04 Understanding Interest Rates

7/30/2019 04 Understanding Interest Rates

http://slidepdf.com/reader/full/04-understanding-interest-rates 1/70

Banking & Finance

The behavior of interest rates



Overview

So far we have developed some fundamental insights

– Financial markets are the place of exchange of funds between borrowers and lenders.

– Since a significant part of these funds are used byfirms to invest, financial markets have a highsignificance for economic growth.

– The price borrowers have to pay and lendersreceive for the provision of funds is measured byinterest rates



Why interest rates?

Because of this relation, macroeconomist are stronglyconcerned about interest rates:

– Interest rates are not only a central determinant ofinvestment and, thus, future economic growth, butalso of household’s consumption and savings

– Interestingly enough, interest rates are not stable at

»the next slide displays the behavior of nominalinterest rates on U.S. 3 month T-bills rate from1954 to 2010



T-Bill rates



Interest rates history

– Interest rates until the middle of the 20th centurywere around 0%-1%, raised all the way up to 16% inthe early 1980s and by 2002 were back to 1%

»What causes these fluctuations in interest rates?

»We already discovered that asset prices andinterest rates are negatively related.

»In order to explain interest rate fluctuations we,thus, will focus on the determinants of assetdemand and supply



The theories

Two theories are commonly used to discuss the behaviorof interest rates:

»The loanable funds framework

»The (Keynesian) liquidity preference framework

In discussing these, we will focus our discussion mainlyon bonds



The demand for assets

The price of bonds and, thus, the interest rate on bondsis determined by shifts in demand and supply of bonds

»Generally an individual’s demand for assets is –

ceteris paribus - determined by four factors:

»An individual’s wealth, the expected returns toholding an asset, the asset’s risk and theliquidity of an asset

– Let’s look at each of these four step by step



Wealth

»Wealth indicates the total resources available to an individual (including all ofher/his assets)

»Everything else the same an increase inan individual’s wealth will raise her/hisdemand for (all forms of) assets, et vice

versa.



The demand for assets

• We determined the return to a specific bond as its

interest rate + capital gains (/losses)

• Essentially all factors (other than the price)determining the return on a bond are unknown atthe time of its purchase:

• Potential future changes in asset prices, its interest

rateand

shifts in inflationare unknown.

c RET i g



Expected Return

– The demand for a specific bond relative to anotherasset is, thus, determined by the expectations anindividual forms about the return on this bondrather than by its actual return.

– A concept we use in economics to modelexpectations are so called expected values.Expected values of an outcome have aninterpretation similar to an average outcome and

are constructed in the following way.



Expected Return Calculation

»To find the expected value on any action we firsthave to find all possible outcomes of thataction.

»Then we have to assign a value or payoff to eachof these outcomes and a probability of thisoutcome occurring

»Finally we sum up the products of theprobability and the payoffs for each possibleoutcome.



Expected Return – An Example

»Assume you play roulette and put $100 on black.

»In American roulette, there are three possibleoutcomes: The ball comes to rest on a red

number, a green number or a black number.

»If the ball comes to a rest on a green or red number we receive nothing, if the ball comes to

rest on a black number we receive $200.



Expected Return – An Example 2.

– Finally, the probability that the ball comes to a

rest on black is about 0.47

– The expected return E to playing black on aroulette table is, thus, given by:

– So on average you’re likely to win $94 on by

putting $100 on black at a roulette-table.

( ) 0.47*$200 0.53*$0 $94 E black



Expected Return – An Example 3.

• Similar to an expected payoff in the case of playing

roulette, we can form an expectation on the return of a bond.

• For example if we suspect that a bond pays a return

of 15% with a probability of 0.25 and a return of 5% with a probability of 0.75, the expected return onthis bond is given by:

0.25*15% 0.75*5% 7.5%e

RET



Expected Return – Conclusion

• Since individuals do not know ahead of time what theactual return on an asset is going to be, they act

according to their expected returns instead.• In practice these depend on expected changes in the

relative price of an asset, in the interest rate and inparticular on expected inflation, which will decrease thedemand for a particular asset.

• An increase in the expected return of one asset overanother increases the demand for this asset and viceversa.

• Note that inflation does not affect the return to all assets

identically. A bond which is denoted in nominal terms isstronger affected by high inflation than for example therent produced by the ownership of real estate.



