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Chapter Two

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Chapter Two

Determinants of

Interest Rates

- Nominal interest rates - the interest rate actually observed in financial markets
- directly affect the value (price) of most securities traded in the market
- affect the relationship between spot and forward FX rates

- Assumes the basic notion that a dollar received today is worth more than a dollar received at some future date
- Compound interest
- interest earned on an investment is reinvested

- Simple interest
- interest earned on an investment is not reinvested

Value = Principal + Interest

Example:

$1,000 to invest for a period of two years at 12 percent

Value = $1,000 + $1,000(.12)(2)

= $1,240

Value = Principal + Interest + Compounded interest

Value = $1,000 + $1,000(12)(2) + $1,000(12)(2)

= $1,000[1 + 2(12) + (12)2]

= $1,000(1.12)2

= $1,254.40

- PV function converts cash flows received over a future investment horizon into an equivalent (present) value by discounting future cash flows back to present using current market interest rate
- lump sum payment
- a single cash payment received at the end of some investment horizon

- annuity
- a series of equal cash payments received at fixed intervals over the investment horizon

- lump sum payment
- PVs decrease as interest rates increase

PV = FVn(1/(1 + i/m))nm = FVn(PVIFi/m,nm)

where:

PV = present value

FV = future value (lump sum) received in n years

i = simple annual interest

n = number of years in investment horizon

m = number of compounding periods in a year

PVIF = present value interest factor of a lump sum

nm

PV = PMT (1/(1 + i/m))t = PMT(PVIFAi/m,nm)

t = 1

where:

PV = present value

PMT = periodic annuity payment received

during investment

i = simple annual interest

n = number of years in investment horizon

m = number of compounding periods in a year

PVIFA = present value interest factor of an annuity

You are offered a security investment that pays $10,000 on the last day of every quarter for the next 6 years in exchange for a fixed payment today.

PV = PMT(PVIFAi/m,nm)

at 8% interest - = $10,000(18.913926) = $189,139.26

at 12% interest - = $10,000(16.935542) = $169,355.42

at 16% interest - = $10,000(15.246963) = $152,469.63

- Translate cash flows received during an investment period to a terminal (future) value at the end of an investment horizon
- FV increases with both the time horizon and the interest rate

- FV of lump sum equation
- FVn = PV(1 + i/m)nm = PV(FVIF i/m, nm)

- FV of annuity payment equation
- (nm-1)
- FVn = PMT (1 + i/m)t = PMT(FVIFAi/m, mn)
- (t = 1)

Present

Value

(PV)

Future

Value

(FV)

Interest Rate

Interest Rate

Rate returned over a 12-month period

taking the compounding of interest into

account

EAR = (1 + i/m)m - 1

At 8% interest - EAR = (1 + .08/4)4 - 1 = 8.24%

At 12% interest - EAR = (1 + .12/4)4 - 1 = 12.55%

Money market instruments (e.g., Treasury

bills and commercial paper) that are bought

and sold on a discount basis

idy = [(Pt - Po)/Pf](360/h)

Where:

Pf = Face value

Po = Discount price of security

Money market securities (e.g., jumbo CDs,

fed funds) that pay interest only once during

their lives: at maturity

ibey = ispy(365/360)

- A theory of interest rate determination that views equilibrium interest rates in financial markets as a result of the supply and demand for loanable funds

Demand

Supply

Interest

Rate

Quantity of Loanable Funds

Supplied and Demanded

Funds SuppliedFunds Demanded

Households $31,866.4 $ 6,624.4

Business -- nonfinancial 7,400.0 30,356.2

Business -- financial 27,701.9 29,431.1

Government units 6,174.8 10,197.9

Foreign participants 6,164.8 2,698.3

D

S

Interest

Rate

I H

i

E

I L

Q

Quantity of Loanable Funds

Supplied and Demanded

Increased supply of loanable funds

Increased demand for loanable funds

DD*

Interest

Rate

SS

SS

DD

DD

SS*

i**

E*

E

i*

E

i*

E*

i**

Q*

Q**

Q*

Q**

Quantity of

Funds Supplied

Quantity of

Funds Demanded

- Inflation
- continual increase in price of goods/services

- Real Interest Rate
- nominal interest rate in the absence of inflation

- Default Risk
- risk that issuer will fail to make promised payment

(continued)

- Liquidity Risk
- risk that a security can not be sold at a predictable price with low transaction cost on short notice

- Special Provisions
- taxability
- convertibility
- callability

- Time to Maturity

The interest rate should compensate an investor

for both expected inflation and the opportunity

cost of foregone consumption

(the real rate component)

i = Expected (IP) + RIR

Example: 5.08% - 2.70% = 2.38%

The risk that a security’s issuer will default

on that security by being late on or missing

an interest or principal payment

DRPj = ijt - iTt

Example: DRPAaa = 7.55% - 6.35% = 1.20%

DRPBbb = 8.15% - 6.35% = 1.80%

Interest payments on municipal securities are exempt from federal taxes and possibly state and local taxes. Therefore, yields on “munis” are generally lower than on equivalent taxable bonds such as corporate bonds.

im = ic(1 - ts - tF)

Where: ic = Interest rate on a corporate bond

im = Interest rate on a municipal bond

ts = State plus local tax rate

tF = Federal tax rate

(a) Upward sloping

(b) Inverted or downward

sloping

(c) Humped

(d) Flat

Yield to

Maturity

(a)

(d)

(c)

(b)

Time to Maturity

- Unbiased Expectations Theory
- at a given point in time, the yield curve reflects the market’s current expectations of future short-term rates

- Liquidity Premium Theory
- investors will only hold long-term maturities if they are offered a premium to compensate for future uncertainty in a security’s value

- Market Segmentation Theory
- investors have specific maturity preferences and will demand a higher maturity premium

Forward rate is an expected or “implied” rate

on a security that is to be originated at some

point in the future using the unbiased

expectations theory

__

R2 = [(1 + R1)(1 + (f2))]1/2 - 1

where

f2 = expected one-year rate for year 2, or the implied

forward one-year rate for next year