FNCE 4070: FINANCIAL MARKETS AND INSTITUTIONS Lecture 3: Understanding Interest Rates

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FNCE 4070 FINANCIAL MARKETS AND INSTITUTIONS
Lecture 3 Understanding Interest Rates

• Various Measures of Interest Rates
• Relationship of Market Interest Rates to Bond
  Prices
• Risks in the Bond Markets
• Real Interest Rate

2
Where is this Financial Center?
3
Can you explain this headline?

• Treasuries Decline as Weekly Jobless Claims Drop
• Treasuries declined as first-time claims for
  unemployment insurance fell to the lowest since
  July 2008.

4
Interest Rate Defined

• Dual Definition
• Borrowing the cost of borrowing or the price ()
  paid for the rental of funds.
• A financial liability for deficit entities.
• Saving the return from investing funds or the
  price () paid to delay consumption.
• A financial asset for surplus entities.
• Both concepts are expressed as a percentage per
  year (Percent per annum p.a.).
• True regardless of maturity of instrument of the
  financial liability or financial asset.
• Thus, all interest rate data is annualized.
• See http//www.federalreserve.gov/releases/h15/up
  date/

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Savings and Borrowing Rates They Move Together,
1977 2011

• Regression analysis 1964 2010 (monthly data,
  564 observations) CD rate as dependent variable.
  R-squared 88.55

6
Regulation Q (Glass Steagall Act, 1933) and
Market Interest Rates
7
Seeds of Disintermediation
8
Regulation Q Phased out by 1986 (Large
denomination CDs exempt in 1970)

• Monetary Control and Deregulations Act, 1980

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(No Transcript)
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The Demise of the SLs Maturity Mismatch of
Asset and Liability
11
Commonly Used Interest Rate Measures

• There are four important ways of measuring (and
  reporting) interest rates on financial
  instruments. These are
• Coupon yield The promised annual percent
  return on a coupon instrument.
• Current Yield Bonds annual coupon payment
  divided by its current market price.
• Discount Yield and Investment Yield The yield
  on T-bills (and other discounted securities, such
  as commercial paper) which are selling at a
  discount of their maturity values.
• Yield to Maturity The interest rate that
  equates the future payments to be received from a
  financial instrument (coupons plus maturity
  value) with its market price today (i.e., to its
  present value).

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Benchmarking with Interest Rates

• Interest rates can be used for cross-country
  assessments or changes in individual country
  assessments over time.
• The 2 most common benchmark rates are yields to
  maturity on 10-year Government U.S. Treasuries
  and German Bunds.
• We assume both of these are default-free.
• Thus we can compare other sovereigns to these
  (and to one another) to assess
• Credit ratings risk
• Inflation risk
• The markets overall assessment of country risk
• See http//markets.ft.com/markets/bonds.asp

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Coupon Yield

• Coupon yield is the annual interest rate which
  was promised by the issuer when a bond is first
  sold.
• Information is found in the bonds indenture.
• The coupon yield is expressed as a percentage of
  the bonds par value.
• In the United States, all bonds have a par value
  of 1,000
• Example 3.125 U.S. Treasury bond due November
  2041
• This bond will pay 31.25 per year in interest
  (.03125 x 1,000)
• The coupon yield on a bond will not change during
  the lifespan of the bond.

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Par Values Other Countries

• Par values different in other countries
• UK Government bonds (generally 100 par value
  called gilts)
• Japanese Government bonds (10,000 par value
  called JGBs)
• German Government bonds (minimum amount of 100
  par value, called bunds)
• Canadian Government bonds (CAD1,000 par value)
• Par value is also called the maturity value (or
  face value).
• Government bonds generally pay interest
  semi-annually.

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Current Yield

• Since bond prices are likely to change, we often
  refer to the current yield which is measured by
  dividing a bonds annual coupon payment by its
  current market price.
• This provides us with a measure of the interest
  yield obtained at the current market price (i.e.,
  cost of investing)
• Current yield annual coupon payment/market
  price
• So, if our 4.5 coupon bond is currently selling
  at 900 the calculated current yield is
• 45/900 5.00
• And if the bond is selling at 1,100, the current
  yield is
• 45/1,100 4.09

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Discount and Investment Yield

• Discount yields and investment yields are
  calculated for U.S. T-bills and other short term
  money market instruments (e.g., commercial paper
  and bankers acceptances) where there are no
  stated coupons (and thus the assets are quoted at
  a discount of their maturity value).
• The discount yield relates the return to the
  instruments par value (or face or maturity).
• The discount yield is sometimes called the bank
  discount rate or the discount rate.
• The investment yield relates the return to the
  instruments current market price.
• The investment yield is sometimes called the
  coupon equivalent yield, the bond equivalent
  rate, the effective yield or the interest yield.

