125220_16(T2): Interest Rates

  1. Importance of Interest Rates
    • Interest rate movements affect personal decisions-save or consume & business decisions –invest or save
    • Helps ensure current savings investment. Rations the available supply of credit, (loanable funds)  investment products with highest expected returns.
    • Balances the supply of money with public’s demand for money.
    • An important govt tool through its influence on the volume of investment & saving
  2. Understanding interest rates - The most accurate measure of an interest rate is...
    • Yield-to-maturity (YTM) = present value of future payments of a debt instrument with today’s value
    • Others include current yield, discount yield
  3. Determination of Interest Rate Levels - "Loanable Funds (LF) Approach"
    • Loanable funds: Amount of funds available for lending within financial system
    • Treats the risk-free interest rates as an outcome of the forces of demand & supply in financial markets
    • Modelled by supply & demand curve
    • Downward sloping demand curve & upward-sloping supply curve
    • The equilibrium interest rate is at intersection of curve
  4. Loanable Funds Approach Graph
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  5. Loanable Funds Approach - "Sources of Funds ('S' from surplus units)"
    • 1.Savings of various institutions, households, firms & Government & dishoarding (= changes in cash holdings to buy more securities)
    • 2.Additions to stock of money -money creation by the central bank. E.g. central bank buys govt. bonds
    • 3. A inflow of foreign funds usually to purchase local securities.
  6. Loanable Funds Approach - "Demand Side ('D' deficit units)"
    • 1.Households borrow to buy goods & services (relatively inelastic demand)
    • 2. Investors borrow for plant & equipment-(more elastic demand)
    • 3. Governments tend to borrow to finance deficits (inelastic=non sensitive)
  7. A rise in interest rates should result more funds supplied (in an increase in the money supply). This encourages...
    • Encourage further foreign capital inflows providing no FX rate risk.
    • Encourage banks to loan out more of their reserves.
    • Encourage public to save & so decrease demand for cash, raising deposits
  8. Example 1: Effect of increase in demand from borrowers   DLF to D'LF(supply unchanged-all else equal)
    Image Upload 2

    Demand for LF > supply of LF at iso i0 toi1 (holding supply constant) so an increase in interest rates
  9. Example 2: Increase in money supply-central Bank supplies more LF, then SLFS´LF (with demand unchanged)
    Image Upload 3
  10. The Interaction of Demand and Supply - the rate
    • The rate: the equilibrium point at which supply of loanable funds = demand for funds. 
    • If interest rate is temporarily above intersection point, quantity of loanable funds exceeds total demand & rate of interest will be bid down
  11. The loanable funds framework is a useful framework for
    Analysing broad movements in interest rates.
  12. Note: The L-F framework can represented as demand & supply curves for bonds
    • The demand for bonds comes from investors who supply  loanable funds.
    • The suppliers of bonds = issuers who demand loanable funds

    In other words, demand curve for loanable funds is equivalent to supply curve of bonds &  supply curve of loanable funds is equivalent to demand curve for bonds
  13. Central banks ability influence interest rates in the financial markets. Specifically, the S/T
    • If higher rates are wanted, then central bank can contract money supply & interest rates will tend to (assuming the demand for money is unchanged). 
    • If demand for money is high, & central bank want to tighten up monetary policy, it can bring about higher rates by ensuing that money supply grows more slowly than money demand
  14. More Examples: a) Real savings in community decreases:
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  15. More Examples: b) Real capital inflows from off shore
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  16. More Examples: c) Banks decreases money supply by credit rationing
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  17. Income effect
    Suggests negative relationship between interest rates & savings

    • If interest rates rise
    • Economic activity slows
    • Income falls
    • Allows interest rates to ease
  18. Wealth effect
    • Whether individual investors hold their wealth in debt or equity assets
    • Depends upon perceived riskiness of securities. Greater the whether individual investors hold their wealth in debt or equity assets
  19. Interest rates and Inflation
    • Anticipated rates of inflation also help to determine interest rate levels
    • If suppliers of funds expect inflation to increase, then they will demand a higherrate of interest.
    • Fisher effect: Effects of changes in inflationary expectations
  20. Fisher Effect Example - Consider investor who invests $10,000 for 1 year at 10%. At year end,  investor is paid $11,000 & has gain of $1,000 from nominal rate of 10%. However, assume inflation is 5% p.a. Then real value of the $10,000 is
    • $11,000 1.05 = $10,476
    • The real return on investment is  4.76% 

