FNCE 4070: FINANCIAL MARKETS AND INSTITUTIONS Lecture 6: Forecasting With the Term Structure of Interest Rates

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FNCE 4070 FINANCIAL MARKETS AND INSTITUTIONS
Lecture 6 Forecasting With the Term Structure
of Interest Rates

• Forecasting Business Cycle Turning Points (A
  Recession)
• Forecasting Future Interest Rates (Estimating
  Forward Rates)
• Forecasting Inflation with Treasury Inflation
  Protected Securities (TIPS)

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Where is This Financial Center?
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Downward Sweeping or Inverted Yield Curve And
Economic Activity

• Inverted Yield Curve

• Discussion

• Inverted Yield Curve An interest rate
  environment in which long-term debt
  instruments have a lower yield than short-term
  debt instruments of the same credit quality.
• This type of yield curve is the rarest of the
  three main curve types and is considered by some
  to be a predictor of an economic recession (i.e.,
  business cycle turning point).
• Why An inverted yield curve signals a future
  fall in interest rates which is consistent with a
  recession.

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Interest Rates and Business Cycles 1969 1983
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Interest Rates Spreads and Business Cycles 1969
1983 (Monthly Data)
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Interest Rates and Business Cycles 1987 2011
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Interest Rate Spreads and Business Cycles 1987
2011 (Daily Data)
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Probability of a Recession Using Yield Curves
(Fed of New York)
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Monthly Yield Curve Analysis

• Refer to the Fed of Cleveland web site for a
  monthly analysis of the yield curve.
• http//www.clevelandfed.org/research/data/yield_cu
  rve/index.cfm?DCS.navLocal
• Link to early 2007 to see what this site was
  saying about the probably of a recession in the
  United States.
• Recall the recession officially began in Dec 2007

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Forecasting Interest Rates with The Expectations
Theory

• Recall that the Expectations Theory assumes that
  the current long term spot interest rate is
  comprised of
• (1) Current (spot) short term interest rate
  (which can designate as iss) and
• (2) Expected, future (forward) short-term
  interest rates (which we can designate as ie).

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Forecasting Interest Rates

• If we assume the long term spot rate (ils) is an
  average of short term rates (iss and ie),
• Then it is possible to derive the expected
  forward rate (ie), on a one-period bond for some
  future time period (n-t) through the following
  formula

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Forecasting With The Expectations Model Example
1

• Assume the following
• Current 1 year spot (iss1) 4.75 (0.0457)
• Current 2 year spot (ils2) 5.50 (0.055)
• Use the formula on the previous slide to
  calculate the implied forward rate, or the 1year
  rate, 1 year from now
• Or using an approximation formula (ils x 2)
  iss
• (5.5 x 2) 4.75 11.0 4.75 6.25

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Yield Curve For Example 1

• Yield Curve

• The Forward Rate

• The calculated forward rate of 6.26 is the
  markets expected 1 year interest rate one year
  from now.
• This rate of 6.26 becomes our forecasted
  interest rate using the pure expectations model.

• interest rate
• 6.0 oie (6.26)
• 5.5 oils2 (5.50)
• 5.0 o iss1 (4.75)
• 1y 2y
• Term to Maturity

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Forecasting With The Expectations Model Example
2

• Assume the following
• Current 1 year spot (iss1) 7.0 (0.07)
• Current 2 year spot (ils2) 5.0 (0.05)
• Use the formula on the previous slide to
  calculate the implied forward rate, or the 1year
  rate, 1 year from now
• Or as an approximation (ils x 2) iss
• (5.0 x 2) 7.0 10.0 7.0 3.00

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Yield Curve For Example 2

• Yield Curve

• The Forward Rate

• The calculated forward rate of 3.04 is the
  markets expected 1 year interest rate one year
  from now.
• This rate of 3.04 becomes our forecasted
  interest rate using the pure expectations model.

• interest rate
• 7.0 oiss1 (7.0)
• 5.0 oils2 (5.0)
• 3.0 oie (3.04)
• 1y 2y
• Term to Maturity

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Using Current Yield Curve Data to Forecast
Interest Rates

• Bloomberg Data U.S. Treasuries, April 3, 2012

• Expectations Model

• What is the yield curve data telling us about the
  markets expectation regarding future interest
  rates
• Going up or going down? Now calculate some
  forward rates?
• 3 month rate, 3 months from now?
• 1 year rate, 1 year from now?

