EC3115MonetaryEconomics - WordPress.com · 2016. 1. 28. · Lecture 14: The term and risk...

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EC3115 :: L.14 : The term and risk structures of interest rates Almaty, KZ :: 29 January 2016 EC3115 Monetary Economics Lecture 14: The term and risk structures of interest rates Anuar D. Ushbayev International School of Economics Kazakh-British Technical University https://anuarushbayev.wordpress.com/teaching/ec3115-2015/ Tengri Partners | Merchant Banking & Private Equity [email protected] – www.tengripartners.com Almaty, Kazakhstan, 29 January 2016 ISE – KBTU A.D. Ushbayev (2016)

Transcript of EC3115MonetaryEconomics - WordPress.com · 2016. 1. 28. · Lecture 14: The term and risk...

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EC3115 :: L.14 : The term and risk structures of interest rates Almaty, KZ :: 29 January 2016

EC3115 Monetary EconomicsLecture 14: The term and risk structures of interest rates

Anuar D. Ushbayev

International School of EconomicsKazakh-British Technical University

https://anuarushbayev.wordpress.com/teaching/ec3115-2015/

Tengri Partners | Merchant Banking & Private [email protected] – www.tengripartners.com

Almaty, Kazakhstan, 29 January 2016

ISE – KBTU A.D. Ushbayev (2016)

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Relevant reading

Book treatment

F. Mishkin. (2013). The Economics of Money, Banking and Financial Mar-kets, 10th edition, Pearson Education, Chapters 6.

C. Goodhart. (1989). Money, Information and Uncertainty, London:Macmillan, Chapter 11.

Must-read articles

B. Malkiel. (1970). “The Term Structure of Interest Rates: Theory, Empiri-cal Evidence, and Applications”, reprinted in Contemporary Developmentsin Financial Institutions and Markets, T. Havrilesky and R. Schwietzer (eds.),Harlan Davidson, Inc.: Arlington Heights, 1983.

F. Mishkin. (1994). “The yield curve”, in The New Palgrave Dictionary ofMoney and Finance, P. Newman, M. Milgate and J. Eatwell (eds.), London:Macmillan.

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Recommended articles

R. Shiller. (1979). “The Volatility of Long-Term Interest Rates and Expec-tations Models of the Term Structure”, Journal of Political Economy, Vol.87, No. 6, pp. 1190-1219.

R. Shiller. (1990). “The term structure of interest rates”, in Handbookof Monetary Economics, B. Friedman and F. Hahn (eds.), Amsterdam:North-Holland.

S. Russell. (1992). “Understanding the Term Structure of Interest Rates:The Expectations Theory”, Federal Reserve Bank of St. Louis Review, Vol.28, No. 2, pp. 36-50.

B. McCallum. (2005). “Monetary policy and the term structure of inter-est rates”, Economic Quarterly, Federal Reserve Bank of Richmond, Vol.91, No. 4, pp. 1-21.

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Up to now we have only ever considered just one interest rate, that isthe one set by the monetary authorities with a following endogenousdetermination of the money supply1.

In reality, there are a large number of interest rates, from those ongovernment debt to those on subprime mortgages, and from thoseon debts that mature overnight to the interest rates on debt thatmature up to several decades years in the future.

Now we will complete the interest-rate picture by examining therelationship of the various interest rates to one another.

1Alternatively, in the naive theory that assumed money supply as the instrument of policy,this interest rate was allowed to change to clear the money markets.

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Two observations:

1. Interest rates differ among bond categories with the same term tomaturity at a given point in time. The spread (i.e. difference) betweenthese interest rates fluctuates over time.

The relationship among these interest rates is called the risk structure ofinterest rates, although risk, liquidity, and income tax rules all play a rolein determining the risk structure.

2. Interest rates on the same category of bond differ depending the onthe term to maturity.

The relationship among interest rates on bonds with different terms tomaturity is called the term structure of interest rates.

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Section 1

The risk structure of interest rates

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Refers to interest rate differentials for bonds with identical maturities thatare related to:

1. Credit (default) risk.Associated with the assessed ability (or willingness) of issuer of the bondto make interest payments and/or pay off the face value.

2. Liquidity.Associated with the ease and the cost with which an asset can beconverted into cash.

3. Income tax considerations.Associated with the differential tax treatment (e.g municipal bonds) ofthe interest income gains accruing to the bond holder.

