FNCE 3020 Financial Markets and Institutions Fall Semester 2006

1
FNCE 3020Financial Markets and Institutions
Fall Semester 2006

• Lecture 5 Part 2
• Forecasting Interest Rates with the Yield Curve

2
Forecasting Interest Rates with the Term
Structure (Yield Curve)

• In the previous lecture (Lecture 5 Part 1), we
  discussed the term structure of interest rates,
  i.e., the yield curve.
• The previous lecture introduced you to three
  major theories which are used to explain why the
  yield curve takes the shape it does.
• In this lecture, we will see how we can apply
  these three theories forecasting interest rates.

3
Why is Forecasting Important?

• Interest rate forecasts are important to a
  variety of possible organizations. These
  include
• Lenders of funds.
• A lender of funds could use an interest rate
  forecast to set lending rates today. This is
  especially important in committing to longer term
  loans.
• Asset managers.
• The future direction of interest rates will have
  an impact on the financial asset holdings of
  these organizations. A forecast will help
  establish appropriate portfolio allocations.

4
Why is Forecasting Important?

• Other organizations interested in interest rate
  forecast would include
• Investment bankers.
• Interest rate forecasts would assist these
  organizations in determining the timing of issues
  which they intend to bring to market for their
  clients.
• Corporations.
• Decisions about when to borrow, and the method of
  borrowing, to invest in possible projects might
  depend upon interest rate forecasts.
• Economic forecasters.
• Given the possible impact of interest rate
  changes on key sectors of the economy,
  forecasters need to utilize interest rate
  forecasts in their macro-economic forecasts.

5
Theories to Explain the Shape of the Yield Curve

• Recall, that there are three main theories or
  explanations of the yield curve.
• These theories which attempt to explain why a
  yield curve has the shape that it does, are
• (Pure) Expectations Theory
• Liquidity Premium Theory
• Market Segmentations Theory
• The question for this lecture is whether or not
  these, theories may be used to forecast (i.e.,
  predict) future moves and levels of interest
  rates!

6
Forecasting Interest Rates Using the Expectations
Model

• The Expectations Model may be used to forecast
  expected future spot interest rates.
• This model assume that the long term spot
  interest rate is an average of short term (both
  spot and forward) rates.
• Thus, if we observe a
• Short term spot rate and
• A long term spot rate
• We can calculate what the forward rate must be to
  produce the observed long term spot rate.

7
Formula for Forecasting Interest Rates Using the
Expectations Model

• The formula we use to derive the Expectations
  Model expected forward rate (ie), on a
  one-period bond for some future time period (n-t)
  is as follows, where
• Ils the observed long term rate.
• Iss the observed short term rate.

8
Expectations Forecasting Example 1

• Assume current 1 year short term spot interest
  rate (iss1) and current 2 year long-term spot
  interest rate (ils2) as follows
• iss1 5.0 and
• ils2 5.5
• Then, in equilibrium, the expected 1 year forward
  rate, 1 year from now (ien-t) must be
• Note A 6 forward rate is the only rate which
  will produce the two observed spot rates.

9
Yield Curve Example 1

• i rate
• 6.0 oie This is the forecast
  (forward rate)
• 5.5 o
• 5.0 o This is the observed
  yield curve
• 1y 2y
• Term to Maturity ?

10
Expectations Forecasting Example 2

• Assume current 1 year short term spot (iss1) and
  current 2 year long-term spot (ils2) rates are as
  follows
• iss1 7.0 and
• ils2 5.0
• Then, in equilibrium, the expected 1 year forward
  rate, 1 year from now (ien-t) must be
• Note A 3 forward rate is the only rate which
  will produce the two observed spot rates.

11
Yield Curve Example 2

• i rate
• 7.0 o
• 5.0 o This is the observed
  yield curve
• 3.0 oie This is the forecast
  (forward rate)
• 1y 2y
• Term to Maturity ?

12
Liquidity Premium Theory

• The Liquidity Premium Theory assumes that long
  term bonds carry greater risks and therefore
  investors require greater premiums (i.e.,
  returns) to commit funds for longer periods of
  time.
• Therefore, if we use the Liquidity Premium Theory
  to forecast future interest rates, we need to
  observe the follow
• We need to make some estimate as to the liquidity
  premium per maturity.
• We then subtract our estimated liquidity premium
  out of the forecast (i.e., forward) rate.

13
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

14
Forecasting Interest Rates Using the Liquidity
Premium Theory

• We can use the Liquidity Premium Theory to
  forecast future interest rates. But to do so
• (1) We need to make some estimate as to the
  liquidity premium per maturity, and
• (2) We then subtract our estimated liquidity
  premium out of the forecast forward rate.

15
Formula for Forecasting Interest Rates Using the
Liquidity Premium Model

• The formula we use to derive the Liquidity
  Premium expected forward rate (ie), on a
  one-period bond for some future time period
  (n-t), is a follows, where
• Ils the observed long term rate.
• Iss the observed short term rate.
• lp the assumed liquidity premium in the long
  term rate.