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Answer to Previous Examples

• 3 month rate, 3 months from now

• 1 year rate, 1 year from now

• PE Model 0.21004
• 0.21004
• Approximation 0.21
• (0.14 x 2) 0.07
• 0.21

• PE Model 0.54028
• 0.54028
• Approximation 0.5400
• (0.37 x 2) 0.20
• 0.54

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Treasury Inflation-Protected Securities

• Treasury Inflation-Protected Securities, or TIPS,
  are securities whose principal (par value) is
  tied to the Consumer Price Index (CPI) .
• First issued in the U.S. in January 1997 (U.K.
  first issued in 1981).
• The par amount (principal value) increases with
  inflation and decreases with deflation.
• TIPs have a fixed coupon rate and they pay
  interest against the adjusted par value every six
  months.
• When the security matures, the U.S. Treasury pays
  the original (1,000) or adjusted principal,
  whichever is greater.

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TIPs Example Work Through Example and Fill in
Years 4 and 5
Year Par Value Beginning of Year (Par 1,000 when issued) CPI Change for Year Adjustment to Par Value (Based on CPI for Year) New Par Value End of Year Coupon Rate (Fixed 3.5 at Offering) Interest Paid (Against New Par Value)
1 1,000 2.2 22.00 1,022.00 3.5 35.77
2 1,022 0.0 00.00 1,022.00 3.5 35.77
3 1,022 -1.0 -10.22 1,011.78 3.5 35.41
4 1.5
5 -0.5
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Answers to Previous Slide (Years 4 and 5)
Year Par Value Beginning of Year (Par 1,000 when issued) CPI Change for Year Adjustment to Par Value (Based on CPI for Year) New Par Value End of Year Coupon Rate (Fixed 3.5 at Offering) Interest Paid (Against New Par Value)
1 1,000 2.2 22.00 1,022.00 3.5 35.77
2 1,022 0.0 00.00 1,022.00 3.5 35.77
3 1,022 -1.0 -10.22 1,011.78 3.5 35.41
4 1,011.78 1.5 15.18 1,026.96 3.5 35.94
5 1,026.96 -0.5 -5.14 1,021.82 3.5 35.76
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Estimating Future Rates of Inflation

• Using the TIPS market to determine the
  breakeven inflation rate.
• Assumptions
• Conventional Treasury rate (yield to maturity)
  includes both real rate and inflation premium.
• TIPS rate (yield to maturity) is simply the real
  rate.
• Breakeven inflation rate Yield to maturity on
  conventional Treasuries Yield to maturity on
  TIPS.
• Difference (i.e., Breakeven rate) is the markets
  annual inflation expectation over the maturity
  period.
• Important Use similar maturities when
  calculating Breakeven rate.

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10-Year Break Even Inflation Rate (10 Year
Conventionals -TIPs 10)
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5-Year Break Even Inflation Rate (5 Year
Conventionals -TIPs 5 year yield)
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TIPs Breakeven 5-Year Forecast (i.e., average
annual expected 5 year rate) with Actual CPI
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What Determines Inflationary Expectations?

• Inflation targeting by a central bank
• Levin (2004) found that inflationary expectations
  (measured by private-sector inflation forecasts)
  were not found to be sensitive to actual
  inflation in inflation targeting countries but
  that in non-inflation targeting countries
  inflationary expectations were highly correlated
  to lagged inflation.
• Commodity Prices
• IMF (2012) study found that commodity prices have
  a significant impact on inflationary expectations

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U.S. Treasury Yield Curve Site for Observing
Breakeven Rate of Inflation

• Link to the U.S. Treasury site below for the
  nominal and TIPS yield curve.
• http//www.treasury.gov/resource-center/data-chart
  -center/interest-rates/Pages/Historic-Yield-Data-V
  isualization.aspx
• Set the date for January 2, 2009 and observe the
  breakeven rate.
• What was this date telling you about the markets
  expectation regarding inflation?
• Recall The breakeven inflation rate is the
  difference between the two yield curves.

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U.S. Treasury Yield Curve Site for Observing
Breakeven Rate of Inflation

• Again, link to the U.S. Treasury site below for
  the nominal and TIPS yield curve.
• http//www.treasury.gov/resource-center/data-chart
  -center/interest-rates/Pages/Historic-Yield-Data-V
  isualization.aspx
• What is the most recent data telling you about
  the markets expectation regarding inflation?
• Note The 5-year, 7-year and 10-year TIPS yield
  curve data point is incorrect (however, the
  actual data is correct).
• According to the Treasury Department, the
  graphing function is flawed.
• From this site, one can also download the actual
  data (link to text version of Treasury Yield
  Curve).
• Can you explain the current TIPs yield to
  maturity?