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Calculating the Discount Yield

• Discount yield (PV - MP)/PV 360/M
• PV par (or face or maturity) value
• MP market price
• M maturity of bill.
• For a new three-month T-bill (13 weeks) use 91,
  and for a six-month T-bill (26 weeks) use 182.
• For outstanding issues, use the actual days to
  maturity.
• Note 360 is the number of days used by banks
  to determine short-term interest rates.

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Discount Yield Example

• What is the discount yield for a 182-day T-bill,
  with a market price of 965.93 (per 1,000 par,
  or face, value)?
• Discount yield (PV - MP)/PV 360/M
• Discount yield (1,000) - (965.93) / (1,000)
  360/182Discount yield 34.07 / 1,000
  1.978022Discount yield .0673912 6.74

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Investment Yield

• The investment yield is generally calculated so
  that we can compare the return on T-bills to
  coupon investment options.
• The calculated investment yield is comparable to
  the yields on coupon bearing securities, such as
  long term bonds and notes.
• As noted The investment yield relates the return
  to the instruments current market price.
• In addition, the investment yield is based on a
  calendar year 365 days, or 366 in leap years.
• Investment yield (PV - MP)/MP 365 or
  366/M

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Investment Yield Example

• What is the investment yield of a 182-day T-bill,
  with a market price of 965.93 per 1,000 par, or
  face, value?
• Investment yield (PV - MP)/MP
  365/MInvestment yield (1,000 965.93) /
  (965.93) 365/182Investment yield 34.07
  / 965.93 2.0054945Investment yield
  .0707372 7.07

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Comparing Discount and Investment Yields

• Looking at the last two examples we found
• Discount yield (PV - MP)/PV 360/M
• Discount yield (1,000 - 965.93) / (1,000)
  360/182Discount yield 34.07 / 1,000
  1.978022Discount yield .0673912 6.74
• Investment yield (PV - MP)/MP
  365/MInvestment yield (1,000 965.93) /
  (965.93) 365/182Investment yield 34.07 /
  965.93 2.0054945Investment yield .0707372
  7.07
• Note The discount formula will tend to
  understate yields relative to those computed by
  the investment method, because the market price
  is lower than the par value (1,000).
• However, if the market price is very close to the
  par value, the yields will be similar.
• See http//www.ustreas.gov/offices/domestic-finan
  ce/debt-management/interest-rate/daily_treas_bill_
  rates.shtml
• And http//www.treasurydirect.gov/RI/OFBills

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Bloomberg and Reported Yields on T-Bills

• Go to http//www.Bloomberg.com
• Go to Market Data
• Go to Rates and Bonds
• You will see for U.S. Treasuries the following
  data (note this is an example from the Feb 4,
  2011 site)
• Coupon Maturity Current
  Date Price/Yield
• 3-month 0.000 05/05/2011 0.14/.15
• 6-month 0.000 08/04/2011 0.16/.17
• 12-month 0.000 01/12/2011 0.27/.28
• Key These are T-bills, thus the coupon is 0
  (recall they are sold at a discount). At maturity
  date they will pay the holder 1,000. The
  current price is the discount yield (bank
  discount yield) and the current yield is the
  investment yield (bond or coupon equivalent
  yield).

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Yield to Maturity

• The yield to maturity uses the concept of present
  value in its determination.
• Yield to maturity is the interest rate which will
  discount the incomes (i.e., cash-flows) of a bond
  to produce a present value which is equal to the
  bonds current market price (or produce a net
  present value 0).
• Yield to maturity (i) is calculated as
• MP Market price of a bond (i.e., present value)
• C Coupon payments (a cash flow)
• PV Par, or face value, at maturity (a cash
  flow)
• n Years to maturity
• Note i is also the internal rate of return

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Yield to Maturity Example

• Assume the following given variablesC 40
  (thus a 4.0 coupon issue paid annually)N 10
  PV 1,000MP 1,050 (note bond is selling at
  a premium of par)
• 1050 40/(1 i)1 40/(1 i)2 . . . 40/(1
  i)10 1000/(1 i)10
• Solve for i, the yield to maturity
• Note The i" calculated using this formula will
  be the return that you will be getting when the
  bond is held until it matures and assuming that
  the periodic coupon payments are reinvested at
  the same yield. In this example, the i" is 3.4.
  

