Chapter 4 Understanding Interest Rates

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Chapter 4Understanding Interest Rates
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Learning Objectives

• 1. Detail terms present value and interest rate
• 2. Discern measurments of interest rates YTM,
  Current Yield, Yield on Discount basis
• 3. Illustrate inverse relationship of bond prices
  and interest rates
• 4. Explain difference between nominal and real
  interest rates
• 5. Explain difference between interest rates and
  rates of return

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Contents

• Present Value and Interest Rates
• Subprime Mortgages and Interest Rates
• Measuring Interest Rates
• Bond Prices and Interest Rates
• International Interest Rates
• Nominal vs Real Interest Rates
• Interest Rates vs Rates of Return

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Present Value and Interest Rates

• PV FV / (1i) t
• A dollar paid to you 1 year from now is worth
  less than one dollar paid to you today
• Ex. PV of 250 paid in 2 years, i15
• PV 250 / (1 .15) 2
• 189.04

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Credit Market Instruments

• 1 Simple Loan
• 2 Fixed-Payment Loan
• 3 Coupon Bond
• 4 Discount Bond

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Simple Loan

• Lender provides borrower funds, borrower repays
  at maturity date plus additional interest amount
• 500 loan with 10 interest
• 1 year 500 (1 0.10) 550
• 2 years 550 (1 0.10) 605
• P F (1 i) t
• P Total payment
• F Face Value
• i interest rate
• t number of periods

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Coupon Bond

• Face value amount is paid to issuer for ownership
  of bond, then issuer pays owner of bond fixed
  interest payment every period until maturity,
  then pays face value to owner
• Three pieces of information Issuer of bond,
  maturity date of bond, coupon rate of bond

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Coupon Bond

• P C (1 (1 / (1 i) t)) / r F / (1
  i) t
• P bond price
• C Coupon rate
• i interest rate
• t number of periods
• F face value
• Ex. 1000, 5 coupon, annual bond with 15 year
  maturity. What would the price be if the
  interest rate was 6.5?
• A. 858.96

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Discount Bond

• Like a coupon bond, but without coupons
• No interest payments, is issued at a discount of
  face value
• Ex. Face value of 1000 may be bought for 900
  and in one years time the owner will be paid
  1000
• Examples include Canadian government treasury
  bills and long term zero-coupon bonds

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Discount Bond

• Similar formula as Coupon Bond, just missing the
  coupon section
• P F / (1 i) t
• P price of bond
• F face value
• i interest rate
• t number of periods
• 10,000, zero-coupon bond maturing in 7 years,
  interest rate is 4. Selling price?
• A. 7,599.18

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Fixed Payment Loan

• Lender provides borrower funds, borrower pays
  back lender in fixed payments every period until
  the loan is paid off (ie. Mortgage or auto loan)
• http//www.tdcanadatrust.com/mortgages/

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Subprime Loans

• A mortgage granted to a borrower considered
  subprime, that is, a person with a
  less-than-perfect credit report. Subprime
  borrowers have either missed payments on a debt
  or have been late with payments. Lenders charge a
  higher interest rate to compensate for potential
  losses from customers who may run into trouble or
  default.

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Subprime Meltdown

• Background
• U.S. housing bubble began in early 2000s
• Low interest rates and new mania for buying
  houses caused housing prices to skyrocket
• Some banks and newly-formed lending institutions
  took advantage of the situation by offering long
  term mortgages to people who could normally not
  afford them subprime borrowers
• These borrowers relied on the capital value of
  their new homes to pay off the mortgage, rather
  than their earning power

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Subprime Meltdown Outcome

• The rapid rise in housing prices created a
  bubble, which burst in late 2005
• Housing prices began to fall and, eventually,
  many subprime borrowers began to default on their
  loans
• This caused the collapse and bankruptcy of many
  of these institutions, and has hurt the financial
  industry substantially

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Subprime Meltdown

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Subprime Meltdown Outcome

• This meltdown has depressed the US economy,
  causing the Federal Reserve to lower its
  benchmark rate
• Has caused a weakening of the US dollar, and
  billions of dollars of losses for investment funds

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Subprime Meltdown International

• All of this has caused Canada to be affected as
  well
• Canadian dollar has risen against US dollar and
  is now at parity
• Depressed US housing market and high dollar has
  resulted in a crisis for the forestry industry
  (ie. Canfor mill closures)

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Subprime Meltdown

• Initially, it was all caused by extremely low
  interest rates in the early 2000s in order to
  stimulate the economy after the dot-com crash

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Measuring Interest Rates

• Yield to Maturity
• Current Yield
• Yield on a Discount Basis

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Yield to Maturity

• Interest rate that equates PV of cash flow
  payments received with its value today
• Most accurate measure of interest rates
• 1. Simple Loans
• 2. Fixed-Payment Loans
• 3. Coupon Bonds
• 4. Perpetuity
• 5. Discount Bonds

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Yield to Maturity

• Simple Loans
• Q. Pete borrows 100 from Bob and Bob wants back
  110 from him next year. YTM?
• A. PV FV / ( 1 i ) t
• 100 110 / (1 i ) 1
• r 0.1 10
• In a simple loan, i YTM

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Yield to Maturity

• Fixed Payment Loan
• Q. 100,000 loan, payments of 9439.29 for next
  20 years. YTM?
• LV FP / (1 i) FP / (1 i)2 ...
  FP / (1 i) n
• LV Loan Value
• FP Fixed Yearly Payment
• n number of years until maturity
• A. 0.7 7