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Bloomberg Sites for TIPs and Breakeven Rates

• Current TIPs Yields

• Breakeven Rates (10-Year)

• http//www.bloomberg.com/
• April 11, 2012

• http//www.bloomberg.com/quote/USGGBE10IND

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Appendix 1

• Why Do Markets Care about Yield Curves?
• The following is from Bonds on Line and
  summarizes why yield curves are important.
  http//www.bondsonline.com/Corporate_Bond_Yield_In
  dex.phpwhy

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Using Yield Curves

• The shape of the yield curve is closely followed
  by bond investors.  It provides information about
  the yields of short term compared to long term
  fixed-income investments.  Investors analyze and
  interpret the yield curve shape to give some
  insights on the future direction of rates and the
  economy.   
• A yield curve normally has an upward sloping
  shape. That is, in a normal yield curve,
  shorter-term yields are lower than longer-term
  yields, with yields generally increasing as years
  to maturity increase.  The yields are higher on
  securities with longer maturities because these
  securities are more vulnerable to price changes
  caused by changes in interest rates over time. 
  Investors in longer-term securities are typically
  rewarded with a higher yield for taking the risk
  that interest rates could rise and cause the
  prices of their securities to fall. 
• Investors pay attention to both the current shape
  of the yield curve, whether it is steep or flat,
  and yield curve movements.  That is, investors
  will look at whether the entire curve is shifting
  up or down in a parallel fashion which suggests
  that rates across the maturity spectrum are
  changing by the same magnitude or, alternatively,
  the shape or slope of the curve is becoming
  flatter or steeper.  For example, when Federal
  Reserve monetary policy is more accommodative and
  reduces short term rates, the yield curve
  generally steepens, and flattens when monetary
  policy tightens the Fed raises short term rates.

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Using Yield Curves

• When the yield curve is steep, that is when the
  difference between short-term and long-term
  yields is large, the market often expects
  interest rates to rise, though there are a number
  of variables, including the rate of economic
  growth and inflationary expectations, that go
  into interest rate analysis and forecasting the
  risk at the long end of the maturity range is
  therefore greater, and so is the return or
  yield.  When the yield curve is relatively flat,
  the difference between short-term yields and
  long-term yields is not that great.  When this
  happens, the market is not rewarding investors
  for taking the risk of a longer maturity,
  possibly because the market believes interest
  rates will decline, causing bond prices to rise
  and yields to fall.  Investors holding securities
  with longer maturities tend to benefit more from
  a declining interest rate trend. 
• There have been brief and unusual periods of time
  when the there has been what is known as an
  inverted yield curve shape, where, at certain
  points along the maturity spectrum, short-term
  yields have been higher than long-term yields.
  Inversely sloped yield curves are not sustainable
  either short term yields will eventually fall
  or long term yields rise. An inverted yield curve
  is considered an omen of recession as well as
  lower interest rates.

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Appendix 2

• Ben Bernanke and the 2006 Yield Curve.
• Shortly after Bernanke became Chair of the Fed
  (Feb 1, 2006) he spoke before the Economic Club
  of New York.  The presentation to that group was
  given on March 20, 2006.  The yield curve which
  had been upward sweeping in 2004 (and thus
  normal) began to flatten in 2005 through 2006 and
  was approaching almost flat by the time Bernanke
  spoke.  The following is a direct quote from
  Bernankes presentation regarding the flattening
  yield curve in 2006.

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Ben Bernanke Discusses the 2006 Yield Curve

• Although macroeconomic forecasting is fraught
  with hazards, I would not interpret the currently
  very flat yield curve as indicating a significant
  economic slowdown to come, for several reasons.
  First, in previous episodes when an inverted
  yield curve was followed by recession, the level
  of interest rates was quite high, consistent with
  considerable financial restraint. This time, both
  short- and long-term interest rates--in nominal
  and real terms--are relatively low by historical
  standards. Second, as I have already discussed,
  to the extent that the flattening or inversion of
  the yield curve is the result of a smaller
  liquidity term premium, the implications for
  future economic activity are positive rather than
  negative. Finally, the yield curve is only one of
  the financial indicators that researchers have
  found useful in predicting swings in economic
  activity. Other indicators that have had
  empirical success in the past, including
  corporate risk spreads, would seem to be
  consistent with continuing solid economic growth.
  In that regard, the fact that actual and implied
  volatilities of most financial prices remain
  subdued suggests that market participants do not
  harbor significant reservations about the
  economic outlook.
•