Finance Homework
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Chap2.pptxChapter Two
Determinants of Interest Rates
Interest Rate Fundamentals
Nominal interest rates: the interest rates actually observed in financial markets
Used to determine fair present value and prices of securities
Two components:
Opportunity cost
Adjustments for individual security characteristics
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Opportunity cost: All securities’ rates are dependent on rates available on competing investments. These rates will be a function of the underlying supply and demand of funds available.
As indicated later, adjustments for individual security characteristics would include default risk, maturity, liquidity risk and payment terms. Because these characteristics are different for different securities, we have different interest rates on each.
Real Riskless Interest Rates
Additional purchasing power required to forego current consumption
What causes differences in nominal and real interest rates?
If you wish to earn a 3% real return and prices are expected to increase by 2%, what rate must you charge?
Irving Fisher first postulated that interest rates contain a premium for expected inflation.
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The answers are inflation and about 5% respectively.
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Loanable Funds Theory
Loanable funds theory explains interest rates and interest rate movements
Views level of interest rates as resulting from factors that affect the supply of and demand for loanable funds
Categorizes financial market participants – e.g., consumers, businesses, governments, and foreign participants – as net suppliers or demanders of funds
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Supply and Demand for Loanable Funds
Interest
Rate
Quantity of Loanable Funds
Supplied and Demanded
Demand
Supply
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Key Interest Rates Over Time
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Net Supply & Demand of Funds in U.S. in 2016
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A negative number in the last column represents a net demand for funds.
The household (consumer) sector is one of the largest suppliers or loanable funds, while (financial) businesses demanded the most funds.
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Determinants of Household Savings
Interest rates and tax policy
Income and wealth: the greater the wealth or income, the greater the amount saved
Attitudes about saving versus borrowing
Credit availability: the greater the amount of easily obtainable consumer credit the lower the need to save
Job security and belief in soundness of entitlements
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Determinants of Foreign Funds Invested in the U.S.
Relative interest rates and returns on global investments
Expected exchange rate changes
Safe haven status of U.S. investments
Foreign central bank investments in the U.S.
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Foreign funds suppliers examine the same factors as U.S. suppliers except that they must also factor in expected changes in currency values, global interest rates, different tax rates and sovereign risk. There is typically some built in demand for U.S. investments however because the U.S. is considered a safe haven, i.e., a country with relatively low political and economic risk and a stable currency.
High levels of reserves are indicative of foreign central bank activity to limit the growth in the value of their currencies against the dollar. This may be done to stimulate their export sectors. The dollars are often reinvested in the U.S., typically in Treasuries. This provides an additional source of financing to the U.S. and helps remove a market discipline from U.S. borrowers.
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Federal Government Demand for Funds Concluded
Governments borrow heavily in the markets for loanable funds
$23.19 trillion in 2016
United States
National debt was $19.21 trillion in 2016
National debt (and interest payments on the national debt) have to be financed in large part by additional borrowing
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Business Demand for Funds
Level of interest rates:
When the cost of loanable funds is high (i.e., interest rates are high), businesses finance internally
Expected future profitability vs. risk:
The greater the number of profitable projects available to businesses, the greater the demand for loanable funds
Expected economic growth
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Effect on Interest Rates from a Shift in the Supply Curve for Loanable Funds
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Effect on Interest Rates from a Shift in the Demand Curve for Loanable Funds
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Factors that Affect the Supply of and Demand for Loanable Funds for a Financial Security
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Determinants of Interest Rates for Individual Securities
ij* = f(IP, RFR, DRPj, LRPj, SCPj, MPj)
Inflation (IP)
IP = [(CPIt+1 – CPIt)/CPIt] x 100
Real risk-free interest rate (RFR) and the Fisher effect
RFR = i – Expected (IP)
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Define CPI as the consumer price index.
ij* = equilibrium nominal interest rate for a given security
Note: the first two factors (IP and RFR) are common to all financial securities, while the others can be unique to each individual security.
Determinants of Interest Rates for Individual Securities Continued
Default risk premium (DRP)
DRPj = ijt – iTt
ijt = interest rate on security issued by a non-Treasury issuer (issuer j) of maturity m at time t
iTt = interest rate on security issued by the U.S. Treasury of maturity m at time t
Liquidity risk (LRP)
Special provisions (SCP)
Term to maturity (MP)
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DRPs Over Time
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Term Structure of Interest Rates: the Yield Curve
Yield to
Maturity
Time to Maturity
(a)
(b)
(c)
(a) Upward sloping
(b) Inverted or downward
sloping
(c) Flat
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Unbiased Expectations Theory
Current long-term interest rates (1RN) are geometric averages of current and expected future, E(Nr1), short-term interest rates
1RN = actual N-period rate today
N = term to maturity, N = 1, 2, …, 4, …
1R1 = actual current one-year rate today
E(ir1) = expected one-year rates for years, i = 1 to N
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Assumes no interest rate volatility, note these rates should be zero coupon rates called ‘spot’ rates.
Liquidity Premium Theory
Long-term interest rates are geometric averages of current and expected future short-term interest rates plus liquidity risk premiums that increase with maturity
Lt = liquidity premium for period t
L2 < L3 < …LN
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Positive liquidity premia assume that investors prefer short term holdings to long term holdings.
UET vs. LPT
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Market Segmentation Theory
Individual investors and FIs have specific maturity preferences
Interest rates are determined by distinct supply and demand conditions within many maturity segments
Investors and borrowers deviate from their preferred maturity segment only when adequately compensated to do so
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Implied Forward Rates
A forward rate (f) is an expected rate on a short-term security that is to be originated at some point in the future
The one-year forward rate for any year, N years into the future is:
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Time Value of Money and Interest Rates
The time value of money is based on the notion that a dollar received today is worth more than a dollar received at some future date
Simple interest: interest earned on an investment is not reinvested
Compound interest: interest earned on an investment is reinvested, most common
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The formulas that follow are for compound interest.
Present Value of a Lump Sum
Discount future payments using current interest rates to find the present value (PV)
PV = FVt/(1 + r)t
PV = present value of cash flow
FVt = future value of cash flow (lump sum) received in t periods
r = interest rate earned per period on investment
t = number of compounding periods in investment horizon
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Future Value of a Lump Sum
The future value (FV) of a lump sum received at the beginning of the investment horizon
FVt = PV (1 + r)t
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Relation between Interest Rates and Present and Future Values
Present
Value
(PV)
Interest Rate
Future
Value
(FV)
Interest Rate
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Present Value of an Annuity
The present value of a finite series of equal cash flows received on the last day of equal intervals throughout the investment horizon
PMT = periodic annuity payment
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Future Value of an Annuity
The future value of a series of equal cash flows received at equal intervals throughout the investment horizon
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Financial Calculators
Setting up a financial calculator
Number of digits shown after decimal point
Number of compounding periods per year
Key inputs/outputs (solve for one of five)
N = number of compounding periods
I/Y = annual interest rate
PV = present value (i.e., current price)
PMT = a constant payment every period
FV = future value (i.e., future price)
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