Risk

• The expected return on an asset is not its only featureof interest: Apart from the average return individualsalso care about the risk of an asset.

• There are three types of agents according to theirrisk-behavior: Risk-averse agents, risk-neutral agentsand risk-lovers.



Risk – An Example

– To see the difference, consider the followingexample:

»Assume you compare two bonds. The first onehas a return of $100 with a probability of 25% and a return of $50 with a probability of 75%. It’s expected value is then given by: $62.5. Thesecond has a return of $200 with a probabilityof 25% and a return of $16.67 with a probabilityof 75%. The expected value of this second bond is

also equal to $62.5



Risk – An Example 2.

»Clearly these two bonds are not the same!

Bond 1

25% of all cases: $100


Bond 2


75% of all cases: $16.67

Bond 2 has a larger variation and, thus, a higher risk.A risk-neutral person would prefer bond 1, while a risk-lover bond 2.A risk-neutral person would be indifferent between thetwo.



Risk model assumptions

–The standard assumption in most economic models is that

agents are risk-averse. Thus, an agent’s demand for anasset will decrease if the risk of this asset increasesrelative to others.

–Individuals are often inconsistent about their perceptionof risk:

• For example: Many people are afraid of terroristthreat, while they are perfectly fine with riding in a

car. In 2001 the number of individuals in the U.S.killed in terrorist attacks were 2,986, while thenumber of deaths on the street was equal to 42,116.

i idi



Liquidity

• We already discussed that agents prefer assets which

are highly liquid since they have to satisfy uncertaintransaction needs.

• An asset with higher liquidity will, thus, be demanded

more than an asset with lower liquidity, everythingelse the same.

Summary: Response of Asset Demand to Changes in Wealth



Summary: Response of Asset Demand to Changes in Wealth,Expected Returns, Risk, and Liquidity



Factors That Shift the Demand Curve for Bonds

Th l f t



The supply of assets

– Again we will keep focusing on bonds (althoughmost of the following holds for other assets aswell). The supply of bonds depends mainly onthree factors:

»1. The expected profitability of investmentopportunities

»2. Expected inflation

»3. Government activities

E t d fit bilit f i t t t iti



Expected profitability of investment opportunities

• If firms perceive a higher profitability in theirinvestment options, their demand for funds will behigher. Thus, the supply of bonds (or stocks, etc.) willincrease.

• During a business cycle expansion we, thus, see thesupply of bonds increase, while during recessions, wesee the supply of bonds decrease

E t d i fl ti



Expected inflation

• From the Fisher equation follows that highexpected inflation reduces the real interestrate firms or governments have to pay onbonds.

• Thus, if firms or governments expect inflationto be high, their supply of bonds will increase,

since the expected cost of borrowing c.p.becomes smaller in real terms.

G t ti iti



Government activities

• If a government decides to engage in any form of

activity which increases the government deficit, itwill turn to financial markets to obtain funds tofinance this deficit.

• Thus an increase in the government deficit (throughhigher spending or lower taxation) leads to anincrease in the supply of government bonds.

F Th Shif h S l f B d



Factors That Shift the Supply of Bonds

E ilib i i th b d k t L bl F d



Equilibrium in the bonds market – Loanable Funds

• To model equilibrium in the bonds market let’sassume for simplicity that there exists only one

discount bond:

»Let further Bd indicate the demand for this bond and Bs indicate supply of this bond.

»Let this discount bound have a face value of$1,000 and a maturity of one year.

Expected Inflation and Interest Rates (3 Month T-Bills) 1953–2008



Expected Inflation and Interest Rates (3 Month T Bills) 1953 2008

Source: Expected inflation calculated using procedures outlined in Frederic S. Mishkin, “The Real Interest Rate: An Empirical Investi gation,”Carnegie-Rochester Conference Series on Public Policy 15 (1981): 151–200. These procedures involve estimating expected inflation as a function ofpast interest rates, inflation, and time trends.

Equilibrium in the bonds market Loanable funds



Equilibrium in the bonds market – Loanable funds

As usual, demand is a negative function of the price ofthis bond. The more costly a bond is today, the lower

is its expected return tomorrow. The following graphindicates this relationship.