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Yield to Maturity Second Example

• Now assume the following
• C 40 N 10PV 1,000MP 900.00 (note bond
  is selling at a discount of par)
• 900 40/(1 i)1 40/(1 i)2 . . . 40/(1
  i)10 1,000/(1 i)10
• Solve for i, the yield to maturity
• Note The i" calculated in this example is
  5.315.
• What one factor accounts for the yield to
  maturity difference when compared to the previous
  slide, with its i of 3.4?

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Useful Web Site for Calculating a Bonds Yield to
Maturity

• While yields to maturity can be determined
  through a book of bond tables or through business
  calculators, the following is a useful web site
  for doing so
• http//www.money-zine.com/Calculators/Investment-C
  alculators/Bond-Yield-Calculator/

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The Yield to Maturity

• Think of the yield to maturity as the required
  return on an investment.
• Since the required return changes over time, we
  can expect these changes to produce inverse
  changes in the prices on outstanding (seasoned)
  bonds.
• Why will the required return change over time?
• Changes in inflation (inflationary expectations).
• Changes in the economys credit conditions
  resulting from change in business activity.
• Changes in central bank policies.
• Impact on shorter term maturities.
• Changes in the credit risk (i.e., risk of
  default) associated with the issuer of the bond.
• On Governments, also changes in credit ratings
  risk.

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Illustrating the Relationship Between Interest
Rates and Bond Prices

• Assume the following
• A 10 year corporate Aaa bond which was issued 8
  years ago (thus it has 2 years to maturity) has a
  coupon rate of 7, with interest paid annually.
• Thus, 7 was the required return when this bond
  was issued.
• This bond is referred to as an outstanding (or
  seasoned) bond.
• Question How much will a holder of this bond
  receive in interest payments each year?
• This bond has a par value of 1,000.
• Question How much will a holder of this bond
  receive in principal payment at the end of 2
  years?

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What Happens when Interest Rates Rise?

• Assume, market interest rates rise (i.e., the
  required return rises) and now 2 year Aaa
  corporate bonds are now offering coupon returns
  of 10.
• This is the current required return (or i in
  the present value bond formula)
• Question What will the market pay (i.e., market
  price) for the outstanding 2 year, 7 coupon bond
  noted on the previous slide?
• PV 70/(1.10) 1,070/(1.10)2
• PV 947.94 (this is todays market price)
• Note The 2 year bonds price has fallen below
  par (selling at a discount of its par value).
• Conclusion When market interest rates rise, the
  prices on outstanding bonds will fall.

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What Happens when Interest Rates Fall?

• Assume, market interest rates fall (i.e., the
  required return falls) and now 2 year Aaa
  corporate bonds are now offering coupon returns
  of 5.
• This is the current required return (or i in
  the present value bond formula)
• Question What will the market pay (i.e., market
  price) for the outstanding 2 year, 7 coupon
  bond?
• PV 70/(1.05) 1,070/(1.05)2
• PV 1,037.19 (this is todays market price)
• Note The 2 year bonds price has risen above par
  (selling at a premium of its par value).
• Conclusion When market interest rates fall, the
  prices on outstanding bonds will rise.

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Bond Price Sensitivity to Changes in Market
Interest Rates (YTM)
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Change in Markets Required Return Versus Change
in Market Demand

• The examples on the previous slides demonstrated
  the impact of a change in the markets required
  return on bond prices.
• Observation Cause effect relationship runs
  from changes in required return to changes in
  market prices (which produce the markets new
  required return).
• However, it is possible for a change in market
  demand to produce changes in bond prices and thus
  in market interest rates.
• For example Safe haven effects result in
  changes in demand for particular assets.
• Observation Cause effect relationship runs
  from changes in demand to changes in prices
  (which have an automatic impact on yields).

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What if the Time to Maturity Varies?

• Assume a one year bond (7 coupon) and the market
  interest rate rises to 10, or falls to 5.
• PV_at_10 1,070/(1.10)
• PV 972.72
• PV _at_5 1,070/(1.05)
• PV 1,019.05
• Now assume a two year bond (7 coupon) and the
  market interest rate rises to 10, or falls to 5
• PV_at_10 70/(1.10) 1,070/(1.10)2
• PV 947.94
• PV_at_5 70/(1.05) 1,070/(1.05) 2
• PV 1037.19
• Conclusion For a given interest rate change,
  the longer the term to maturity, the greater the
  bonds price change.

