two Regression Results
• DY a b (R10-year R3-month T-Bill)
  R2 0.30 to 0.45
• versus
• DY a b (Stock Price Index as The Leading
  Indicator) R2 -0.004 to 0.045
• (Interpretation) The first is better than the
  second bond market reveals more information
  about future economic growth than stock market.

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When we combine Expectations Theory and
Liquidity Premium Theory

• Lets suppose that the one-year interest rate
  over the next five years is expected to be 5,
  6, 7, 8 and 9. Investors preferences are
  such that the liquidity premiums for one-year to
  five-year bonds are 0, 0.25, 0.5, 0.75, and
  1 respectively. What is the actual interest rate
  on a two-year bond and a five-year bond?
• Answer 5.75 and 8.