    • This is the real interest rate which can be approximated as:
    • Real Interest rate = Nominal Rate -Inflation rate
  21. The nominal interest rate is determined approximately by
    Nominal interest rate = Real interest rate + rate of inflation
  22. This relationship is Fisher relationship that implies when...
    Rate of inflation goes up 1%, Nominal interest rate also goes up 1%
  23. Nominal interest rates compensate savers in 2 ways
    • 1. For a saver's reduced purchasing power
    • 2. Provide an extra premium to savers for foregoing present consumption
  24. Impact of Inflation
    • If rise in price levels is anticipated, lenders supply fewer funds & borrowers will demand more funds at each interest rate & overall nominal interest rate will rise
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  25. Also, could be alternate responses - examples

    1. Govt demand for funds may be reduced by higher inflation so could have D2  instead of D1 or
    2.Higher inflation savers begin dishoarding so S2 , not S1
    Image Upload 8
  26. How to measure an Interest Rate
    • "Usually calculated from financial market instruments "
    • 1. On simple interest basis (money market instruments)
    • 2. On compound basis
  27. Calculating a Simple-Interest Rate of return Yield)
    • The rate of return, r on an investment P for a (discount) security is: Image Upload 9
    • Face value: The proceeds of S/T investment
    • Current price: market price
    • i: is yield % p.a. = rate of interest on the amount paid out to buy asset
  28. Calculating a Simple-Interest Rate of return Yield - Example - "Given a 90-day discount money market instrument with face value = $1,000 Current price = $980, find its yield"
    Image Upload 10
  29. Calculating a Compound Interest Yield
    • The compound rate of return, r, for two cash flows is found by: Image Upload 11
    • PV = present value
    • FV = future value
    • t = time in years
    • i = compound rate of interest
  30. Calculating a Compound Interest Yield - Example (Express the rate of growth for Google share price from its  IPO share price of $85 in July 2004 to $481.32 in July 2008 as an annual rate of return on a compound basis. Note it paid no dividends during this period)
    • Express the rate of growth for Google share price from its  IPO share price of $85 in July 2004 to $481.32 in July 2008 as an annual rate of return on a compound basis. Note it paid no dividends during this period
    • Image Upload 12
  31. What is an interest rate made up of:
    Image Upload 13
  32. Real risk-free rate:
    • Required rate of interest on riskless security if no expected inflation.
    • (Roughly, return on 90-day T-bills minus the inflation premium).
  33. Base or benchmark rate
    The interest rate on the s/t Govt security
  34. nominal rate i(r)
    Market rate = actual rate charged by lender
  35. Spread
    The difference between the interest rate for non-Govt (corporate) security & the Govt security

    • Factors afecting spread include
    • default (credit) risk
    • liquidity risk
    • maturity risk
    • embedded provision
  36. Interest Rate Theory
    • There are a number of factors that influence interest rates & changes in interest rates
    • Plotting each security’s yield to maturity (interest rate) versus its time (term) to maturity, interest rate yield curve -an important tool.
    • Term structure of interest rates: Relationship between interest rates on bonds with different times to maturity
  37. Types of Yield Curves
    Image Upload 14
  38. Types of Yield Curves
    • 1.Normal - upward sloping-positive
    • Preference for higher interest rates for L/T

    • 2.Inverse - downward sloping
    • higher S/T rates declining out to the L/T
    • Common in times of tight liquidity or contractionary monetary policy