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Summary The Interest Rate Bond Price
Relationship

• 1 When the market interest rate (i.e., the
  required rate) rises above the coupon rate on a
  bond, the price of the bond falls (i.e., it sells
  at a discount of par).
• 2 When the market interest rate (i.e., the
  required rate) falls below the coupon rate on a
  bond, the price of the bond rises (i.e., it sells
  at a premium of par)
• IMPORTANT There is an inverse relationship
  between market interest rates and bond prices (on
  outstanding or seasoned bonds).
• 3 The price of a bond will always equal par if
  the market interest rate equals the coupon rate.

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Summary The Interest Rate Bond Price
Relationship Continued

• 4 The greater the term to maturity, the greater
  the change in price (on outstanding bonds) for a
  given change in market interest rates.
• This becomes very important when developing a
  bond portfolio-maturity strategy which
  incorporates expected changes in interest rates.
• This is the strategy used by bond traders
• What if you think interest rates will fall?
  Where should you concentrate the maturity of your
  bonds?
• What if you think interest rates will rise?
  Where should you concentrate the maturity of your
  bonds?
• See Appendix 1 for Excel Calculation of bond
  prices.

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Interest Rate (or Price) Risk on a Bond

• Defined The risk associated with a reduction in
  the market price of a bond, resulting from a rise
  in market interest rates.
• This risk is present because of the inverse
  relationship between market interest rates and
  bond prices.
• The longer the maturity of the fixed income
  security, the greater the risk and hence the
  greater the impact on the overall return.
• For a historical examples, see the next slide.

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Relationship of Maturity to Returns

• Note Return coupon change in market price

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Price Risk 1950 - 1970
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Reinvestment Risk on a Bond

• Reinvestment risk occurs because of the need to
  roll over securities at maturity, i.e.,
  reinvesting the par value into a new security.
• Problem for bond holder The interest rate you
  can obtain at roll over is unknown while you are
  holding these outstanding securities.
• Issue What if market interest rates fall?
• You will then re-invest at a lower interest rate
  then the rate you had on the maturing bond.
• Potential reinvestment risk is greater when
  holding shorter term fixed income securities.
• With longer term bonds, you have locked in a
  known return over the long term.
• For a historical example, see the next slide

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Reinvestment Risk 1985 - 2011
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Concept of Bond Duration

• Issue The fact that two bonds have the same
  term to maturity does not necessarily mean that
  they carry the same interest rate risk (i.e.,
  potential for a given change in price).
• Assume the following two bonds
• (1) A 20 year, 10 coupon bond and
• (2) A 20 year, 6 coupon bond.
• Which one do you think has the greatest interest
  rate (i.e., price change) risk for a given change
  in interest rates?
• Hint Think of the present value formula (market
  price of a bond) and which bond will pay off more
  quickly to the holder (in terms of coupon cash
  flows).

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Solution to Previous Question

• Assume interest rates change (increase) by 100
  basis points, then for each bond we can determine
  the following market price.
• 20-year, 10 coupon bonds market price (at a
  market interest rate of 11) 919.77
• 20-year, 6 coupon bonds market price (at a
  market interest rate of 7) 893.22
• Observation The bond with the higher coupon,
  (10) will pay back quicker (i.e., produces more
  income early on), thus the impact of the new
  discount rate on its cash flow is less.

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Duration and Interest Rate Risk

• Duration is an estimate of the average lifetime
  of a securitys stream of payments.
• Duration rules
• (1) The lower the coupon rate (maturity equal),
  the longer the duration.
• (2) The longer the term to maturity (coupon
  equal), the longer duration.
• (3) Zero-coupon bonds, which have only one cash
  flow, have durations equal to their maturity.
• Duration is a measure of risk because it has a
  direct relationship with price volatility.
• The longer the duration of a bond, the greater
  the interest rate (price) risk and the shorter
  the duration of a bond, the less the interest
  rate risk.

