determinants of interest rates (2)

7/30/2019 Determinants of Interest Rates (2)

1/27

Determinants of Interest Rates


2/27

Interest Rate Fundamentals

Nominal interest rates - the interest rate actuallyobserved in financial markets

directly affect the value (price) of most securitiestraded in the marketaffect the relationship between spot and forward FXrates

Key learnings from the chapter would be:

How fluctuations in exchange rates and interest ratesaffect the value of promises for future payment?Why do market interest rates and exchange ratesfluctuate?


3/27

Time Value of Money andInterest Rates Assumes the basic notion that a dollar received today is worth more than a dollar received at some future dateCompound interest

interest earned on an investment is reinvested

Simple interestinterest earned on an investment is notreinvested


4/27

Pricing Securities Promising aSingle payment

Future Value = Principal(1 + Interest)

Principal = Future Value / (1+Interest)

For Example a bank is offering 10% on a one year CD.If you deposit Rs.1000 now, at the end of the year you will receive,

1,000(1+0.1) = 1,100

If the bank agrees to pay Rs.1000 after one year,I would pay the present vale of same i.e

1,000/ 1.1 = 909.20


5/27

In case of Compound Interest Value = Principal + Interest + Compounded interest

Value = Principal (1+i)(1+i) = p(1+i) 2Present value = Value/ (1+i) 2

i = (Value/ Principal) 1/t - 1Value = $1,000 + $1,000(12)(2) + $1,000(12)(2)

= $1,000[1 + 2(12) + (12) 2]= $1,000(1.12) 2

= $1,254.40What should you pay for a 1 million, 10 year zero coupon bond?

Suppose approropriate interest rate is 9%.

P = 10,00,000/(1.09)10

= 10,00,000(0.4224) = 4,22,400The interest rate that you earn by buying a security at its market price

and holding it to maturity is called market yield .Market price and market yield are alternative

but entirely equivalent ways of describing the value of future payment.


6/27

The Compounding Period

A bank may offer 6-month CDs at an annual percentage rate of 12% compounded monthly, giving an effective annual rate of 12.68%.Compounding period is the period over which interest iscalculated.

Periodic interest rate is the interest rate per compounding period.Effective Annual Rate is the rate returned over a 12-monthperiod taking the compounding of interest into account

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

At 12% interest - EAR = (1 + .12/4)4 - 1 = 12.55%Relationship between periodic rate and effectivbe annual rate isas under:(1+periodic rate) number of periods per year = 1+effective annual rate


7/27

Present Values

PV is the value today of an amount due infuture.PV function converts cash flows received over

a future investment horizon into an equivalent(present) value by discounting future cashflows back to present using current marketinterest rate.

lump sum paymentannuity

PVs decrease as interest rates increase


8/27

Calculating Present Value (PV)of a Lump Sum

PV = FV n (1/(1 + i /m ))nm = FV n (PVIF i/m,nm )

where:PV = present valueFV = future value (lump sum) received in n years

i = simple annual interest

n = number of years in investment horizonm = number of compounding periods in a year

PVIF = present value interest factor of a lump sum


9/27

Calculation of Present Value(PV) of an Annuity

nm

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

where:PV = present valuePMT = periodic annuity payment received

during investment

i = simple annual interestn = number of years in investment horizonm = number of compounding periods in a year

PVIFA = present value interest factor of an annuity


10/27

Calculation of Present Value of an Annuity

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

PV = PMT(PVIFA i/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


11/27

Future Values

Translate cash flows received during aninvestment period to a terminal (future) valueat the end of an investment horizonFV increases with both the time horizon andthe interest rate


12/27

Future Values Equations

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(FVIFA i/m, mn )(t = 1)


13/27

Relation between Interest Rates

and Present and Future Values

PresentValue(PV)

Interest Rate

FutureValue(FV)

Interest Rate


14/27

STRIPS

A security created by breaking up another security into constituent parts.Consider a 2-year one million T Bond with 10% annual coupons.We think of this bond being equivalent to a combination of two T-bills- the first aRs. 1,00,000 one year bill; the second a Rs. 1,100,000 two year bill.STRIPS is the acronym for Separate Trading of Registered Interest andPrincipal of Securities.

