FNCE 3020
Financial Markets
and Institutions
Lecture 5; Part 2
Forecasting with the Yield Curve
Forecasting interest rates
Forecasting business cycles
Summary of Expectations Regarding
Future Interest Rates

The shape and slope of the yield curve reflects the
markets’ expectations about future interest rates.
 Upward Sloping (Ascending) Yield Curves:
 Future (forward) interest rates are expected to
increase above existing spot rates.
 Downward Sloping (Descending) Yield Curves:
 Future (forward) interest rates are expected to
decrease below existing spot rates.
 Flat Yield Curves
 Future (forward) interest rates are expected to
remain the same as existing spot rates.
Forecasting Interest Rates with the
Expectations Model


The Expectations Model can be used to forecast
“expected” future spot interest rates as follows:
If we assume the long term rate is an average of
short term (spot and forward) rates, it is possible to
calculate the “expected” forward rate (ie), on a
bond for some future time period (n-t) through the
following formula:

1  ils n 
ien t 
1  isst 
n
1
Forecasting Example #1




Assume current 1 year short term spot (iss1) and
current 2 year long-term spot (ils2) rates are:
iss1 = 5.0% and
ils2 = 5.5%
Then the calculated “expected” 1 year rate, 1 year
from now (ien-t) is:

1  0.055

2
ien t
1  0.05
 1  0.06  6%
Yield Curve Example #1
i rate
6.0
oie
And this is the forecasted rate
5.5
o
5.0 o
This is the observed yield curve
1y 2y
Term to Maturity →
Forecasting Example #2




Assume current 1 year short term spot (iss1) and
current 2 year long-term spot (ils2) rates are:
iss1 = 7.0% and
ils2 = 5.0%
Then the calculated “expected” 1 year rate, 1 year
from now (ien-t) is:
ien t
2

1  0.05

 1  0.03  3%
1  0.07
Yield Curve Example #2
i rate
7.0 o
This is the observed yield curve
5.0
o
3.0
oie
And this is the forecasted rate
1y 2y
Term to Maturity →
Using the Current Yield Curve

What is the current yield curve telling us about
the markets expectation regarding future interest
rates:

Going up or going down? Can you approximate some forward
rates? (e.g., 3 month rate, 3 months from now)
Forecasting Future Economic Activity
with the Yield Curve



In addition to its potential use in forecasting
future interest rates, the yield curve may also
be applicable for forecasting future economic
activity (i.e., business cycles).
Forecasting future economic activity assumes
that the historical pattern of interest rate
changes over the course of a business cycle
will repeat in the future.
What are these historical patterns?
Interest Rates Movements over the
Business Cycles

What can we observe as the historical pattern
of interest rates over the course of a business
cycle? Specifically:




Which interest rates (short or long term) fluctuate
more over a business cycle?
What happens to interest rates during a business
expansion (recession) and why?
Does the relationship between short term and
long term interest rates change over a business
cycle?
Look at the following charts for answers!
Short and Long Term Interest Rates,
1970 - 2008
Cyclical Pattern of Interest Rates, 1970
- 2008
Observations From Last 2 Slides


(1) Over the course of time, short term rates are
more volatile than long term interest rates.
(2) During a business expansion interest rates
gradually drift up (just before shaded area). Why?


Increasing business activity is pushing up the demand for
funds
 Corporates and individuals increasing borrowing
(demand shifting out)
 Central bank likely to be raising interest rates (impact on
short term rates)
 Inflationary expectations may be increasing (impact on
inflationary expectations component in interest rates)
(3) During a business recession interest rates come
down. Why?

Decreasing business activity is bring down the demand for
funds.
Cyclical Moves of Short and Long
Term Interest Rates, 1969-1978
Cyclical Moves of Short and Long
Term Interest Rates, 1978-1984
Cyclical Moves of Short and Long
Term Interest Rates, 1988-1993
Observations from Last 3 Slides


Near the end of a business expansion (period before
shaded areas) short term interest rates rise above long
term interest rates.
 Thus, during these periods the yield curve would be
downward sloping yield curve, which would forecast a
recession.
Into a recession (shaded area), short term rates come
down faster than long term and eventually, near the end
of the recession or beginning of the expansion, short
term rates fall below long rates.
 Thus, during these periods the yield curve would be
upward sweeping yield curve, which would forecast an
expansion
Yield Curves and Recessions


According to one source: “Inverted yield curves are
rare. Never ignore them. They are always followed by
economic slowdown -- or outright recession -- as well
as lower interest rates across the board.” (Fidelity
Investments)
But how long is the lead time to a recession?



