125.220 Week 2: Interest Rates
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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.
- • impact on money market & capital market instruments with certain expected effects on fixed-income securities
The most accurate measure of an interest rate is:
Yield-to-maturity= present value of future payments of a debt instrument with today’s value
Other interest rates: current yield & Discount yield
Determination of Interest Rate Levels
– Loanable Funds (LF) Approach
- - This treats the risk-free interest rates as an
- outcome of the forces of demand & supply in financial markets.
- - Modelled by supply & demand curves
- -In the loanable funds approach, have downward sloping demand curve & upward-sloping supply curve
Loanable funds Approach (graph)
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.
Demand Side (D deficit units)
- 1. Households borrow to buy goods & services (relatively inelastic demand)
- 2. Investors borrow for plant & equipment- (more elastic)
- 3. Governments tend to borrow to finance deficits (inelastic=non sensitive)
A rise in interest rates should result in...
Increase in the money supply as:
- • 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
DLF → D′LF (supply unchanged-all else equal)
- Demand for LF > supply of LF at r0 so i0 → i1
- (holding supply constant)...so an increase in interest rates
Example 2: Increase in money supply-
Central Bank supplies more LF, then SLF → SLF (with demand unchanged)
S'LF moves to the right
So a decrease in interest rates
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 higher rate of interest.
Effects of changes in inflationary expectations known as Fisher effect.
Real interest rate = the nominal interest rate minus the expected inflation rate
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.
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)
- Face Value = proceeds of S/T investment
- Current Price = market price
- r = yield % p.a.
- r = rate of interest on the amount paid out to buy asset
Calculating a Compound Interest Yield
The compound rate of return, r, for two cash flows is found by: If FV = PV(1 + r)t
- PV = present value
- FV = future value
- t = time in years
- r = compound rate of interest
What is an interest rate made up of:
Components of interest rates are:
r = r* + IP + RP + T
- r* is real risk-free return
- IP is the expected inflation premium
- RP is risk factors
- T is taxes
Real risk-free rate
required rate of interest on riskless security if no expected inflation
base or benchmark rate
The interest rate on the s/t Govt security
The difference between the interest rate for non-Govt (corporate) security & the Govt security
Factors that affect the spread include risk factors such as default (credit), liquidity, maturity risk & embedded provisions e.g. call
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.
Theories to explain the Term Structure of Interest Rates
1. Unbiased (Pure) Expectations theory
Suggests that 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.
- Borrowers prefer to issue L/T securities⇒ large supply ⇒ downward pressure on prices- yields up.
- Net effect = upward sloping
If 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-, inverse-, and humped-curve...
- Normal yield curve = result from expected short-term rates to be higher than current short-term rates.
- inverse yield curve will result from expected short-term rates to be lower than current short-term rates.
- humped yield curve will result from expected short-term to be higher initially then subsequently fall in longer term
In general, to find forward rate implied by spot rates of adjacent maturities:
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+k ⇒ k 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
Implied forward rates:
Estimate expected market interest 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
- • Unbiased Expectations theory assumes that everyone correctly anticipates interest changes.
- • 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.
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.
- Example: institutions that operate in short-term markets
Risk structure of interest rates
- Relationship between bonds with same term to maturity and their different interest rates is called the risk structure.
- Default risk is the risk that the borrower (i.e. issuer) will fail to meet its interest payment obligations.
– Some borrowers may have greater risk of default. (i.e. private sector firms)
– Government bonds are assumed to have zero default risk. As they are risk-free, they offer a risk-free rate of return
– Investors will require compensation for bearing the extra default risk
For different securities, their varying default risks will have an impact on their yield curves
Risk structure of interest rates
- Red = Treasury bonds
- Blue = Corporate bonds (AA-rated)
- Black = Corporate bonds (BBB-rated)
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:
- P = Price or present value of bond
- C = Interest payment calculated from coupon
- F = Face value of bond, usually 100 here
- i = interest rate or Yield to Maturity (YTM)
- t = Number of years of bond
Importance of the Structure of Interest
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 & long term lending.
The problem of the inverse yield curve
If FI has cash flow problems (a run) ⇒ bad situation - lenders want money back, borrowers are borrowing long.
Negative yield curve bad because hard to encourage people to lend long, they want to lend short unless they expect interest rate to decrease soon.
Example: 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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