STRIPS let investors hold and trade the individual interest and principalcomponents of eligible Treasury notes and bonds as separate securities.STRIPS are popular with investors who want to receive a known payment on aspecific future date.STRIPS are called zero -coupon securities. The only time an investor receivesa payment from STRIPS is at maturity.STRIPS are not issued or sold directly to investors. STRIPS can be purchased

and held only through financial institutions and government securities brokersand dealers.


15/27

Loanable Funds Theory

A theory of interest rate determination thatviews equilibrium interest rates in financial

markets as a result of the supply anddemand for loanable funds


16/27

Supply of Loanable

Funds Interest

Rate

Quantity of Loanable FundsSupplied and Demanded

Demand Supply


17/27

Funds Supplied and Demanded by Various Groups (in billions of dollars)

Funds Supplied Funds Demanded

Households $31,866.4 $ 6,624.4Business -- nonfinancial 7,400.0 30,356.2Business -- financial 27,701.9 29,431.1

Government units 6,174.8 10,197.9Foreign participants 6,164.8 2,698.3


18/27

Determination of

Equilibrium Interest Rates

InterestRate

Quantity of Loanable FundsSupplied and Demanded

D S

I H

i I L

E

Q


19/27

Effect on Interest rates from a Shift inthe Demand Curve for or Supply curve

of Loanable Funds Increased supply of loanable funds

Quantity of

Funds Supplied

Interest

Rate DD SS

SS*

E E*

Q*

i*

Q* *

i* *

Increased demand for loanable funds

Quantity of

Funds Demanded

DD DD* SS

E E*

i*

i* *

Q* Q* *


20/27

Factors Affecting NominalInterest Rates

Inflationcontinual increase in price of goods/services

Real Interest Ratenominal interest rate in the absence of inflation

Default Riskrisk that issuer will fail to make promised payment

(continued)


21/27

Liquidity Risk risk that a security can not be sold at apredictable price with low transaction cost onshort notice

Special Provisions taxabilityconvertibilitycallability

Time to Maturity


22/27

Inflation and Interest Rates: TheFischer Effect

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%


23/27

Default Risk and InterestRates The risk that a securitys issuer will defaulton that security by being late on or missing

an interest or principal payment

DRP j = i j t - i Tt

Example: DRP Aaa = 7.55% - 6.35% = 1.20%DRP Bbb = 8.15% - 6.35% = 1.80%


24/27

Tax Effects: The Tax Exemption of Interest on Municipal Bonds

Interest payments on municipal securities areexempt from federal taxes and possibly state andlocal taxes. Therefore, yields on munis are

generally lower than on equivalent taxable bondssuch as corporate bonds.

i m = i c (1 - t s - t F )

Where: ic = Interest rate on a corporate bondim = Interest rate on a municipal bondt s = State plus local tax ratet F = Federal tax rate


25/27

Term to Maturity and InterestRates: Yield Curve

Yield toMaturity

Time to Maturity

(a)

(b)(c)

(d)

(a) Upward sloping(b) Inverted or downward

sloping

(c) Humped(d) Flat


26/27

Term Structure of Interest Rates

Unbiased Expectations Theoryat a given point in time, the yield curve reflectsthe markets current expectations of futureshort-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 securitys value

Market Segmentation Theory investors have specific maturity preferencesand will demand a higher maturity premium


27/27

Forecasting Interest Rates

Forward rate is an expected or implied rateon a security that is to be originated at some

point in the future using the unbiasedexpectations theory

_ _ R 2 = [(1 + R 1)(1 + (f 2))] 1/2 - 1

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

forward one-year rate for next year

determinants of interest rates (2)

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