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Default risk

Interest rates on corporate bonds are typically higher than ongovernment bonds.

U.S. T-bonds are considered virtually default-free.Unlike a company, the US government can raise taxes.

If taxes are insufficient, the government can print money.

The solvency of private firms is much less certain.

Risk premium.The spread between the interest rates on bonds with default risk and theinterest rates on T-bonds.

Rating agencies.Assign ratings to bonds according to default risks (e.g. Standard andPoor’s, Moody’s, Fitch).

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Initially PC1 = PT

1 and the risk premium is zero.An increase in default risk on corporate bonds shifts the demand curve fromDC

1 to DC2 , which raises the risk premium.

Simultaneously, it shifts the demand curve for Treasury bonds from DT1 to DT

2 .The equilibrium price for corporate bonds falls from PC

1 to PC2 , and the

equilibrium interest rate on in the corporate bond market rises to iC2 .

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In the Treasury market, the equilibrium bond price rises from PT1 to PT

2 , andthe equilibrium interest rate falls to iT

2 .The brace indicates the difference between iC

2 and iT2 , the risk premium on

corporate bonds.(Note that because PC

2 is lower than PT2 , iC

2 is greater than iT2 .)

The risk premium is always positive on bonds that carry non-zero default risk.ISE – KBTU A.D. Ushbayev (2016)

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The risk structure of the yield curve

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Liquidity

A liquid asset is one that can be quickly and cheaply converted intocash if the need arises.

The more liquid an asset is, the more desirable it is, ceteris paribus.Interest rates on corporate AAA bonds are higher than on T-bonds.

Liquidity.How easily and at what cost can I sell the bond for cash if I need to?Depends on development of a secondary market.

Treasury securities are traded in highly active secondary markets.Secondary markets for corporate bonds are less active.

Illiquidity.If the corporate bond becomes less liquid because it is less widelytraded, then (as the theory of portfolio choice indicates) demand for itwill fall, shifting its demand curve downward.Contributes to a higher risk premium.This is why a risk premium is more accurately a “risk and liquiditypremium”.

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Income tax considerations

Municipal bonds are not default free and less liquid, but still pay lower interestrates than US Treasury Bonds.Because (e.g. in the US) it is a tax-exempt security, you pay no taxes on thecoupon income, so you earn more after taxes.

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Clearly, as you earn more on the municipal bond after taxes, you are willing tohold the riskier and less liquid municipal bond even though it has a lowerinterest rate than the U.S. Treasury bond.Gives rise to municipal bond arbitrage strategies.

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Section 2

The term structure of interest rates

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The US yield curve (as of 27.01.2016)

Bonds with identical risk, liquidity, and tax characteristics may havedifferent interest rates because the time remaining to maturity isdifferent.

Yield curve – a plot of the yield on bonds with differing terms tomaturity but the same risk, liquidity and tax treatment.

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Why is the yield curve of importance to policy-makers?

Central Banks, when setting interest rates, usually only set oneinterest rate, and typically at the very short end of the spectrum2. (Inthe US, the Federal Reserve sets overnight rates).

However, investment decisions and aggregate demand in theeconomy will tend to depend on long-term interest rates since firmswill compare the rate of return on investment projects that accrueover the entire life of the project, to the alternative of buyingequivalent dated bonds maturing in a similar timeframe.

If aggregate demand depends on long-term interest rates and themonetary authorities set short-term rates but wish to affect aggregatedemand, they will need to know the relationship between short-termand long-term rates of return (i.e. they need to know the shape of theyield curve).

2Although there is nothing to prevent them from intervening in longer dated segment ofthe market in the same way as they do in the overnight rate segment. More on this later.

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Temporal movements of rates on US T-Bonds with different maturities

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Section 3

Theories of the yield curve

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Empirical facts to be explained

There are three features of the term structure that any theory of the yieldcurve should be able to explain:

1. Interest rates on bonds of different maturities move together overtime.

2. When short-term interest rates are low, yield curves are more likely tohave an upward slope. When short-term rates are high, yield curvesare more likely to slope downward and be inverted.

3. Yield curves almost always slope upward.Upward-sloping – long-term rates are above short-term rates.

Flat – short- and long-term rates are the same.

Inverted – long-term rates are below short-term rates.