    • 3. Flat
    • May indicate that interest rates are in transition or stable

    • 4. Humped
    • Immediate liquid conditions but anticipated temporary tightness in the near future.
  39. Theories to explain the Term Structure of Interest Rates
    • 1. Unbiased (Pure) Expectations theory
    • 2. Liquidity Premium Theory
    • 3. Market Segmentation Theory
  40. 1.Unbiased (Pure) Expectations theory
    • The S/T interest rates implied by the yield curve are unbiased estimates of the market consensus of future rates
    • If interest rates are expected to rise, then investors will invest mainly in S/T
  41. Net effect of slope when: Borrowers prefer to issue L/T securities, large supply, downward pressure on prices - yields up
    • Borrowers prefer to issue L/T securities, large supply, downward pressure on prices - yields up
    • Net effect: upward sloping
  42. Net result of slope when: Interest rates are expected to fall, then investors prefer long term securities & borrowers prefer to issue short-term.
    • Interest rates are expected to fall, then investors prefer long term securities & borrowers prefer to issue short-term.
    • Net result - downward sloping
  43. Under Expectations theory, normal yield curve will result from...
    Expected short-term rates to be higher than current short-term rates
  44. Under Expectations theory, inverse yield curve will result from...
    Expected short-term rates to be lower than current short-term rates
  45. Under Expectations theory, humped yield curve will result from...
    Expected short-term to be higher initially then subsequently fall in longer term
  46. Expected rate (or forward rate) Equations are
    Image Upload 15
  47. Expected rate (or forward rate) - Example (Given interest rate table (yield curve) for Govt bonds, What is the implied forward 1-year rate during the year 2 (beginning one year from now)? (Assume yearly coupon payments)Image Upload 16
    Image Upload 17
  48. To find forward rate implied by spot rates of adjacent maturities
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  49. Example: Determine the implied forward 1-yr rate for year 4 to 5? (implied 1-yr rate beginning four years from now).
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  50. Yields for future multi periods can be inferred by market.
    • Suppose the specific period of interest begins at time n & ends at time n+kk periods, then...
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  51. Example 2 - Suppose an investor wants to determine the implied forward rate for the two-year period beginning three years from now at end of year 3 given above rates
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  52. Example 3 - To find the yield for a 6 year bond given the implied future 1-year rate for year 5 is 8.50% and 5 year spot rate of 8.20%
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  53. 2. Liquidity Premium Theory suggests...
    • Liquidity Premium theory suggests that investors desire an extra risk premium for compensating them for holding longer term securities.
    • This theory implies a bias to an upward sloping curve.
  54. 2. Liquidity Premium Theory equation
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  55. 2. Liquidity Premium Theory
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  56. 3. Market Segmentation Theory
    • Rejects two assumptions-all bonds perfect substitutes & investors are indifferent between S/T & L/T
    • This suggests that market participants operate essentially in one maturity band that is determined by their sources & uses of funds.
    • The yield curve is determined by forces of demand & supply in segmented markets
  57. Risk structure of interest rates
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  58. Other factors influencing yield curves are
    • Government policy e.g. MS growth
    • Govt spending & debt
    • Trade balance
    • Level of business activity & consumer spending
  59. Recent interest rate research major factors on overall shape
    • Increased inflation influences level of yield curve
    • Monetary policy influences slope or steepness
    • Shift in economic conditions affect curvature
  60. Relationship between Interest Rates and Security prices
    • The price of any financial instrument = present value of the expected cash flow (s)
    • For a bond, current price or present value is given by equation
    • Image Upload 26
  61. Example of effect of interest rates on prices: Given the following two Government security options, each of which pays interest yearly. Their price for investor (or cost for borrower)
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    Scenario 1: where interest rates fall: Let us assume that the YTM changes to 10% for the 3-year bond, (i.e. current market yields on comparable instruments are 10% ) then:
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  62. Scenario 2 where interest rates increase: Let us now assume that the YTM changes to 14% on the 3-year bond, then:
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  63. Scenario 3: Now let us assume that the YTM changes to 10% and consider the 5 year bond, then:
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  64. Importance of the Structure of Interest Rates
    • Yield spreads based on maturity may be exploited for the purpose of forecasting interest rates.
    • Term structure studies may benefit corporations seeking funds in various financial markets.
    • FIs -directly affected by relationship between S/T & L/T funds, especially banks with short-term deposits & longterm lending
  65. Example 1: Given T-bill maturing in 90 days has a face value of $100 000 & current rate of interest is 10% p.a. What is the current value of the T-bill?
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  66. Example 1 cont: If market interest rates change to 12%
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  67. Example 1 cont: If market interest rates change to 8%
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Card Set
125220_16(T2): Interest Rates