Empirical studies suggest a lead time of generally from 2
to 4 quarters.
Empirical studies also note that the steeper the yield
curve (i.e., the greater the spread between long term and
short term interest rates) the greater the probability of a
recession – see next slide.
As one example of an empirical study, refer to
http://www.ny.frb.org/research/current_issues/ci2-7.pdf
The Probability of a Recession Using Yield
Curves (1960-1995 data) ; by Estrella and
Mishkin, 1996, Federal Reserve of New York
What is the Interest Rate Pattern
Suggesting Today?
Yield Curves and Business Cycle
Useful Yield Curve Web Sites

http://www.bondsonline.com/Todays_Market/
Treasury_Yield_Curve.php


This site not only has a picture of the most recent
yield curve, but data as well.
http://fixedincome.fidelity.com/fi/FIHistoricalYi
eld

This site discusses various shapes of the yield
curve and has a very interesting interactive yield
curve chart with yield curves from March 1977 to
the present.
Appendix 1: Liquidity Premium
and Market Segmentations
Theory of the Yield Curve
These slides will introduce you to the last two
explanations of the yield curve and in addition
illustrate how they might be useful in forecasting
interest rates and economic activity.
Liquidity Premium Theory




The second explanation of the yield curve shape is
referred to as the Liquidity Premium Theory.
Assumptions: Long term securities carry a greater
risk and therefore investors require greater
premiums (i.e., returns) to commit funds for longer
periods of time.
Interest rate on a long term bond will equal an
average of the expected short term rates PLUS a
liquidity premium!
What are these risks associated with illiquidity:


Price risk (a.k.a. interest rate risk).
Risk of default (on corporate issues).
Price Risk (Interest Rate Risk)
Revisited


Observation: Long term securities vary more
in price than shorter term.
Why?

Recall: The price of a fixed income security is the
present value of the future income stream
discounted at some interest rate, or:
Price = int/(1+r)1 + int/(1+r)n + … principal/(1+r)n
Example of Price Risk

Price = int/(1+r)1 + int/(1+r)n + … principal/(1+r)n

Assume two fixed income securities:




A 1 year, 5% coupon, par $1,000
A 2 year, 5% coupon, par $1,000
Assume discount rate = 6% (market rate; or
opportunity cost)
What will happen to the prices of both issues?

Both bonds should fall in price (sell below their par
values). See new prices on next slide!
Price Changes and Maturity










1 year bond:
Price = int/(1+r)1 + … principal/(1+r)n
Price = $50/(1+.06) + $1,000/(1+.06)
Price = $47.17 + $943.40
Price = $990.57
2 year bond
Price = int/(1+r)1 + int/(1+r)2 + … principal/(1+r)n
Price = $50/(1+.06) + $50/(1+.06)2 + 1,000/(1+.06)2
Price = $47.17 + $44.50 + $890.00
Price = $982.67
Price Change Comparisons

Price Change over par ($1,000)






1 year bond = $ 9.43
2 year bond = $17.33
Note: The long term (2 year) bond experienced greater
price change!
Thus, there is greater price risk with longer term
bonds!
Thus, investors want a higher return on long term
bonds because of the potential for greater price
changes.
This is called a liquidity premium!!!
Liquidity Premium

Liquidity Premium is added by market participants to
longer term bonds.