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Theories of the yield curve

Three theories have been put forward to explain the term structure ofinterest rates – that is, the relationship among interest rates on bonds ofdifferent maturities reflected in yield curve patterns:

1. The expectations theory.Does a good job of explaining the first two facts on our list, but not thethird.

2. The market segmentation theory.Can account for fact 3 but not the other two facts, which are wellexplained by the expectations theory.

3. The liquidity premium theory.Combines features of the two theories above, and can cover all threefacts.

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Bond prices and the rate of return

There are, in general, two types of bonds a government can issue:

Coupon bonds – promise to pay a fixed sum of money, the coupon,every period, whether it is every month, quarter or year, and alsopromise to pay the holder of the bond its face value on maturity.

For example, a ten-year bond may be bought from the government for$100 that promises to pay $5 (the coupon payment) every year for thenext ten years. In the final year, both the last $5 coupon and thematurity value of the bond, $100, are paid.

Discount bonds – do not offer any interest or coupon payments.Instead, they are sold at a ‘discount’ and pay a larger amount onmaturity.

For example, a ten-year discount bond may be sold today for $60 thatpays no coupons at all but pays $100 on maturity, ten years from now.

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A perpetual annuity is an instrument pays a fixed amount of moneyeach year forever. In financial markets it is not always possible topurchase a perpetual annuity3.

Suppose that a coupon amount C is paid at the end of each periodfrom now to perpetuity, and that the per-period interest rate is R4.

The present value of this perpetual annuity is then:

A =C

1+ R+

C

(1+ R)2+

C

(1+ R)3+ · · ·

=∞∑

k=1

C

(1+ R)k=

C

R

3In the UK such a products used to be common, and are called consoles (consolidatedannuities). Consoles still exist today, but form only a small part of the UK government’s debtportfolio.

4For simplicity assumed constant for now.ISE – KBTU A.D. Ushbayev (2016)

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Discount bonds have a maturity date, say N , and thus repay principal,P , but don’t pay coupons, so their price is given by:

D =P

(1+ R)N

For bonds that pay coupons and have a maturity date, the aboveformula changes to:

B =C

1+ R+

C

(1+ R)2+

C

(1+ R)3+ · · ·+

C

(1+ R)N+

P

(1+ R)N

=N∑

k=1

C

(1+ R)k︸ ︷︷ ︸

PV of coupon payments

+P

(1+ R)N︸ ︷︷ ︸

PV of par redemption

There is then a negative relationship between the price of a bond andthe interest rate (cf. Keynes money demand theory)

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Intuitively, if the interest rate increased, people would be willing to payless for a bond that pays a fixed coupon payment each period.

If a perpetuity bond that paid a coupon of $5 had a price of $100, thisimplies the market interest rate is 5%.

If the market interest rate doubled to 10%, no investor would bewilling to pay more than $50 for the same bond since the $5 couponon a $50 bond is 10%.

Hence the bond price and interest rate are negatively related.

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The expectations hypothesis

Links the rate of return on short-term bonds to that on long-termbonds, essentially by assuming that short and long-dated bonds areperfect substitutes.

Says that the interest rate on a long-term bond will equal an averageof the short-term interest rates that people expect to occur over thelife of the long-term bond.

Buyers of bonds do not prefer bonds of one maturity over another;they will not hold any quantity of a bond if its expected return is lessthan that of another bond with a different maturity.

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Consider someone who wishes to save a fixed amount of money for nperiods.

They could either buy long-dated bonds now, at date t , that pay tRt+nper cent per year.

(The left-hand subscript denotes the time when the bond is bought andthe right-hand subscript denotes when the bond will mature.)

Alternatively, they could buy a bond that matures at date t + 1 (aone-period bond) paying a rate of return t rt+1.

When this matures she will buy another one-period bond (at datet + 1 that matures at date t + 2) paying a rate of return t+1rt+2 andwill continue doing this until date t + n.

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If the return from a portfolio made up of long-dated bonds is notidentically equal to the expected return from continually rolling overone-period debt, then arbitrage opportunities will be exploited tobring the two returns together.

Suppose for example that a two-year bond paid a rate of return of 4%per year. If the rate of return on a one-year bond was 3% today andexpected to remain at 3% next year, investors will rush in to buy thelonger-dated bond as it pays a higher rate of return.

The increased demand for the two period bonds will push the price upand, as explained above, will push the rate of return down from 4%.

Also, the reduction in demand for one-period bonds will push theprice down, causing the one-period rate of return to increase from 3%.

