FNCE 3020 Financial Markets and Institutions

1
FNCE 3020Financial Marketsand Institutions

• Lecture 5 Part 2
• Forecasting with the Yield Curve
• Forecasting interest rates
• Forecasting business cycles

2
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.

3
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

4
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

5
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 ?

6
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

7
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 ?

8
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)

9
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?

10
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!

11
Short and Long Term Interest Rates, 1970 - 2008
12
Cyclical Pattern of Interest Rates, 1970 - 2008
13
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.

14
Cyclical Moves of Short and Long Term Interest
Rates, 1969-1978
15
Cyclical Moves of Short and Long Term Interest
Rates, 1978-1984
16
Cyclical Moves of Short and Long Term Interest
Rates, 1988-1993
17
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

18
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

19
The Probability of a Recession Using Yield Curves
(1960-1995 data) by Estrella and Mishkin, 1996,
Federal Reserve of New York
20
What is the Interest Rate Pattern Suggesting
Today?
21
Yield Curves and Business Cycle
22
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/FIHistoricalYie
  ld
• 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.

23
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.

24
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).

25
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/(1r)1 int/(1r)n
  principal/(1r)n

26
Example of Price Risk

• Price int/(1r)1 int/(1r)n
  principal/(1r)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!

27
Price Changes and Maturity

• 1 year bond
• Price int/(1r)1 principal/(1r)n
• Price 50/(1.06) 1,000/(1.06)
• Price 47.17 943.40
• Price 990.57
• 2 year bond
• Price int/(1r)1 int/(1r)2
  principal/(1r)n
• Price 50/(1.06) 50/(1.06)2
  1,000/(1.06)2
• Price 47.17 44.50 890.00
• Price 982.67

28
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!!!

29
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!!!

30
Liquidity Premium Theory Formula for Long Term
Interest Rates

• Need to modify the expectations theory formula to
  take into account liquidity premiums, or
• Where, Ln is the liquidity premium for holding a
  bond of n maturity.

31
Liquidity Premium Examples

• Assume One-year (spot and forward) interest
  rates over the next five years as follows
• one year spot 5
• (one year) forwards 6, 7, 8, and 9
• 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
• 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.

32
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

33
Yield Curve Liquidity Premium

• i rate
• 8.0
  o LP Yield Curve
• 7.75
• 7.50
  Difference is the liquidity premium
• 7.25
• 7.0
  o PE Yield Curve
• 6.75
• 6.50
• 6.25
• 6.0
• 5.75 o
• 5.5 o
• 5.25
• 5.0
• 2yr 5yr
  Years to Maturity

34
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

35
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 markets 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).

36
Forecasting Example 3

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

37
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 markets forecast for the 1 year
  rate, one year from now.
• Forecast both for the liquidity premium and
  assuming no liquidity premium.

38
Forecasting Example 4

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

39
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 markets forecast for the 1 year
  rate, one year from now.
• Forecast both for the liquidity premium and
  assuming no liquidity premium.

40
Forecasting Example 5

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

41
Differences in Forecasts

• 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

42
Yield Curve Liquidity Premiums and 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

43
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?

44
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!

45
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)

46
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.

47
Market Segmentations Yield Curve Near the End of
an Expansion

• i rate
• o Lenders supplying
  longer
• term funds (pushes down
  rates)
• Borrowers demanding shorter
  o
• term funds (pushes up rates)
• (st) Term to Maturity (lt)

48
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)

49
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.

50
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!!!

51
Upward Sweeping Yield Curve in Early 2002
Recession Ended in Early 2003