It is actually a premium for giving up the liquidity associated
with shorter term issues.
Thus, if observed long term rates are higher than
short term rates, the question is:



Are higher long term rates due to expectations of higher
rates in the future (Expectations Theory), OR
Are higher long term rates due to added on liquidity
premiums (Liquidity Premium Theory)?
There is no good answer to this question!!!
Liquidity Premium Theory Formula
for Long Term Interest Rates

Need to modify the expectations theory formula to
take into account liquidity premiums, or
ils t ,n

iss t  iet 1  iet  2  ...  ien

 Ln
n
Where, Ln is the liquidity premium for holding a
bond of n maturity.
Liquidity Premium Examples

Assume: One-year (spot and forward) interest
rates over the next five years as follows:




Assume: Investors' preferences for holding
short-term bonds so liquidity premium for one- to
five-year bonds as follows:
0%, 0.25%, 0.5%, 0.75%, and 1.0%
Calculate the market interest rate on:



one year spot = 5%
(one year) forwards = 6%, 7%, 8%, and 9%
1) a two year bond (Ln = .25%)
2) a five year bond (Ln = 1.0%)
Compare calculated long term rates with those
for the pure expectations theory formula.
Calculations and Comparisons






Market interest rate on the two-year bond:
(5% + 6%)/2 + 0.25% = 5.75%
Market interest rate on the five-year bond:
(5% + 6% + 7% + 8% + 9%)/5 + 1.0% = 8%
Compare Liquidity Premium rates to Pure Expectations
Rates
2 year: 5.75% (LP); 5.5% (PE)
5 year: 8.00% (LP); 7.0% (PE)
Thus:
 liquidity premium theory produces yield curves more
steeply upward sloped
Yield Curve: Liquidity Premium
i rate
8.0
7.75
7.50
7.25
7.0
6.75
6.50
6.25
6.0
5.75
5.5
5.25
5.0
o LP Yield Curve
Difference is the liquidity premium
o PE Yield Curve
o
o
2yr
5yr Years to Maturity
Forecasting Interest Rates Using the
Liquidity Premium Theory

We can use the Liquidity Premium Theory to
forecast future interest rates. But to do so:


We need to make some estimate as to the liquidity
premium per maturity.
We then subtract our estimated liquidity premium out of
the forecast rate.

Start with the Pure Expectations Forecast formula:

1  ils 

n
ien t
t ,n
1  iss t 
1
Forecasting Example #3: Assuming a
Liquidity Premium





Assume current 1 year short term spot (iss1) and
current 2 year long-term spot (ils2) rates are as
follows:
iss1 = 5.0% and
ils2 = 5.75%
Also assume the liquidity premium on a two year
bond is .25%.
Calculate the market’s forecast for the 1 year rate,
one year from now.

Forecast both for the liquidity premium and assuming no
liquidity premium (and compare the two).
Forecasting Example #3

The 1 year rate, 1 year from now without a
liquidity premium (ien-t) is “expected” to be:
ie n t


1  0.05752

 1  0.065  6.5%
1  0.05
The 1 year rate, 1 year from now with a 25 basis
point liquidity premium (ien-t -lp) is “expected” to
be:
ie n t lp

1  (0.0575 0.0025) 2

1  0.05
 1  0.06  6.0%
Forecasting Example #4





Assume current 1 year short term spot (iss1) and
current 2 year long-term spot (ils2) rates are as
follows:
iss1 = 5.0% and
ils2 = 5.75%
Also assume the liquidity premium on a two year
bond is .75%.
Calculate the market’s forecast for the 1 year rate,
one year from now.

Forecast both for the liquidity premium and assuming no
liquidity premium.
Forecasting Example #4

The 1 year rate, 1 year from now without a
liquidity premium (ien-t) is “expected” to be:
ie n t


1  0.05752

 1  0.065  6.5%
1  0.05
The 1 year rate, 1 year from now with a 75 basis
point liquidity premium (ien-t -lp) is “expected” to
be:
2
ie n t lp

1  (0.0575 0.0075) 

1  0.05
 1  0.05  5.0%
Forecasting Example #5





Assume current 1 year short term spot (iss1) and
current 2 year long-term spot (ils2) rates are as
follows:
iss1 = 5.0% and
ils2 = 5.75%
Also assume the liquidity premium on a two year
bond is 1.00%.
Calculate the market’s forecast for the 1 year rate,
one year from now.