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In equilibrium, under the expectations hypothesis, the total returnfrom each portfolio must be equal to avoid arbitrage opportunities.

Using the same notation as above, but noting that at date t when thesaving decision is made, all future one-period rates are not known andhave to be estimated, then the discount bond reads:�

1+ tRt+n

�n=�

1+ t rt+1

� �

1+ t+1r et+2

� �

1+ t+2r et+3

···�

1+ t+n−1r et+n

The left-hand side is the total return from holding n period bondsuntil they mature.

The right-hand side is the total expected return from holding andcontinually rolling over one period bonds, n times.

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The rates of return on all bonds bought at date t + 1 onwards are notknown at date t , hence the e (expectation) superscript.

Taking logs of the above, noting that ln (1+ X )≈ X for small X , gives:

n · tRt+n = t rt+1 + t+1r et+2 + t+2r e

t+3 + · · ·+ t+n−1r et+n

=⇒ tRt+n =1

n

t+n−1∑

s=tsr

es+1

This is one of the main results of the expectations hypothesis: thelong-term interest rate is an average of the current and all futureexpected short-term interest rates.

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Critiques of the expectations hypothesis

It cannot explain the empirical fact that the yield curve has apersistent upward slope. If the long rate is an average of current andexpected future short rates, this can only be explained if the short rateincreases through time. This clearly is not the case.

If the long rate is an average of current and future short rates, the longrate must be a smoother series (when plotted through time) than theshort rate. This is not true; the long rate is just as volatile.

In order to avoid arbitrage opportunities and keep total returns equal,if the rate of return on long-term bonds is greater than the return onshort bonds, then holding long-dated bonds must be accompanied bya capital loss (i.e. the price of long-term bonds must fall).

If the price of long-term bonds falls, the rate of return must increasestill further in the next period. Putting this another way: if the long rateis higher than the short rate, the long rate must increase. This does nothappen in reality.

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The expectations hypothesis and expected inflation

If the long rate is an average of the current and expected future shortrates, then an upward-sloping yield curve suggests that the short rateis expected to increase in the future.

If the real interest rate is constant then the increase in expected futurenominal interest rates must be associated with an increase inexpected future inflation, as per the Fisher equation.

The greater the slope of the yield curve, the more short-term rates areexpected to rise and so the faster is inflation expected to increase.

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The segmentation hypothesis

Whereas the expectations hypothesis assumes short- and long-termbonds are perfect substitutes so the decision as to whether to holdlong- or short-dated debt depends entirely on expected returns, thesegmentation hypothesis assumes short- and long-term bonds arenot substitutes at all.

The interest rate for each bond with a different maturity is determinedby the demand for and supply of that bond.

Investors have preferences for bonds of one maturity over another.

If investors have short desired holding periods and generally preferbonds with shorter maturities that have less interest-rate risk, thenthis explains why yield curves usually slope upward.

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The rate of return on m period bonds will not depend on the marketfor, or the return on, m− j period bonds at all. Instead, its rate ofreturn will depend entirely on the demand for and supply of creditthat matures in m periods’ time.

If the demand for m period bonds increased, caused by more peoplewanting to save for m periods, then the price of m period bonds willincrease and the rate of return will fall. The markets for m, m+ 1,m+ 2, etc. period debt are said to be segmented.

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Whereas the expectations hypothesis could not explain the persistentupward sloping nature of the yield curve, this feature can be easilyexplained if we use the segmentation hypothesis.

If people generally prefer to hold short-dated debt (i.e. save by buyingshort-term bonds), then this will cause the price of short-term bondsto be high, relative to long-term bonds, and so the rate of return onshort-term debt will then be lower than the long-term rate, implyingan upward-sloping yield curve.

Despite being able to explain persistent upward-sloping yield curves,the segmentation hypothesis cannot explain the fact that interestrates move together since the markets are completely segmented.

Also, the theory cannot explain why yield curves are upward(downward)-sloping when short rates are low (high).

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Liquidity premium theory

States that the interest rate on a long-term bond will equal an averageof short-term interest rates expected to occur over the life of thelong-term bond plus a liquidity premium (also referred to as a termpremium) that responds to supply and demand conditions for thatbond.

In other words, bonds of different maturities are assumed to besubstitutes but not perfect substitutes.

For these reasons, investors must be offered a positive liquiditypremium to induce them to hold longer-term bonds.