– Note that in this example demand for this bond for

each level of price is arbitrary:

Equilibrium in the bonds market Loanable funds




100 200 300 400 500 600 600

1900

1700

1500

1300

1100

900

Bd

Quantity of bonds in $ bil.

Price in $

Equilibrium in the bonds market Loanable funds 2



Equilibrium in the bonds market – Loanable funds 2.

• We further know that the price of a bond and the interest rateare negatively related.

• For a one period discount bond, the price is determined by itspresent discounted value:

Here:

(1 )

B

t

FV P

i

$2,000

(1 )

B

t P

i

Equilibrium rates in the bonds market LF



Equilibrium rates in the bonds market – LF

• For different prices, we can, thus determine thebonds equilibrium interest rates, e.g.:

»Pb= $1,900

»Pb = $1,700

»Pb=$1,500

$2,000 $1,9005.26%

$1,900i

$2,000 $1,700 17.65%$1,700

i

$2,000 $1,500 33.33%$1,500

i

Equilibrium in the bonds market LF graphics extended



Equilibrium in the bonds market – LF graphics extended

– Graphically we can illustrate this inverse

relationship by adding a second vertical axis on theright side of our graph indicating the interest ratefor each price

– In addition, we can add the supply curve of bonds,which is an upward-sloped function of the bondprice, since a borrower obtains more funds, thehigher the price he can sell a bond for c.p.

Equilibrium in the bonds market Loanable funds chart



Equilibrium in the bonds market – Loanable funds chart

100 200 300 400 500 600 600

1900

1700

1500

1300

1100

900

Bd


Price in $

5.26

33.3

81.81

Interest rate in %Bs

17.65

E





– E indicates the equilibrium in the bonds market, since at E

Bd =Bs.

– From this diagram we can find the equilibrium price for thisbonds ($1,700), the equilibrium interest rate (17.65%) andthe equilibrium quantity ($300 bill. worth of bonds).

– If any of the determinants of supply or demand of bondschanges, we can now easily analyze, how bond prices andinterest rates are going to be affected.

Equilibrium in the bonds market – Loanable funds 2




Usually we do care more about interest rates than aboutbonds prices.

– Let’s, thus, get rid of the bond prices in ourdiagram and flip around the vertical axisindicating the interest rate. The resulting graph is

shown on the next slide:

Equilibrium in the bonds market – Loanable funds 3




100 200 300 400 500 600 600

Bs


5.26

33.3

81.81

Interest rate in%

Bd

17.65 E

Equilibrium in the bonds market – LF redrawn



Equilibrium in the bonds market LF redrawn

This diagram allows us to directly determine howchanges in the demand and supply of assets affect

the interest rate, which is what we are ultimatelyinterested in.

– It has one undesirable feature, however: Thedemand curve in this graph is upward-sloping.

– We solve this problem with a trick:

Equilibrium in the bonds market – LF concept



Equilibrium in the bonds market LF concept

Remember that every bond is essentially a debt contract.

» While a bond can be viewed as supplied by the borrower and demanded by the lender, it can also be viewed assupply of funds by the lender and demand for these funds by the borrower.

» If we denote the supply of these loanable funds by Ls andtheir demand by Ld we can re-label our graph, such thatwe have a standard upward sloped supply and downwardsloped demand curve:

Equilibrium in the bonds market – LF chart



Equilibrium in the bonds market LF chart

100 200 300 400 500 600 600

Ls

Loanable fundsin $ bil.

5.26

33.3

81.81

Interest rate in% Ld

17.65 E

Equilibrium in the bonds market – LF analysis



Equilibrium in the bonds market LF analysis

– This diagram is one of the most common

instruments to analyze the causes in the changesof interest rates and is known as loanable fundsframework

– An important feature is that supply and demandfor loanable funds is given in stocks of funds,rather than in flows. This approach is called assetmarket approach.

The Liquidity Preference Framework



The Liquidity Preference Framework

– Other than the loanable funds framework thereexists another instrument to analyze interestrates.

– This instrument has been developed out of the

Keynesian model and is known as the LiquidityPreference Framework

– When Keynes wrote his “General Theory of Employment, Interest and Money” in 1935 hemade the simplifying assumption thatindividuals could hold their wealth only in twoforms of assets

5. The Liquidity Preference Framework



5. The Liquidity Preference Framework

Bonds B and Money (Cash) M.