Forecast both for the liquidity premium and assuming no
liquidity premium.
Forecasting Example #5

The 1 year rate, 1 year from now without a
liquidity premium (ien-t) is “expected” to be:
ie n t


1  0.05752

 1  0.065  6.5%
1  0.05
The 1 year rate, 1 year from now with a 100 basis
point liquidity premium (ien-t -lp) is “expected” to
be:
1  (0.0575 0.0100) 2
ie n t lp 
 1  0.45  4.5%
1  0.05


Differences in Forecasts

Assuming
Forecasted
Forecasted
Spot Rate
Change in
1 yr from Now
Spot

Rate*
No Liquidity Premium
LP of .25%
LP of .75%
LP of 1.00%

*In basis points over current 1 year spot rate of 5.0%



6.5%
6.0%
5.0%
4.5%
+150bps
+100bps
no change
- 50 bps
Yield Curve: Liquidity Premiums and
Forecasts (Oie)
i rate
6.75
6.50
6.25
6.0
5.75
5.5
5.25
5.0
4.75
4.5
oie (No Liquidity Premium) = 6.5%
oie (.25% LP) = 6.0%
o
o
Observed Yield Curve
oie (.75% LP) = 5.0%
oie (1.00% LP) = 4.5%
1yr
2yr Years to Maturity
Liquidity Premium Conclusions


If there are liquidity premiums on longer term
rates, NOT subtracting them out will result in
“over” forecasting errors.
Question (Problem):


Is there a liquidity premium, and if so
HOW MUCH IS IT?
Market Segmentations Theory



The third theory of the yield curve is the Market
Segmentations Theory.
Assumptions: the yield curve is determined by the
supply of and the demand of loanable funds (or
securities) at a particular maturity.
Begin with a “neutral” position


What would be the natural tendencies of borrowers and
lenders?
 Borrowers prefer longer term loans (or to supply longer
term securities)
 Lenders prefer shorter term loans (or to demand shorter
term securities)
What type of yield curve would this neutral (natural)
position result in?

Upward sweeping!
Natural (Neutral) Upward Sweeping
Market Segmentations Yield Curve
i rate
Lenders supplying shorter
term funds (pushes down rates)
o
o
Borrowers demanding longer
term funds (pushes up rates)
(st) Term to Maturity (lt)
Near the End of a Business
Expansion: Explanation of Yield Curve



Short term rates exceeding long term.
Downward sweeping yield curve.
Why this shape?




Interest rates have risen during the expansionary period
and are now “relatively” high.
Borrowers realizing that rates are relatively high, finance in
the short term (not wanting to lock in long term liabilities at
high interest rates).
Lenders realizing that rates are relatively high, lend in the
long term (wanting to lock in long term assets at high
interest rates)
Note: Both borrowers and lenders move away from their
natural tendencies.
Market Segmentations Yield Curve
Near the End of an Expansion
i rate
o
Lenders supplying longer
term funds (pushes down rates)
Borrowers demanding shorter
term funds (pushes up rates)
(st) Term to Maturity (lt)
o
Market Segmentations Yield Curve
Near the End of Recession
i rate
Lenders supplying shorter
term funds (pushes down rates)
o
Borrowers demanding longer
o
term funds (pushes up rates)
(st) Term to Maturity (lt)
Forecasting with Market
Segmentations Theory


The Market Segmentations Theory CANNOT be
used to forecast future spot rate (forward rates).
The Market Segmentations Theory can be used to
identify (signal) turning points in the movement of
interest rates (and in the economy itself) based on
the shape of the curve.


Downward sweeping curve suggests a fall in interest rates,
the end of an economic expansion, and a future economic
(business) recession.
Severe upward sweeping curve suggests a rise in interest
rates, the end of an economic recession, and a future
economic (business) expansion.
Lag Problem with Market Segmentations
Theory



Lags between what the
yield curve is suggesting
and what may eventually
happen are variable and
potentially very long.
Upward sloping yield curve
on Jan 2, 2002 suggested
the end of a recession.
When did it end?

A year later!!!
Upward Sweeping Yield Curve in Early
2002; Recession Ended in Early 2003