
Importance of Interest Rates
 Interest rate movements affect personal decisionssave 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

Understanding interest rates  The most accurate measure of an interest rate is...
 Yieldtomaturity (YTM) = present value of future payments of a debt instrument with today’s value
 Others include current yield, discount yield

Determination of Interest Rate Levels  "Loanable Funds (LF) Approach"
 Loanable funds: Amount of funds available for lending within financial system
 Treats the riskfree interest rates as an outcome of the forces of demand & supply in financial markets
 Modelled by supply & demand curve
 Downward sloping demand curve & upwardsloping supply curve
 The equilibrium interest rate is at intersection of curve

Loanable Funds Approach Graph

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.

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)

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

Example 1: Effect of increase in demand from borrowers D^{LF} to D'_{LF}(supply unchangedall else equal)
Demand for LF > supply of LF at i _{0 }so i _{0} toi _{1} (holding supply constant) so an increase in interest rates

Example 2: Increase in money supplycentral Bank supplies more LF, then S_{LF}S´_{LF} (with demand unchanged)

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

The loanable funds framework is a useful framework for
Analysing broad movements in interest rates.

Note: The LF 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

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

More Examples: a) Real savings in community decreases:

More Examples: b) Real capital inflows from off shore

More Examples: c) Banks decreases money supply by credit rationing

Income effect
Suggests negative relationship between interest rates & savings
 If interest rates rise
 Economic activity slows
 Income falls
 Allows interest rates to ease

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

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

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

The nominal interest rate is determined approximately by
Nominal interest rate = Real interest rate + rate of inflation

This relationship is Fisher relationship that implies when...
Rate of inflation goes up 1%, Nominal interest rate also goes up 1%

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

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

Also, could be alternate responses  examples
1. Govt demand for funds may be reduced by higher inflation so could have D_{2} instead of D_{1} or
2.Higher inflation savers begin dishoarding so S_{2} , not S_{1}

How to measure an Interest Rate
 "Usually calculated from financial market instruments "
 1. On simple interest basis (money market instruments)
 2. On compound basis

Calculating a SimpleInterest Rate of return Yield)
 The rate of return, r on an investment P for a (discount) security is:
 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

Calculating a SimpleInterest Rate of return Yield  Example  "Given a 90day discount money market instrument with face value = $1,000 Current price = $980, find its yield"

Calculating a Compound Interest Yield
 The compound rate of return, r, for two cash flows is found by:
 PV = present value
 FV = future value
 t = time in years
 i = compound rate of interest

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

What is an interest rate made up of:

Real riskfree rate:
 Required rate of interest on riskless security if no expected inflation.
 (Roughly, return on 90day Tbills minus the inflation premium).

Base or benchmark rate
The interest rate on the s/t Govt security

nominal rate i(r)
Market rate = actual rate charged by lender

Spread
The difference between the interest rate for nonGovt (corporate) security & the Govt security
 Factors afecting spread include
 default (credit) risk
 liquidity risk
 maturity risk
 embedded provision

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


Types of Yield Curves
 1.Normal  upward slopingpositive
 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.

Theories to explain the Term Structure of Interest Rates
 1. Unbiased (Pure) Expectations theory
 2. Liquidity Premium Theory
 3. Market Segmentation Theory

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

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

Net result of slope when: Interest rates are expected to fall, then investors prefer long term securities & borrowers prefer to issue shortterm.
 Interest rates are expected to fall, then investors prefer long term securities & borrowers prefer to issue shortterm.
 Net result  downward sloping

Under Expectations theory, normal yield curve will result from...
Expected shortterm rates to be higher than current shortterm rates

Under Expectations theory, inverse yield curve will result from...
Expected shortterm rates to be lower than current shortterm rates

Under Expectations theory, humped yield curve will result from...
Expected shortterm to be higher initially then subsequently fall in longer term

Expected rate (or forward rate) Equations are

Expected rate (or forward rate)  Example (Given interest rate table (yield curve) for Govt bonds, What is the implied forward 1year rate during the year 2 (beginning one year from now)? (Assume yearly coupon payments)

To find forward rate implied by spot rates of adjacent maturities

Example: Determine the implied forward 1yr rate for year 4 to 5? (implied 1yr rate beginning four years from now).

Yields for future multi periods can be inferred by market.
 Suppose the specific period of interest begins at time n & ends at time n+kk periods, then...

Example 2  Suppose an investor wants to determine the implied forward rate for the twoyear period beginning three years from now at end of year 3 given above rates

Example 3  To find the yield for a 6 year bond given the implied future 1year rate for year 5 is 8.50% and 5 year spot rate of 8.20%

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.

2. Liquidity Premium Theory equation

2. Liquidity Premium Theory

3. Market Segmentation Theory
 Rejects two assumptionsall 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

Risk structure of interest rates

Other factors influencing yield curves are
 Government policy e.g. MS growth
 Govt spending & debt
 Trade balance
 Level of business activity & consumer spending

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

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

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)
Scenario 1: where interest rates fall: Let us assume that the YTM changes to 10% for the 3year bond, (i.e. current market yields on comparable instruments are 10% ) then:

Scenario 2 where interest rates increase: Let us now assume that the YTM changes to 14% on the 3year bond, then:

Scenario 3: Now let us assume that the YTM changes to 10% and consider the 5 year bond, then:

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 shortterm deposits & longterm lending

Example 1: Given Tbill 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 Tbill?

Example 1 cont: If market interest rates change to 12%

Example 1 cont: If market interest rates change to 8%