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Yield to Maturity

• Coupon Bond
• PP C ((1-(1/(1i)n)/i) FV/ (1i)n
• PP Value of Bond
• C Coupon Payment
• i YTM
• N number of periods
• FV Face value of bond

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YTM

• Price of 8 coupon bond is 1122, FV of 1000, 12
  years to maturity, paid annually, what is YTM?
• PP C ((1-(1/(1i)n)/i) FV/ (1i)n
• PP Value of Bond
• C Coupon Payment
• i YTM
• N number of periods
• FV Face value of bond
• A. 0.65 6.5

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Yield to Maturity

• Perpetuity
• Coupon bond with no maturity date (goes on
  forever)
• P C / i
• P Price of perpetuity
• C Yearly Payment
• i YTM
• Q. Bond with price of 2000 and pays 100
  annually forever, what is YTM?
• Answer 100 / 2000 0.05 5

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Yield to Maturity

• Discount Bond
• i (F P) / P
• F Face Value
• P Current Price
• Ex. Treasury Bills that pays a FV of 1000 in 1
  year. Purchase Price is 900. YTM?
• A. i (1000 900) / 900 0.111 11.1

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Yield to Maturity

• Yield to Maturity for bonds is the actual
  interest rate
• Bond prices and interest rates are negatively
  related

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Current Yield

• Yield of a bond at a point in time
• Does not reflect total return
• Used as approximation to describe interest rates
  for long term bonds
• CY C / P
• C Coupon payment
• P Current price

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Current Yield

• Q. What is the current yield of a 1000, 8
  coupon bond maturing in 3 years and selling for a
  price of 1200?
• A. CY C / P
• 80 / 1200
• 0.0666 6.66

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Yield on a Discount Basis

• Most accurate measure of interest rates for short
  term bonds
• Yield of bills with a maturity of less than one
  year
• i (F P) / P 365 / Days to Maturity
• i Yield on a discount basis
• F Face Value
• P Purchase Price

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Yield on a Discount Basis

• Q. 91 day treasury bill selling for 988 with FV
  of 1000
• A. i (F P) / P 365 / Days to Maturity
• i (1000 988) / 988 365 / 91 0.0487
  4.87

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Central Banks and Interest Rates

• Very important in determining interest rates
• Central banks determine lending rates and heavily
  influence market interest rates
• Lending rate is the rate that the central bank
  will lend to other banks, thereby insuring that
  all lending rates (inter-bank or otherwise) are
  above this rate

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Central Banks

• Can be government controlled, or independent of
  government (Bank of Canada, Federal Reserve)
• Determine countries monetary policy
• Sole issuer of the countries' currency
• Supervises banking industry
• Lender of last resort and governments banker
• Manages gold reserves
• Sets interest rate

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International Interest Rates

• Canada - 4.5
• United States - 4.75
• United Kingdom - 5.75
• Europe - 4.0
• Japan - 0.5
• Australia - 6.5
• China - 7.02
• India - 7.75

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Canada

• Determined by the Bank of Canada

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United States

• Determined by the Federal Reserve

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United Kingdom

• Determined by the Bank of England

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Japan

• Determined by Bank of Japan

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Japan

• Island nation with no natural resources and very
  high population, and yet has the second largest
  economy in the world with the highest life
  expectancy, and very technologically advanced
• For past 15 years has been in prolonged
  stagnation due to many factors

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Japan

• As a result, the interest rate has been very low
  (0.1 for past 5 years) in order to stimulate the
  economy
• Extremely low compared to Canada (4.5)
• Low interest rate has resulted in negative
  inflation

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Interest Rates vs Returns

• Rate of return on a bond not necessarily the
  yield to maturity of the bond
• Rate of return is dependant on behaviour of
  market interest rates over the holding period of
  the bond
• If a bond is held for its entire life, then yield
  to maturity is equal to the return of the bond
• RET (C / Pt) (Pt1 Pt) / Pt
• RET Return
• Pt Initial Price of Bond
• Pt1 Selling Price of Bond
• C Coupon Payment

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Interest Rates vs Returns

• Q. What is the rate of return on a bond bought
  for 988 and sold one year later for 1200? The
  coupon rate is 5, and face value is 1000.
• A. (C / Pt) (Pt1 Pt) / Pt
• ( 50 / 988) (1200 988) / 988
• 0.0506 0.2146
• 0.2652 26.5

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Volatility of Bonds

• Longer term larger risk/more volatility
• Known as interest rate risk

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Real vs Nominal Rates

• So far, i nominal interest rate
• Real interest rate is a more accurate rate that
  is adjusted for inflation
• i real interest rate expected inflation
• OR
• Real interest rate i expected inflation
• i nominal rate
• Actual inflation is not known until later

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Real vs Nominal Rates

• When real interest rate is low, there are greater
  incentives to borrow and fewer to lend
• Measured by indexed bonds
• Interest and principal payments are adjusted for
  price levels by indexing to the Consumer Price
  Index (CPI)

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Real vs Nominal Rates

• Real rate is lower than nominal rate because of
  inflation

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Learning Objectives

• 1. Detail terms present value and interest rate
• 2. Discern measurements of interest rates YTM,
  Current Yield, Yield on Discount basis
• 3. Illustrate inverse relationship of bond prices
  and interest rates
• 4. Explain difference between nominal and real
  interest rates
• 5. Explain difference between interest rates and
  rates of return

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The End
Questions?