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
    Image Upload 1
  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
    • Image Upload 7
  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
    Image Upload 18
  49. Example: Determine the implied forward 1-yr rate for year 4 to 5? (implied 1-yr rate beginning four years from now).
    Image Upload 19
  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...
    • Image Upload 20
  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
    Image Upload 25
  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)
    Image Upload 27

    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?
    Image Upload 31
  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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Author
jordan_hs
ID
328195
Card Set
125220_16(T2): Interest Rates
Description
int
Updated