– Note, that the amount of bonds and moneydemanded in an economy must, thus, equal totalwealth in that economy.

– In equilibrium the quantity of bonds and moneyheld in an economy must, then, equal their supply

d d s s

M B B M d s s d M M B B

Liquidity Preference Framework – Walras’ law



Liquidity Preference Framework Walras law

The second equation above tells us something aboutequilibrium in bonds and money markets:

– If the supply of bonds is equal to the demand forbonds, the right hand side of this equation isequal to zero.

– As a consequence the second market must clear,too, since the left hand side of this equation mustbe zero as well in equilibrium (this is known asWalras’ Law)

The Liquidity Preference Framework Equilibrium



The Liquidity Preference Framework Equilibrium

• Thus, the equilibrium interest rate in the bonds

market is also the one at which the money market isin equilibrium!

• We can, therefore, use demand and supply in the(nominal) money market to analyze changes in theinterest rate.

• This is especially helpful when we try to analyze shiftsin money supply and inflation.

The Liquidity Preference Framework - argument



The Liquidity Preference Framework argument

– The key argument here is that holding money

earns no interest.

– If this is the case, the interest rate on bonds actsas the opportunity cost of holding money, since

every time you hold money, you forego interest.

– Thus, the demand for money will be negativelyrelated to the interest rate on bonds (in this

sense, the interest rate is the “price” of money) asdemonstrated in the following graph.

The Liquidity Preference Framework - chart



q y

i

M

i0

i1

Md0 Md1

The Liquidity Preference Framework - supply



q y pp y

The supply of money is assumed to be exogenous, i.e.not determined within the model.

– In reality the Ms is set by the Federal Reserve,which makes this a somewhat plausibleassumption.

– The important feature of this assumption is that Ms is not a function of the interest rate and can,thus, be displayed as a vertical line in our diagram

The Liquidity Preference Framework - equilibrium



q y q

i

M

i*

Ms

Md

Md = Ms

E

The Liquidity Preference Framework - Ms and Md



q y

– Where Ms and Md intersect the money market is inequilibrium.

– This point E 0 corresponds to a specific equilibriuminterest rate which will also clear the bondsmarket

– We can now use this diagram to analyze interestrate behavior induced by shifts in money demandand money supply

Liquidity Preference Framework: determinants of Md



q y

There are two major determinants of money demand:

1. Households’ income determines demand for money for reasons

of transactions: – As an individual’s income increases (e.g. during a business

cycle expansion), her or his demand for money willincrease, since her or his consumption increases (et v.v.)

2. Changes in the price level (in-/deflation). If prices rise, the realvalue of money declines.

– Thus, in order to keep the real purchasing power of moneyconstant, individuals will want to hold a larger nominalamount of money in order to meet their transactionsdemand. Thus, increases in prices of goods c.p. lead to ahigher nominal demand for money (keeping the real demandMd /P constant)

Liquidity Preference Framework- new equilibrium



q y q

– If money demand increases for one of the two

reasons starting from an original equilibrium E 0 inthe graph below c.p. people will try to sell theirbonds for money.

– However, the total supply of money in the

economy has not increased! How does the marketreturn to its equilibrium?

LP Framework - moves to equilibrium



q

• The attempt of individuals to sell bonds will lower theprices at which these bonds actually sell and increase

their interest rates.

• Since this in turn

– increases the opportunity cost of holding money,

– more individuals will be willing to hold bondsagain,

– such that in the new equilibrium E 1 interest rateshave increased, such that they exactly balance

both markets again.

– The aggregate quantities of money and bonds held have not changed!

The Liquidity Preference Framework – new equilibrium



i

M

i*0

Ms

Md0

Md0 =Md1=Ms

i*1

Md1

E0

E1

LP Framework - supply



– While an increase in the demand for money leads to

an increase in interest rates et vice versa, anincrease in money supply decreases interestrates.

– The argument here (simply speaking) works through

so called open market policies. If a central bankfrom an equilibrium E 0 increases the supply of money it does so by buying bonds. This creates anexcess supply of money at the old equilibriuminterest rate and an excess demand for bonds

LP Framework - new equilibrium



– The central bank decreases the supply of bondsdriving up the prices of these bonds, which in turn

lowers the interest rate.

