Download two-year interest rate

Lecture 6
• Key issues:
• Understanding bond prices and bond yields
• Being able to interpret the market
expectations expressed in the yield curve
• The effect of stock market movements
Structure of lecture
1.
2.
3.
4.
5.
6.
The vocabulary of the bond market
Bond Prices and Bond Yields
Yield Curve and economic activity
Stock Market movements
The Stock market and economic activity
Bubbles, Fads and Stock Prices
1. Vocabulary of bond markets
 Government bonds are bonds issued by government
agencies to raise finance/borrow.
• Corporate bonds are bonds issued by firms to raise
finance/borrow (e.g. Eskom).
 Bond ratings are issued by Standard and Poor’s Corporation
and Moody’s Investors Service. (Highly criticised for giving
AAA ratings to what turned out to be toxic sub-prime
assets)
• The risk premium is the difference between the interest
rate paid on a given bond and the interest rate paid on the
bond with the highest rating (ie. with high spreads from the
bonds with the lowest interest rates).
• Bonds with high default risk are often called junk bonds.
(High yielding bonds as high risk is associated with high
reward)
Vocabulary of bond markets
 Bonds that promise a single payment at maturity are called discount
bonds. The single payment is called the face value of the bond.
 Bonds that promise multiple payments before maturity and one payment
at maturity are called coupon bonds. The payments before maturity are
called coupon payments.


The ratio of the coupon payments to the face value of the bond is called the
coupon rate.
The current yield is the ratio of the coupon payment to the price of the bond.
 The life of a bond is the amount of time left until the bond matures. U.S.
government bonds classified by maturity:
• Treasury bills, or T-bills: Up to one year. (SA – 91-day Treasury Bill)
• Treasury notes: One to ten years. (e.g. SA - R189 and R153 bonds
(maturing 2013))
• Treasury bonds: Ten years or more. (e.g. SA - R197 and R186 bonds
(maturing 2023)).
 Bonds typically promise to pay a sequence of fixed nominal payments
(R100). However, other types of bonds, called indexed bonds, promise
payments adjusted for inflation (R100x(1+π) rather than fixed nominal
payments. (SA – inflation-linked bonds)
2.Bond Prices and Bond Yields
• Bonds differ in two basic dimensions:
– Default risk, the risk that the issuer of the bond (e.g. government or
company) will not pay back the full amount promised by the bond.
– Maturity, the length of time over which the bond promises to make
payments to the holder of the bond.
• Bonds of different maturities each have a price and an associated interest
rate called the yield to maturity, or simply the yield.
•
•
Yields on bonds with a maturity of a year or less are called short-term interest rates
Yields on bonds with a longer maturity are called long-term interest rates
Yield Curve
• The relation between maturity and yield is called
the yield curve, or the term structure of interest
rates.
• On any given date the yields on bonds of different
maturities are traced or plotted along the yield
curve. See Fig 15.1 for US Nov 2000 vs June 2001
• A normal yield curve is upward sloping as longterm interest rates > short-term interest rates
• An inverted yield curve is downward sloping as
long-term interest rates < short-term interest
rates
The yield curve, which was slightly downward sloping in November 2000,
was sharply upward sloping seven months later
Bond Prices as Present Values
• Consider two types of bonds:
– A one-year bond—a bond that promises one payment of $100 in one
year. Price of the one-year bond (where i1t indicates the one year
interest rate):
$100
$ P1t 
1  i1t
– The price of the one-year bond varies inversely with the current one
year nominal interest rate
– A two-year bond—a bond that promises one payment of $100 in two
years. Price of the two-year bond:
$100
$ P2 t 
(1  i1t )(1  i e 1t 1 )
– The price of the two-year bond varies inversely both with the current
one year nominal interest rate and with the one-year nominal rate
expected for next year
Arbitrage and Bond Prices
• Arbitrage is defined as the proposition that
expected returns on two assets must be equal
(this equal expected return is due to market
participants bidding up and down asset prices as
they aim to make riskless profit out of
price/valuation differences)
• Question regarding bonds: If you have a choice
between one-year bonds or two year bonds and
what you care about is how much you will have
one year from today, which bonds should you
hold?
