FISD-01

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Tarheel Consultancy Services

Bangalore

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Part-01:Interest Rates

&

The Time Value of Money

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Interest Rates

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Introduction

All of us have either paid and/or receivedinterest at some point of time.

Those of us who have taken loans have paid

interest to the lending institutions.

Those of us who have invested have receivedinterest from the borrowers.

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Introduction (Cont)

Types of LoansEducational Loans

Housing Loans

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Introduction (Cont)

Automobile Loans

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Introduction (Cont)

InvestmentsSavings accounts, and

Fixed deposits (Time deposits) with banks

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Introduction (Cont)

Bonds & Debentures

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Introduction (Cont)

Definition of interest

Compensation paid by the borrower of capital tothe lender

For permitting him to use his funds

An economists definition

Rent paid by the borrower of capital to the

lenderTo compensate for the loss of opportunity to use the

funds when it is on loan

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Introduction (Cont)

Concept of rent

When we decide not to live in anapartment/house owned by us

We let it out to a tenant

The tenant pays a monthly rental

Because as long as he is occupying our property weare deprived of an opportunity to use it

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Introduction (Cont)

The same concept applies to a loan of funds

The difference is

Compensation in the case of property is called RENT

Compensation in the case of capital is called INTEREST

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The Real Rate of Interest

In a free market

Interest rates are determined by

Demand for capital

And

The supply of capital

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The Real Rate (Cont)

One of the key determinants of Interest is

The Pure rate of interest a.k.a

The Real rate of interest

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Definition of the Real rate:The rate of interest that would prevail on a risk-less

investment in the absence of inflation.

Example of a risk-less investmentLoan to the Federal/Central government

Such loans are risk-less because there is no riskof defaultThe central government of a country is the only

institution authorized to print money

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But they say that certain governments (in LatinAmerica etc.) have defaulted on debt

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Yes they have defaulted on dollardenominated debt

The government of Argentina for instance can

print its own currency but not U.S. dollars

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The Real Rate Illustrated

The price of a banana is Rs 1

Assume that the price of a banana next yearwill also be Rs 1That is, there is no inflation

In other words there is no erosion in the purchasingpower of money

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Illustration (Cont)

Take the case of a person who lendsRs 10 to the Government of India (GOI)

Obviously there is no fear of non-payment

If the GOI pays back Rs 11 after one year

The amount will be sufficient to buy 11bananas.

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Illustration (Cont)

In this case a loan of Rs 10 has beenreturned with 10% interest in money terms

Since the investor is in a position to buy10% more in terms of bananas

The return on investment in terms of the abilityto buy goods is also 10%

The rate of interest as measured by the abilityto buy goods and services is termed as

THE REAL RATE of INTEREST

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In the real world price levels are notconstant.

Erosion in the purchasing power of money is a

fact of lifeThis is termed as inflation

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Inflation

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Most people who invest do so by acquiringfinancial assets such as

Shares of stock

Shares of a mutual fund

Or bonds/debentures

Many also keep deposits with commercial

banks

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Financial assets give returns in terms ofmoney

Without any assurance about the investors

ability to acquire goods and services at the timeof repayment.

Financial assets therefore give a

NOMINAL or MONEYrate of return.In the example, the GOI gave a 10% return on

an investment of Rs 10.

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In the example the 10% money rate ofreturn was adequate to buy 10% more interms of bananas.

This was because we assumed that the price ofa banana would remain fixed at Rs 1.

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But what if the price of a banana after a year isRs 1.05.Rs 11 can then acquire only

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In this case the nominal rate of return is 10%

But our ability to buy goods has been enhancedonly by 4.80%

Thus the REAL rate of return is only 4.80%

The relationship between the nominal and realrates of return is called the FISHER hypothesisBecause it was first postulated by Irving Fisher.

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The Fisher Equation

Consider a hypothetical economyIt consists of one good say BANANAS

The current price of a banana is Rs P0So Rs 1 can buy

bananas.

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The Fisher Equation (Cont)

Assume that the price of a banana next periodis P1.P1is known with certainty today but need not be equal

to P0In other words although we are allowing for inflation,

we are assuming that there is no uncertaintyregarding the rate of inflation.

So one rupee will be adequate to buy

bananas after one period

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Assume that the economy has two typesof bonds available

We have FINANCIALbonds and GOODS

bondsIf we invest Rs 1 in a Financial bond, we will get

Rs (1+R) after one period.

If we invest 1 banana in a Goods bond we willget (1+r) bananas after one period.

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In order for the economy to be in equilibriumboth the bonds must yield identical returns.

Therefore it must be true that:

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Let us denote inflation or the rate of change inthe price level by

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This is the Fisher equation.

R or the rate of return on a financial bond is thenominal rate of return

r or the rate of return on a goods bond is thereal rate of return

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If r and are very small, then the productof the two will be much smaller.

For instance if r = 0.03 and = 0.03, the

product is 0.0009

If we ignore the product we can rewrite theexpression as

R = r + This is the approximate Fisher equation.

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Uncertainty

Thus far we have assumed that the rate ofinflation is known with certainty.

In real life inflation is uncertain

Consequently it is a random variable

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Uncertainty (Cont)

In the case of random variables

We do not know the exact outcome inadvance

All we know is the expected value of thevariable

Which is a probability weighted average of thevalues that the variable can take.

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Uncertainty (Cont)

Inflation Probability

2.50% 0.20

5.00% 0.20

7.50% 0.20

10.00% 0.20

12.50% 0.20

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Uncertainty (Cont)

The expected value is given by

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Uncertainty (Cont)

The Fisher equation can therefore be re-written as

R = r + E()

Thus when inflation is uncertain

The actual real rate that we will eventually get isunpredictable and uncertain

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Uncertainty (Cont)

Assume that the required real rate is4.50%

Since the expected inflation is 7.50%

an investor will demand a nominal rate of returnof 12%

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Uncertainty (Cont)

Once the nominal rate is fixed, it will notvary

But there is no guarantee that the realizedrate of inflation will equal the expected rateIn this case if the realized inflation is 9%, the

realized real rate will be only 3%

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Ex-ante versus Ex-post

An economist will say that the ex-ante rateof inflation need not equal the ex-post rate

Ex-ante means anticipated or forecasted value

Ex-post connotes actual or realized value

Obviously the ex-ante real rate of interestneed not equal the ex-post real rate

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Uncertainty & Risk Aversion

In the real world investors are characterized byRISK AVERSION.This does not mean that they will not take risk

What does it mean therefore?

To induce an investor to take a greater level of risk hemust be offered a higher expected rate of return.

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Risk Aversion (Cont)

Given a choice between two investments withthe same expected rate of returnThe investor will choose the less risky option

In the case of inflationThe investor will not accept the expected inflation as

compensation

Why?

The actual inflation could be higher than anticipatedWhich implies that the actual real rate could be lower than

anticipated.

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To tolerate the inflation risk

The investor will demand a POSITIVE riskpremium

That is, compensation over and above the expectedrate of inflation

The Fisher equation may be restated as

R = r + E() + R.P.

Where R.P is the risk premium

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Does the provision of a risk premiumguarantee that the

ex-ante real rate = ex-post real rate

NO!

Suppose the required real rate is 4.5%,that E() = 7.5%, and that R.P = 1.5%

Then the required nominal rate will be 13.50%

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In the absence of a risk premiumA rate of inflation > 7.5% implies a realized real rate 9% implies a realized real rate

FISD-01

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Transcript of FISD-01