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Preferred habitat theory

Closely related to the liquidity premium theory is the preferred habitattheory, which takes a somewhat less direct approach to modifying theexpectations hypothesis but comes to a similar conclusion.

It assumes that investors have a preference for bonds of one maturityover another, a particular bond maturity (preferred habitat) in whichthey prefer to invest.

Because they prefer bonds of one maturity over another, they will bewilling to buy bonds that do not have the preferred maturity (habitat)only if they earn a somewhat higher expected return.

Because investors are likely to prefer the habitat of short-term bondsover that of longer-term bonds, they are willing to hold long-termbonds only if they have higher expected returns.

This reasoning leads to the same equation as implied by the liquiditypremium theory, with a term premium that typically rises withmaturity.

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Thus people have a preferred bond maturity they wish to hold (as inthe segmentation hypothesis) but will be willing to move to anotherbond maturity if the gains from doing so are significant (so exploitingexcess arbitrage opportunities as in the expectations hypothesis).

Such an outcome would modify the expectations theory by adding apositive liquidity premium to the equation that describes therelationship between long- and short-term interest rates. The liquiditypremium theory is thus written as:

tRt+n =1

n

t+n−1∑

s=tsr

es+1 + t kn

This is exactly the same as the expectations hypothesis, except for theinclusion of a liquidity premium (or term premium), t kn.

If n period bonds were not the bond of choice, then people wouldneed an extra rate of return in order to encourage them to hold suchdebt. In this case t kn would be positive.

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If people generally tend to prefer short-dated debt then the termpremium will be a monotonic function of maturity; in order to holdlonger and longer dated debt, an increasing term premium must beoffered.

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When combined with the expectations hypothesis component, theabove can explain the persistent upward slope of the yield curve,along with the other empirical regularities: the co-movement of shortand long rates, and the fact the yield curve tends to be upward(downward)-sloping when short rates are low (high).

How can the liquidity premium and preferred habitat theories explainthe occasional appearance of inverted yield curves if the liquiditypremium is positive?

It must be that at times short-term interest rates are expected to fall somuch in the future that the average of the expected short-term rates iswell below the current short-term rate. Even when the positive liquiditypremium is added to this average, the resulting long-term rate will stillbe lower than the current short-term interest rate.

Rather than assuming the existence of the term premium ad hoc forthe purposes of fitting the data, it is arguably better to provide atheory of the term premium.

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Evidence on the term structure

In the 1980s, researchers examining the term structure of interestrates questioned whether the slope of the yield curve providesinformation about movements of future short-term interest rates.

They found that the spread between long- and short-term interestrates does not always help predict future short-term interest rates, afinding that may stem from substantial fluctuations in the liquidity(term) premium for long-term bonds.

More recent research using more discriminating tests now favors adifferent view.

It shows that the term structure contains quite a bit of information forthe very short run (over the next several months) and the long run (overseveral years) but is unreliable at predicting movements in interest ratesover the intermediate term (the time in between).

Research also finds that the yield curve helps forecast future inflationand business cycles.

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Interpreting yield curves

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Above can be seen several yield curves that have appeared for U.S.government bonds in recent years.

What do these yield curves tell us about the public’s expectations offuture movements of short-term interest rates?

January 15, 1981.The steep inverted yield curve, indicated that short-term interest rateswere expected to decline sharply in the future.

For longer-term interest rates with their positive liquidity premium to bewell below the short-term interest rate, short-term interest rates mustbe expected to decline so sharply that their average is far below thecurrent short-term rate.

Indeed, the public’s expectations of sharply lower short-term interestrates evident in the yield curve were realized soon after January 15; byMarch, three-month Treasury bill rates had declined from the 16% levelto 13%.

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March 28, 1985, and July 11, 2011.The steep upward-sloping yield curves, indicated that short-terminterest rates would climb in the future.

The long-term interest rate is higher than the short-term interest ratewhen short-term interest rates are expected to rise because theiraverage plus the liquidity premium will be higher than the currentshort-term rate.

May 16, 1980, and March 3, 1997.The moderately upward-sloping yield curves, indicated that short-terminterest rates were expected neither to rise nor to fall in the near future.

In this case, their average remains the same as the current short-termrate, and the positive liquidity premium for longer-term bonds explainsthe moderate upward slope of the yield curve.

February 6, 2006.The flat yield curve, indicated that short-term interest rates wereexpected to fall slightly.

