Lecture 36.pdf

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Money, Bonds and Interest Rates

Module Convenor: Luke Buchanan-Hodgman

Contact: [email protected] Office: Keynes D2.12 Contact Hours: Thursday 10-11

Website: https://sites.google.com/site/buchananhodgman

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Learning Objectives

1. LO1: the inverse relationship between the return on an asset (yield or interest rate) and its market price or present value

2. LO2: Build a simple model of the money market

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A Money Market Model: Preliminaries

Assumptions;

I Wealth =Money + Bonds. This limits to manageble proportions the range of financial assets.

I Agents can hold either money or bonds

I Money is assumed not to pay interest. Theopportunity cost of holding money is the interest foregone on holding a bond.

Recognise that;

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Asset Pricing: Bonds

Pricing Fixed Interest Securities (Bonds):

I Treasury 10% 2020 Bond sold for£100 which pays £10 coupon per annum to the holder till 2020 when it will be redeemed for£100. Bonds are traded every day at prices which differ from £100. Used forlong-term loans to the government

What does this imply about the interest rate?

I Example 1: if the price is £100 today, and coupon£10 per annum, then the interest rate is 10%.

I Example 2: if the price is £90 today, and coupon£10 per annum, then the interest rate is 11.11%

I Example 3: if the price is £70 today, and coupon£10 per annum, then the interest rate is 14.28%

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Asset Pricing: Bills (present value)

Pricing Fixed Terminal Value Securities (Bills)

I £1000 commercial bill will be redeemed in 3 months for£1000, so sold todayat a discount. Suppose the selling price is£960, the 3 month return is 1000/960 = 1.0417 which implies a 4.2% interest rate per quarter.

What does this imply about the interest rate?

I Example 1: if the price is £950 today, and terminal value is£1000, then the interest rate is 5.26%.

I Example 2: if the price is £925 today, and terminal value£1000, then the interest rate is 8.1%

I Example 3: if the price is £900 today, and terminal value£1000, then the interest rate is 11.11%

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What determines money demand (Md

)?

Problem:

I If bonds yield a financial return, while money does not, then why would optimising agents desire to hold a stock of money?

Keynes suggestedthreemain reasons:

I Transactional motive:- in order to undertake economic transactions and minimise the cost of said transactions

I Precautionary motive:- to hedge against uncertain events occurring.

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Specifying money demand

Md

=

f

(

P

(+)

,

i

(−)

,

Y

(+)

)

Nominal money demand (Md) is a function of;

I Price level (P):- nominal money demand moves proportionally with the price level.

I Interest on bonds (i):- this is related to the speculative motive. As the nominal rate of interest increases, the opportunity cost of money balances increases.

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Money demand: nominal to real

It is believed that if the price level increase by 10%, then the stock

of money will increase by an equal amount to facilitate the existing

level of transactions. So we can write in terms of real money

balances;

Md

P

=

f

(

i

,

Y

)

But what is real money demand?

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Movements in the Money Demand Schedule

1,000 1,200 1,400 1,600 3

4 5

6 ⇑interest rate

⇓interest rate

Md

Real Money

Interest

Rate

(p

e

rcent

p

er

yea

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Shifts in the Money Demand Schedule

1,000 1,200 1,400 1,600 3

4 5

6 ⇑ Real GDP

⇓ Real GDP or

Financial Innovation

Md0 Md1

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Introducing Money Supply

I In the context of the UK, the BoE influences, via Open Market Operations (OMO), the quantity of reserves in the banking sector, which, through the mechanism described in the previous lecture, will change the money supply at any given interest rate.

We can make two assumptions regarding the money supply;

1. The money supply is exogenously determined directly by the BoE, and the interest rate is endogenous;

2. Policy makers decide on an interest rate and money supply adjusts accordingly.

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Equilibrium and Disequilibrium

1,000 1,200 1,400 1,600 3

4 5

6 Ms >Md: demand

for bonds ↑, so↓ir

Md>Ms: demand

for bonds↓, so↑ ir Md

Ms E0 Real Money Interest Rate (p e rc ent p er yea

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Equilibrium and Disequilibrium

Interaction between the bond market and the money market provides the economic process for adjustment to equilibrium

I In other words, the interest rate adjusts so that the supply of money is willingly held, and there is no excess supply or demand for bonds

I Equivalently, when the money market is in equilibrium the bond market must also be in equilibrium due to their

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Shifts in the Money Supply Schedule

1,000 1,200 1,400 1,600 3

4 5 6

↓Ms ⇒↑ir

↑Ms ⇒↓ir

Ms1 Ms0 Ms2

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Summary

1. LO1: the inverse relationship between the return on an asset (yield or interest rate) and its market price or present valueX

2. LO2: Build a simple model of the money marketX