– Since

»this reduces the opportunity cost of holdingmoney,

»more individuals will be willing to hold moneyagain

– This process is stopped once a new equilibrium E 1

is reached. at which the additional money incirculation is held by households

LP Framework - new equilibrium 2



i

M

i*0

Ms0

Md0

Md = Ms0

i*1

Md1

E0

E1

Ms1

Md = Ms1

LP Framework - critique



• Further, low interest rates are associated with highinvestment levels, which in turn are associated with

higher economic growth and well-being.• In the aftermath of the Keynesian revolution it was

common wisdom for a while to use increases in moneysupply as a policy tool to fight off recessions.

• However, early critique of this approach was broughtforward by Milton Friedman and this year’s Nobelprize winner Edmund Phelps.

Money Supply and its Effect on Interest Rates



– The very short-run effect of an increase in the money supply

is a decrease in the interest rate given money demand is thesame.

» However, as pointed out by Milton Friedman1, theeffectiveness of monetary policy is limited since there

are also secondary effects on money demand.

» Other than the primary decrease in interest rates, whichhe called liquidity effect, there are income, price level and expected inflation effects if the money supply isincreased.

Effects on Interest Rates



• One by one:

» Income effect: Increases in Ms

increase national income and, thus increase Md - leading to an increase in i

» Price level effect: An increase in Ms increases prices atleast in the medium run (see the AS-AD framework),which in turn will lead to increases of Md and i

» Finally, expected increases in Ms may lead to higherexpected inflation, which in turn will lead to a lowerdemand for and higher supply of bonds and, thus, to anincrease in i.

Will a higher rate of growth of Ms lower interest rates?



• Politicians advocate: a greater growth rate of money

supply decreases interest rates

• Generally

– the rising money supply leads to immediate decline

in equilibrium interest rate– the income, price level and expected inflation effect

takes time to work,

• if they are weaker together than liquidity effect,

• the interest rate will climb back, but to a lowerlevel

If Liquidity effect > all other effects



Liquidity effect Income, price l. and

exp. Inflation effect

T

i2

i1

Interest rate i

Time

Liquidity effect Income, price l. and


T

i2

i1

Interest rate i

Time

The two ways of adjustment: slow



• If the liquidity effect is weaker than others

– if the adjustment is slow:

• there is an quick fall in the interest rate (liquidityeffect)

• the income, price level and expected inflationeffects start to work slowly

• they overpower the decline

• the new interest rate is higher than in the previousequilibrium

Liquidity effect < other effects, low adjustment of exp. inflation



Liquidity effect Income and price

level effect

T

i2

i1

Interest rate i

Time

The two ways of adjustment: fast



• If the liquidity effect is weaker than the expectedinflation effect

– the adjustment is fast:

• when people calculate with imminent inflation,

• the expected inflation effect dominates the

system overpowering liquidity effect• the interest rate rises

• income and price level effects start to work later

• they also push interest rates up, but in a slowing

way

Liquidity effect < other effects, fast adj. of exp. inflation



Liquidity

effect

Income, price l. and


T

i2

i1

Interest rate i

Time

Changes in the Ms and its Effect on Interest Rates



• To summarize:

» An increase in the money supply leads to a decrease ini, the so called liquidity effect

» An increase in the money supply leads to shifts in moneydemand through the income, price level and expectedinflation effects all of which increase i.

» Which effect is stronger is an empirical question, but anincrease in the money supply might very well increaseinterest rates! (see the figures below).

Ms and its Effect on Interest Rates: empirical evidence



• Some empirical evidence:

» Milton Friedman and Ann Schwartz in their epochalresearch “A monetary history of the United States” (1963)have argued, that booms are typically preceded byincreases in the money supply, while recessions aretypically preceded by decreases in the money supply.

» From this observation they concluded that money leadsoutput and, hence, that there exists at least some(although limited) room for the Fed to affect growththrough changes in the money supply.

M2 Growth (Annual Rate) and Interest Rates (3 Month T-Bills),1950–2008



Sources: Federal Reserve: www.federalreserve.gov/releases/h6/hist/h6hist1.txt.

04 Understanding Interest Rates

Documents

Transcript of 04 Understanding Interest Rates