44
Calculated Durations

• Duration for a 10 year bond assuming different
  coupons yields
• Coupon 10 Duration 6.54 yrs
• Coupon 5 Duration 7.99 yrs
• Zero Coupon Duration 10 years
• Duration for a 10 coupon bond assuming different
  maturities
• 5 years Duration 4.05yrs
• 10 years Duration 6.54 yrs
• 20 years Duration 9.00 yrs
• Note See Appendix 2 for Excel calculations

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Using Duration in Portfolio Management

• Given that the greater the duration of a bond,
  the greater its price volatility (i.e., interest
  rate risk), we can apply the following
• (1) For those who wish to minimize interest rate
  risk, they should consider bonds with high coupon
  payments and shorter maturities (also stay away
  from zero coupon bonds).
• Objective Reduce the duration of their bond
  portfolio.
• (2) For those who wish to maximize the potential
  for price changes, they should consider bonds
  with low coupon payments and longer maturities
  (including zero coupon bonds).
• Objective Increase the duration of their bond
  portfolio

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The Real Interest Rate

• Real interest rate
• This is the market (or nominal) interest rate
  that is adjusted for expected changes in the
  price level (i.e., inflation) and is calculated
  as follows
• irr imr - pe

Where irr real rate of interest (
p.a.) imr market (nominal) rate of interest
( p.a.) pe expected annual rate of
inflation, i.e., the average annual price level
change over the maturity of the financial asset
( p.a.)
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Real Interest Rate Impacts on Borrowing and
Investing

• We assume that real interest rates more
  accurately reflect the true cost of borrowing and
  true returns to lenders and/or investors.
• Assume imr 10 and pe 12 then
• irr 10 - 12 -2
• When the real rate is low (or negative), there
  should be a greater incentive to borrow and less
  incentive to lend (or invest).
• Assume Imr 10 and pe 1 then
• Irr 10 - 1 9
• When the real rate is high, there should be less
  incentive to borrow and more incentive to lend
  (or invest).

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U.S. Real and Nominal Interest Rates 1953-2007
49
Real Interest Rate as an Indicator of Monetary
Policy

• The real interest rate (on the fed funds rate) is
  also assumed to be a better measure of the stance
  of monetary policy than just the market interest
  rate.
• Why Real rate affects borrowing decisions.
• If the real rate is negative, or very low,
  monetary policy is very accommodative and
  borrowing will be encouraged.
• If the real rate high, monetary policy is very
  tight and borrowing will be discouraged.
• A neutral monetary policy occurs when the real
  rate is zero.

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Example of Nominal Versus Real Rate

• Economic Background

• Nominal Fed Funds Rate

• U.S. experiences the 2000 dot-com stock market
  crash and terrorist- attack induced recession
  of 2001
• March 11, 2000 to October 9, 2002, Nasdaq lost
  78 of its value.
• In response the Fed pushed the fed funds rates to
  1.0 (levels not seen since the 1950s)

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Real Fed Funds Rate

• Where is it today?

• Real Rate Goes Negative 2003/04

• Effective Rate ______
• Go to http//www.bloomberg.com/apps/quote?ticker
  FEDL013AIND
• Latest Inflation ______
• Go to
• http//www.bls.gov/bls/inflation.htm
• Your analysis of monetary policy and credit
  conditions in the economy?

52
Another Web Site for Calculating Yields

• Visit the web site below. It allows you to
  calculate the current yield and yield to maturity
  for specific data you input on
• Current Market Price
• Coupon Rate
• Years to Maturity
• It also allows you to calculate present values.
• Use this web site to test your understanding of
  the relationship between bond prices and interest
  rates.
• See what happens to the calculated interest rates
  when you change the bond price above and below
  the par value.
• Note the inverse relationship.
• http//www.moneychimp.com/calculator/bond_yield_ca
  lculator.htm

53
Internet Source of Interest Rate Date

• Historical and Current Data for U.S.
• http//www.federalreserve.gov/releases/h15/update/
  
• Real Time Data (U.S. and other major countries)
• http//www.bloomberg.com
• Go to Market Data and then to Rates and Bonds
• Other Countries
• Economist.com (both web source or hard copy)

54
Appendix 1

• Using Excel to Calculate the Market Price
  (Present Value) of a Bond

55
Using Excel to Calculate Bond Price

• Go to Formulas in Microsoft Excel
• Go to Financial
• Go to Price
• Insert Your Data
• Example for 20 year, 10 coupon bond with market
  rate of 11
• Settlement DATE(2009,2,1) Assume, Feb 1, 2009
• Maturity DATE(2029,2,1) Note 20 years to
  maturity
• Rate 10 (this is the coupon yield)
• Yld 11 (this is the yield to maturity)
• Redemption 100 (this is the price per 100)
• Frequency 2 (assume interest is paid
  semi-annually)
• Basis 3 (this basis uses a 365 day calendar
  year)
• Formula result (i.e., price per 100 face value)
  91.97694 (or 919.77)