One-year bonds vs two-year bonds (for one year)
• One-year bonds ($1):
– For every dollar you put in one-year bonds, you will get (1+ i1t) dollars
next year = ($1 x (1+ i1t)) (See Fig 15.2)
• Two-year bonds:
– The price of two-year bonds is $p2t, Therefore each $ you put into twoyear bonds buys you $1/$P2t bonds today
– When next year comes the bond bond will have one more year until
maturity and will in effect be a one-year bond, with an expected price
of a one-year bond at that time i.e. $Pe1t+1
– Therefore, when next year comes the 1$ that you have put into twoyear bonds is equal to the quantity of two-year bonds that you bought
($1/$P2t) times the price at which you can sell one-year bonds ($Pe1t+1 )
– You can expect to receive $1/$P2t times $Pe1t+1 dollars next year, which
equals $Pe1t+1 /$P2t = ($1 x $Pe1t+1 /$P2t ) (See Fig 15.2)
Figure 15.2 Returns from Holding One-Year and
Two-Year Bonds for One Year
Arbitrage and Bond Prices
• Based on arbitrage forces it can be assumed that the
expected returns are equal for holding a one year bond or
for holding a two-year bond for one year i.e.
$ P e 1t 1
1  i1t 
$ P2 t
• If this were not the case and for e.g. the expected returns
were higher for holding a two-year bond for one year, then
there would be no demand for holding one-year bonds
• This is also based on the expectations hypothesis – that
investors are only about expected returns (abstracting away
from questions for the relative riskiness of the two bonds –
of which the two-year bond would be more risky as the price
at which it will be sold after one year is uncertain)
Arbitrage and Bond Prices
• If two bonds offer the same expected one-year return, then: 1  i1t
which is equal to:

$ P e 1t 1
$ P2 t
$ P e 1t 1
$ P2 t 
1  i1t
• i.e. arbitrage implies that the price of a two-year bond today is the present
value of the expected price of the bond next year.
• Question: What does the expected price of a one-year bond next year depend
on i.e. what does $Pe1t+1 depend on?
• The price of a one-year bond paying $100 next year will depend on the one-year
$100
interest rate next year i.e.
e
$P
• This gives:
1t  1

(1  i e 1t 1 )
$100
$ P2 t 
(1  i1t )(1  i e 1t 1 )
• Which tells us that the arbitrage between one- and two-year bonds implies that
the price of two year bonds is the present value of the payment in two years
(namely $100) discounted using the current and next year’s expected one year
interest rates
From Bond Prices to Bond Yields
Bond yields contain the same information about future expected interest rates
as bond prices – but they do so in a clearer way.
Definition: The yield to maturity on an n-year bond, or the n-year interest rate,
is the constant annual interest rate that makes the bond price today equal to the
present value of future payments of the bond.
For example: the yield two maturity, or two-year interest rate, based on the
previous example, would make the present value of $100 in two years equal to
the price of the bond today i.e.:
$100
$ P2 t 
(1  i2 t ) 2
If the bond sells for $90 today (i.e. $P2t = $90) then the two-year interest rate
(i2t) , (yield to maturity) equals:
$90 = $100/(1+i2t)2
(1+i2t)2 = $100/$90
(1+i2t) = ($100/$90)1/2
i2t = 5,4%
From Bond Prices to Bond Yields
• Question: what is the relation of the two-year interest rate (yield to
maturity) to the current one-year interest rate and the expected
one-year interest rate?
$100
$100
2 
• Eliminating $P2t gives:
(1  i )
(1  i )(1  i e 1t 1 )
2t
1t
1  i2t 2  1  i1t 1  i1et 1 
• Which is equal to:
• This relates the two year interest rate (yield to maturity) (i2t), the
current one-year interest rate (i1t) and next year’s expected oneyear interest rate (ie1t+1), which can be approximated as:
i2 t
1
 (i1t  i1et 1 )
2
• i.e. the two year interest rate is (approx.) the average of the current one-year
interest rate and next year’s expected one-year interest rate
• More generally, the yield on a 10 year bond is (approx.) equal to the average of
the current one-year interest rate and the one-year interest rates expected for
the next nine years
3. Yield Curve and economic activity
•Interpreting the Yield Curve
• By looking at yields for bonds of different maturities we can infer what
financial markets expect short-term interest rates will be in the future
– An upward sloping yield curve means that long-term interest rates are higher than shortterm interest rates. Financial markets expect short-term rates to be higher in the future.
– A downward sloping yield curve means that long-term interest rates are lower than shortterm interest rates. Financial markets expect short-term rates to be lower in the future.