16
Liquidity Premium Forecasting Example 1

• Assume current 1 year short term spot interest
  rate (iss1) and current 2 year long-term spot
  interest rate (ils2) as follows
• iss1 5.0 and
• ils2 5.75
• Also assume the liquidity premium on the two year
  bond is .25.
• Calculate the Liquidity Premium models forecast
  (forward rate) for the 1 year interest rate, one
  year from now.

17
Liquidity Premium Forecasting Example 1

• The expected 1 year forward rate, 1 year from now
  without a liquidity premium (ien-t) is
• The expected 1 year forward rate, 1 year from now
  with a 25 basis point liquidity premium is

18
Liquidity Premium Forecasting Example 2

• Assume current 1 year short term spot interest
  rate (iss1) and current 2 year long-term spot
  interest rate (ils2) as follows
• iss1 5.0 and
• ils2 5.75
• Also assume the liquidity premium on a two year
  bond is .75.
• Calculate the Liquidity Premium models forecast
  (forward rate) for the 1 year rate, one year from
  now.

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Liquidity Premium Forecasting Example 2

• The expected 1 year forward rate, 1 year from now
  without a liquidity premium (ien-t) is
• The expected 1 year forward rate, 1 year from now
  with a 75 basis point liquidity premium is

20
Liquidity Premium Forecasting Example 3

• Assume current 1 year short term spot interest
  rate (iss1) and current 2 year long-term spot
  interest rate (ils2) as follows
• iss1 5.0 and
• ils2 5.75
• Also assume the liquidity premium on a two year
  bond is 1.00.
• Calculate the Liquidity Premium models forecast
  (forward rate) for the 1 year rate, one year from
  now.

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Liquidity Premium Forecasting Example 3

• The expected 1 year rate, 1 year from now without
  a liquidity premium (ien-t) is
• The expected 1 year rate, 1 year from now with a
  100 basis point liquidity premium is

22
Differences in 3 Forecasts

• Note Observed short term rate 5.0 and long
  term rate 5.75
• Then Assuming Forecasted
  Forecasted Spot Rate Change in
  1 yr from Now Spot Rate
• No Liquidity Premium 6.5
  150bps
• LP of .25 6.0 100bps
• LP of .75 5.0 no change
• LP of 1.00 4.5 - 50 bps
• In basis points over current 1 year spot rate of
  5.0

23
Yield Curve and Differences in Liquidity Premium
and Expectations Forecasts (Oie)

• i rate
• 6.75
• 6.50 oie (No
  Liquidity Premium) 6.5
• 6.25
• 6.0 oie (.25
  LP) 6.0
• 5.75 o
• 5.5
• 5.25 Observed Yield
  Curve
• 5.0 o oie (.75 LP)
  5.0
• 4.75
• 4.5 oie (1.00
  LP) 4.5
• 1yr 2yr Years to Maturity

24
Liquidity Premium Forecasting Issues

• If there are liquidity premiums in longer term
  spot interest rates, NOT subtracting them out
  will result in over forecasting errors.
• That is, the Expectations forecast will have a
  upward bias.
• Questions (or problems for forecasting)
• First, Is there a liquidity premium, and if so
• SECOND, HOW MUCH IS IT?

25
Market Segmentations Theory

• The Market Segmentations Theory explains how the
  yield curve might respond over the course of a
  business cycle.
• Essentially, this theory suggests that
• (1) the yield curve may become downward sloping
  just before the economy enters into a recession
  (or slowdown), and
• (2) the yield curve may become upward sweeping
  near the end of a recession, or beginning of an
  expansion.
• This model is based observing yield curve
  patterns and assuming borrowers and lenders will
  move away from their neutral positions in
  financial markets and interest rates change.

26
Yield Curves Prior to a Recession

• Near the end of a business expansion (period
  before shaded areas) short term rates exceed long
  term rates.
• Thus, during this period we would observe a
  downward sloping yield curve.

27
Yield Curves Near the Beginning of an Expansion

• 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 this period we would observe an
  upward sweeping yield curve.

28
Near the End of a Business Recession or Early
Expansion

• Short term rates below long term.
• (Severe) Upward sweeping yield curve.
• Why this shape?
• Interest rates have fallen during the
  recessionary period and are now relatively low.
  
• Borrowers realizing that rates are relatively
  low, finance in the long term (wanting to lock in
  long term liabilities at low interest rates).
• Lenders realizing that rates are relatively low,
  lend in the short term (not wanting to lock in
  long term assets at low interest rates)
• Note Both borrowers and lenders accentuate
  their natural tendencies.

29
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
  perhaps 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.
• But there are problems
• Lags (see next slide)
• And some forecasters think the model no longer
  works.

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Upward Sweeping Yield Curve in Early 2002
Recession Ended in Early 2003
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What Does the Yield Curve Look Like Today and
What Would the Market Segmentations Theory Tells
Us About Future Business Activity?

• U.S. Yield Curve September 6, 2006
• http//www.bloomberg.com/markets/rates/index.html