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Appendix 2

• Using Excel to Calculate the Duration of a Bond

57
Using Excel to Calculate Duration

• Go to Formulas in Microsoft Excel
• Go to Financial
• Go to Duration
• Insert Your Data
• Example for 10 year, 10 coupon bond with market
  rate of 10
• Settlement DATE(2009,2,1) Assume, Feb 1, 2009
• Maturity DATE(2019,2,1) Note 10 years to
  maturity
• Rate 10 (this is the coupon yield)
• Yld 10 (this is the yield to maturity)
• Frequency 2 (assume interest is paid
  semi-annually)
• Basis 3 (this basis uses a 365 day calendar
  year)
• Formula result 6.54266

58
Appendix 3

• The Real Interest Rate during a period of
  deflation

59
What if the Rate of Inflation is Negative (i.e.,
Deflation)

• Assume the following
• imr 3 and pe -2
• Then the calculated real rate would be
• irr 3 - (-2) 5
• Issues
• 1. What will be the economys incentive to
  borrow?
• High or low.
• 2, What are the issues facing the central bank
  when the economy is experiencing deflation?
• How can borrowing be encouraged?

60
Appendix 4

• Types of Debt Instruments and Lending Terms

61
2 Basic Types of Debt Instruments

• Discount Bond (Zero-coupon Bond)
• A bond whose purchase price is below the face (or
  par) value of the bond (i.e., at a discount)
• The entire face (par) value is paid at maturity.
• There are no interest payments.
• U.S. Treasury bills are an example of a discount
  security (as is commercial paper and bankers
  acceptances).
• Coupon Bond
• A bond that pays periodic interest payments
  (stated as the coupon rate) for a specified
  period of time after which the total principal
  (face or par value) is repaid.
• In the United States and Japan, interest payments
  are typically made every six months and in Europe
  typically once a year.
• coupon bonds can sell at either a discount or
  premium (of par value).
• These bonds are generally callable.
• Issuer can retire them before their stated
  maturity date.
• Why do you think they might do this?

62
Important Terms in Lending

• (Loan) Principal the amount of funds the lender
  provides to the borrower.
• Maturity Date the date the loan must be repaid
  or refinanced.
• (Loan) Term the time period from initiation of
  the loan to the maturity date.
• Interest Payment the cash amount that the
  borrower must pay the lender for the use of the
  loan principal.
• (Simple) Interest Rate the annual interest
  payment divided by the loan principal.
• In bond terminology, the coupon interest rate is
  the annual interest payment divided by the par
  value.

63
Types of Loans

• Simple Loan Principal and all interest both
  paid at maturity (i.e., date when loan comes
  due).
• Borrow 1,000 today at 5 and in 1 year pay
  1,050
• Commercial bank loans to businesses are usually
  simply loans.
• Fixed-payment Loan Equal monthly payments
  representing a portion of the principal borrowed
  plus interest. Paid for a set number of years, at
  which time (maturity date) the principal amount
  is fully repaid.
• Referred to as an amortized loan.
• Home mortgages (conventional), automobile loans.

64
Amortization Loan Example Real Estate

• Mortgage Loan
• Principal Amount 500,000
• Years To Maturity 30 years (with monthly
  payments)
• Interest rate 7 (fixed rate mortgage)
• Monthly Payment
• 3,326.51 (for 360 months, i.e., 30 years)
• First Month Payment (n 1)
• Principal 409.84 Interest 2,916.67 (or,
  3,326.51)
• Last Month Payment (n 360)
• Principal 3,307.22 Interest 19.29 (or,
  3,326.51)

65
Appendix 5

• Quoting Treasury Notes and Bonds

66
Treasury Prices in 32nds

• Treasury note and bond prices are quoted in
  dollars and fractions of a dollar.
• By market convention, the normal fraction used
  for Treasury security prices is 1/32 (of 1).
• In a quoted price, the decimal point separates
  the full dollar portion of the price from the
  32nds of a dollar, which are to the right of the
  decimal.
• Thus a quote of 100.08 means 105 plus 8/32 of a
  dollar, or 100.25, for each 100 face value of
  the note.
• Note the symbol refers to ½ of 1/32nd.
• Change data is the difference between the current
  trading day's price and the price of the
  preceding trading day. It, too, is a shorthand
  reference to 32nds of a point.
• For example, a 16 refers to a change of 16/32 or
  50 cents from the previous day.