• Using the following equation, you can find out what financial markets expect
the 1-year interest rate to be 1 year from now: e
i1t 1  2i2t  i1t
• the one-year interest rate expected for next year is equal to twice the yield
on a two-year bond minus the current one-year interest rate
•e.g. Fig 15.1 on June 1 2001 the one-year interest rate it+1 was 3,4% and the
two-year interest rate i2t was 4,1%, therefore the financial markets expected
the one-year interest rate one year later (on June 1 2002) to equal: 2x4.1% 3.4% = 4.8% i.e. 1.4% higher than the one-year interest rate on June 1 2001
(i.e. yield curve is upward sloping)
The Yield Curve and Economic Activity
• Question how did the US Yield Curve in Fig
15.1 go from being downward sloping in
November 2000 to being upward sloping in
June 2001
• Answer: Because the slowdown in the first
half of 2001 led to a sharp decline in shortterm interest rates combined with an
expectation in financial markets that output
would recover and that expected short-term
interest rates returning to higher levels in
future
IS-LM analysis
• In November 2000 (Fig. 15.3) economic growth was being forecast to slow
down i.e. a soft landing back to the natural rate of unemployment, with a
small decrease in the interest rate (as per the slightly downward sloping
Yield Curve in Fig. 15.1)
• From November 2000 to June 2001 (Fig.15.4) the economy deteriorated
more sharply than predicted (IS curve) so the Fed initiated a monetary
policy expansion (LM curve). As result in June 2001 output was higher and
interest rates lower at A’ that economy would have been at B with no
monetary expansion
• In June 2001 (Fig15.5) markets expected investment spending to pick up
(IS curve) and markets expected tighter monetary policy in future (LM
Curve), move from A to A’, therefore upward sloping Yield Curve in June
2001 as in Fig. 15.1
– The anticipation of higher short-term interest rates in future was the reason long-term
interest rates remained high
– The flat portion of the yield curve in June 2001 for maturities of up to one year
indicated that markets did not expect interest rates to start rising until June 2002. In
fact interest rates did not rise until June 2004 (two years later)
The Yield Curve and Economic Activity
Figure 15 - 3
The U.S. Economy as of
November 2000
In November 2000, the U.S.
economy was operating above
the natural level of output.
Forecasts were for a “soft
landing,” a return of output to
the natural level of output, and
a small decrease in interest
rates.
The Yield Curve and Economic Activity
Figure 15 - 4
The U.S. Economy from
November 2000 to
June 2001
From November 2000 to June
2001, an adverse shift in
spending, together with a
monetary expansion, combined
to lead to a decrease in the
short-term interest rate.
The Yield Curve and Economic Activity
From this figure, you can see the
two major developments:
– The adverse shift in spending
was stronger than had been
expected. Instead of shifting
from IS to IS’ as forecast, the
IS curve shifted by much
more, to IS’’.
– Realizing that the slowdown
was stronger than it had
anticipated, the Fed shifted in
early 2001 to a policy of
monetary expansion, leading
to a downward shift in the LM
curve.
The Yield Curve and Economic Activity
Figure 15 - 5
The Expected Path of the
U.S. Economy as of June
2001
In June 2001, financial markets
expected stronger spending
and tighter monetary policy to
lead to higher short-term
interest rates in the future.
The Yield Curve and Economic Activity
•Financial markets
expected two main
developments:
– They expected a pickup
in spending-a shift of
the IS curve to the
right, from IS to IS’.
– They also expected
that, once the IS curve
started shifting to the
right and output
started to recover, the
Fed would start shifting
back to a tighter
monetary policy.
4. Stock Market movements
• Firms raise funds in two ways:
– Through debt finance —bonds and loans; and
– Through equity finance, through issues of stocks
or shares. Instead of paying predetermined
amounts as bonds do, stocks pay dividends in an
amount decided by the firm (typically dividends
move in the same direction as profits, but some
profit is retained to finance future investment).
Stock prices are volatile (See Fig.15.6)
The Stock Market and Movements in Stock Prices
Figure 15 - 6
Standard & Poor’s
Composite Index, in Real
Terms, since 1980
Note the sharp increase in
stock prices in the 1990s,
followed by the sharp
decrease in the early
2000s.
Stock Prices as Present Values
• What determines the price of a stock?
The price of a stock must equal the present value of future expected dividends.