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Yield curve targeting

Usually the central bank influences the yield curve of governmentsecurities by directly setting the interest rate on the short end of thecurve and influencing expectations about future short-term rates byother means.

It should be noted, however – although this is not widelyacknowledged or discussed in the mainstream literature – that thecentral bank could say that it will stand ready to buy or sell whateveramount of debt of particular maturity is necessary to maintain itstarget for the interest rate on that maturity, just as it currently doeswith the short-term interest rate target.

This means that the central bank could – if it wanted to, e.g. to avoidthe uncertainty and volatility of longer-term rates associated with themarket’s changing expectations of the central bank’s future short-termpolicy – target the entire yield curve of risk-free rates at target levels,along with supporting open ended borrowing and lending facilities.

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Yield curve targeting in the U.S. during World War II illustrated

(1943–1946) – Discount window rate was set at 0.5 %.(1942–1947) – 3-month T-bills rate was set at 0.375 %.(1937–1946) – 3-month bankers’ acceptance rate (FFR equivalent then) was set at 0.4375 %.(1942–1945) – 10-year T-bond rate was set almost perfectly at 2.5 %.

(Graph taken from E. Tymoigne, (2014), "Modern Money Theory, and Interrelations Between the Treasuryand Central Bank: The Case of the United States", Journal of Economic Issues, Vol. 48, No. 3, pp. 641-662)

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“If Congress appropriates more money than Congress levies taxes to pay, then, there isnaturally a deficit, and the Treasury is obligated to borrow. The fact that they cannotgo directly to the Federal Reserve bank to borrow does not mean that they cannot goindirectly to the Federal Reserve bank, for the very reason that there is no limit to theamount that the Federal Reserve System can buy in the market. That is the way the warwas financed.

Therefore, if the Treasury has to finance a heavy deficit, the Reserve System creates thecondition in the money market to enable the borrowing to be done, so that, in effect,the Reserve System indirectly finances the Treasury through the money market, and thatis how the interest rates were stabilized as they were during the war, and as they willhave to continue to be in the future.

So it is an illusion to think that to eliminate or to restrict the direct borrowing privilegereduces the amount of deficit financing. Or that the market controls the interest rate.Neither is true.”

– Marriner Stoddard Eccles1, (1947), in “Direct purchases of government securities byfederal reserve banks”, Hearing before the Committee on Banking and Currency, House ofRepresentatives, Eightieth Congress, First session, on H.R. 2233, superceded by H.R. 2413, anact to amend the Federal Reserve act, and for other purposes. March 3, 4, and 5, 1947, UnitedStates Government Printing Office, Washington.

1Chairman of the Federal Reserve (1934-1948).

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Monetary Policy Implications

Because of globalization of capital flows, a country’s interest rates (inparticular, the medium- to long-term maturities) will be determinedmore by global influences and less by domestic factors.

Central banks’ ability to affect long-term rates may thus bediminishing.

Therefore, globalization calls for greater cooperation and coordinationof policy worldwide.

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“These financial stability responsibilities do not stop at our borders, given thesize and openness of our capital markets and the unique position of the U.S.dollar as the world’s leading currency for financial transactions. . . But I shouldcaution that the responsibility of the Fed is not unbounded. My teacher CharlesKindleberger argued that stability of the international financial system couldbest be supported by the leadership of a financial hegemon or a global centralbank. But I should be clear that the U.S. Federal Reserve System is not thatbank. Our mandate, like that of virtually all central banks, focuses on domesticobjectives.”

– Stanley Fischer1, (2014), The Federal Reserve and the Global Economy, Speechat the Per Jacobsson Foundation Lecture, 2014 Annual Meetings of the Interna-tional Monetary Fund and the World Bank Group, Washington, D.C.

1Vice-chairman of the U.S. Federal Reserve System (2014-present), Governor of the Bank ofIsrael (2005-2013), Vice-chairman of Citigroup (2002-2005), First Deputy ManagingDirector of the International Monetary Fund (1994-2001), Vice President and Chief Economistof the World Bank (1988-1990).

Students of Fischer: Ben Bernanke, Mario Draghi, Olivier Blanchard, Lawrence Summers,Gregory Mankiw, Frederick Mishkin, Maurice Obstfeld, Kenneth Rogoff, Jeffrey Frankel, DavidRomer, and others.

ISE – KBTU A.D. Ushbayev (2016)