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
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
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
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 DLF to D'LF(supply unchanged-all else equal)
Demand for LF > supply of LF at i0
(holding supply constant) so an increase in interest rates
Example 2: Increase in money supply-central Bank supplies more LF, then SLFS´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 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
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
Suggests negative relationship between interest rates & savings
- If interest rates rise
- Economic activity slows
- Income falls
- Allows interest rates to ease
- 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 D2 instead of D1 or
2.Higher inflation savers begin dishoarding so S2 , not S1
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 Simple-Interest 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 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"
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 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).
Base or benchmark rate
The interest rate on the s/t Govt security
nominal rate i(r)
Market rate = actual rate charged by lender
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
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 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. FlatMay indicate that interest rates are in transition or stable
- 4. HumpedImmediate 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 short-term.
- Interest rates are expected to fall, then investors prefer long term securities & borrowers prefer to issue short-term.
- Net result - downward sloping
Under Expectations theory, normal yield curve will result from...
Expected short-term rates to be higher than current short-term rates
Under Expectations theory, inverse yield curve will result from...
Expected short-term rates to be lower than current short-term rates
Under Expectations theory, humped yield curve will result from...
Expected short-term 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 1-year 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 1-yr rate for year 4 to 5? (implied 1-yr 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 two-year 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 1-year 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 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
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 3-year 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 3-year 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 short-term deposits & longterm lending
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?
Example 1 cont: If market interest rates change to 12%
Example 1 cont: If market interest rates change to 8%