Where
$Qt = the price of a stock (after the dividend has been paid this year i.e. ex dividend)
$Dt = the expected dividend this year
$Det+1 = the expected dividend next year
$Det+2 = the expected dividend two years from now, etc.
$ Dte1
$ Dte 2
$Qt 

 ...
e
1  i1t 1  i1t 1  i1t 1 
The (nominal) price of a stock is equal to the present value of the dividend next year,
discounted using the current one-year interest rate plus the present value of the dividend two
years from now, discounted using both this year’s one-year interest rate and next year’s
expected one-year interest rate, etc.
Stock Prices as Present Values (Real)
• The real stock price is given as the present
value of real dividends, discounted by a
sequence of one-year real interest rates i.e.
Dte1
Dte2
Qt 

 ...
e
1 r1t  1 r1t 1 r1t 1e 
• Implications:
– Higher expected future real dividends lead to
higher real stock prices
– Higher current and expected future one-year real
interest rates lead to lower real stock prices
5. The Stock Market and Economic Activity
• Stock prices follow a random walk if each step they take is as
likely to be up as it is to be down. (Qt = Qt-1 + μ where μ is a
random error term) Stock movements are therefore
unpredictable.
• Note: if there is wide belief that stocks will be priced 20% higher
in a year’s time (a much better return than the alternative bonds)
then stock prices will be bid up today to equalise returns between
stocks and bonds.
• Even though major movements in stock prices cannot be
predicted, we can still do two things:
– We can look back and identify the news to which the market
reacted.
– We can ask “what if” questions e.g. (1) what if the monetary
authorities embark on expansionary policies (e.g. R cut) or (2)
what if there is a boom in consumer spending
A Monetary Expansion and the Stock Market
• If the monetary authority adopts on expansionary policy then the
LM shifts and interest rates decrease and output increases
(Fig.15.7) in the short-run (prices sticky)
• But, what happens to the stock market?
• Answer: It depends on what participants in the stock market
expect of monetary policy before the expansion takes place.
– If fully anticipated then the stock prices will not reacted (
expected future dividends and future interest rates are
“already factored in” and the is no change to $Qt)
– if the move is (partly) unexpected then stock prices will rise
because:
• (1) there will be lower interest rates for some time and this increases
the present value of $Qt
• (2)the monetary expansion implies higher output and higher dividends
A Monetary Expansion and the Stock Market
Figure 15 - 7
An Expansionary Monetary
Policy and the Stock Market
A monetary expansion
decreases the interest rate
and increases output. What
it does to the stock market
depends on whether
financial markets anticipated
the monetary expansion.
Unexpected increase in consumer spending (IS curve)
• Due to an unexpected increase in consumer spending the IS curve
shifts up leading to increased output and increased interest rates (Fig
15.8a)
• For stock prices this unleashes two contradictory effects
– Firstly, higher output is associated with higher dividends and
increased stock prices
– Secondly, a higher interest rate results in lower stock prices
(reduced present value)
• Which of the two effects dominates?
– This depends on the slope of the LM curve (See Fig.15.8(b) )
– a flat LM curve leads to a small increase in r and a large increase in y
 stock prices rise
– A steep LM curve leads to a large increase in r and a small increase
in y  stock prices fall
– A steep LM curve indicates a high degree of output inelasticity to
changes in interest rates
An increase in consumption spending and the
Stock Market
Figure 15 – 8a
An Increase in Consumption
Spending and the Stock
Market
The increase in
consumption spending
leads to a higher interest
rate and a higher level of
output. What happens to the
stock market depends on
the slope of the LM curve
and on the Fed’s behavior.
An increase in consumption spending and the
Stock Market
Figure 15 – 8b
An Increase in Consumption
Spending and the Stock
Market
If the LM curve is steep, the
interest rate increases a lot,
and output increases little.
Stock prices go down. If the
LM curve is flat, the interest
rate increases little, and
output increases a lot. Stock
prices go up.
An increase in consumption spending and the
Stock Market
• A key question is how will the monetary authorities react to
an increase in consumption spending?
• See Fig.15.8c Accommodation versus tightening
• Accommodation (increase money supply in line with
increased money demand) leads to a downward shift in the
LM curve – stock prices will rise as output is up and interest
rates do not rise
• Tightening – as the monetary authority fears inflation due to
increased consumption they contract money supply (shifting
up LM curve) – stock prices will fall as there is no change in
output (expected profits and dividends) and the interest rate
is likely to be higher for some time
• No change to monetary stance – effect on stock prices is
ambiguous
An Increase in Consumption Spending and the Stock Market
Figure 15 – 8c
An Increase in Consumption
Spending and the Stock
Market
If the Fed accommodates,
the interest rate does not
increase, but output does.
Stock prices go up. If the
Fed decides instead to keep
output constant, the interest
rate increases, but output
does not. Stock prices go
down.
Summary on stock prices
• How stock prices respond to a change in output
depends on a range of factors (See US example from
recent history):
1. What the market expected in the first place – (e.g. is
it factored in)
2. The source of the shocks behind the change in
output (e.g. monetary expansion vs consumption
boom)
3. How the markets expect the monetary authorities to
react to the output change (accommodation vs
tightening)
Making (Some) Sense of (Apparent) Nonsense: Why the Stock Market
Moved Yesterday and Other Stories
Here are some quotes from the Wall Street Journal from April 1997 to August
2001. Try to make sense of them, using what you’ve just learned:
 April 1997.Good news on the economy, leading to an increase in stock
prices: “Bullish investors celebrated the release of market-friendly
economic data by stampeding back into stock and bond markets, pushing
the Dow Jones Industrial Average to its second-largest point gain ever and
putting the blue-chip index within shooting distance of a record just weeks
after it was reeling.” (Output growth – profits dividends stock prices )
 December 1999.Good news on the economy, leading to a decrease in
stock prices: “Good economic news was bad news for stocks and worse
news for bonds. . . . The announcement of stronger-than-expected
November retail-sales numbers wasn’t welcome. Economic strength
creates inflation fears and sharpens the risk that the Federal Reserve will
raise interest rates again.” (Fed will respond with tightening policies due to
inflation fears – interest rates up and stock prices )
Making (Some) Sense of (Apparent) Nonsense: Why the Stock Market
Moved Yesterday and Other Stories
 September 1998. Bad news on the economy, leading to an decrease in stock
prices: “Nasdaq stocks plummeted as worries about the strength of the U.S.
economy and the profitability of U.S. corporations prompted widespread
selling.” (output contraction – profits dividends stock prices )
 August 2001. Bad news on the economy, leading to an increase in stock
prices: “Investors shrugged off more gloomy economic news,
and focused instead on their hope that the worst is now over for both the
economy and the stock market. The optimism translated into another 2%
gain for the Nasdaq Composite Index.” (expectation of output growth and
no risk of higher interest rates – stock prices )
6. Bubbles, Fads, and Stock Prices
• Stock prices are not always equal to their fundamental
value, defined as the present value of expected dividends.
• Stocks are sometimes overpriced or underpriced –
overpricing ends with a crash (US 2009) or a long slide (Japan
1989-1992)
• Such overpricing can occur even when investors are rational
e.g. it is rational to buy a stock whose fundamental value is 0
(it will never make a profit or pay dividends) if they buyer
expects the price at which the stock can be sold in future is
higher than the current purchase price
• i.e. rational speculative bubbles occur when stock prices
increase just because investors expected them to (see
Tulipmania in 17th century Holland and Russia 1994)
• Deviations of stock prices from their fundamental value are
called fads.
Famous Bubbles: From Tulipmania in Seventeenth-Century Holland to
Russia in 1994
Tulipmania in Holland
In the seventeenth century, tulips became increasingly popular in western
European gardens. A market developed in Holland for both rare and common
forms of tulip bulbs. Bulb prices increased to the price of a house in 1637 and
then a few years later fell to 10% of their peak value
The MMM Pyramid in Russia
In 1994 a Russian “financier,” Sergei Mavrody, created a company called
MMM and proceeded to sell shares, promising shareholders a rate of return
of at least 3,000% per year!
The trouble was that the company was not involved in any type of production
and held no assets, except for its 140 offices in Russia. The shares were
intrinsically worthless. The company’s initial success was based on a standard
pyramid scheme, with MMM using the funds from the sale of new shares to
pay the promised returns on the old shares.
The scheme collapsed and shareholders lost their money.
Conclusion
• Our focus this week has been on how
expectations and news on economic activity
effects bond and stock prices
• Next week we will look at how bond and stock
prices affect economic activity by influencing
consumption and investment spending