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)

Where is This Financial Center?

Downward Sweeping or Inverted Yield Curve And Economic ActivityInverted 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.

Interest Rates and Business Cycles: 1969 – 1983

Interest Rates Spreads and Business Cycles: 1969 – 1983 (Monthly Data)

Interest Rates and Business Cycles: 1987 – 2011

Interest Rate Spreads and Business Cycles: 1987 – 2011 (Daily Data)

Probability of a Recession Using Yield Curves (Fed of New York)

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_curve/index.cfm?DCS.nav=Local

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

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).

n

ieieieissils nttt

n

...21

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:

n

ieieieissils nttt

n

...21

11

1

t

nn

tniss

ilsie

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%

%26.606255.01

0475.01

055.01 2

tnie

11

1

t

nn

tniss

ilsie

Yield Curve For Example #1Yield Curve The Forward Rate

The calculated forward rate of 6.26% is the market’s 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 rate6.0% oie (6.26%)

5.5 oils2 (5.50%)

5.0 o iss1 (4.75%)

1y 2y

Term to Maturity

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%

%04.30304.01

07.01

05.01 2

tnie 11

1

t

nn

tniss

ilsie

Yield Curve For Example #2Yield Curve The Forward Rate

The calculated forward rate of 3.04% is the market’s 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 rate7.0% oiss1 (7.0%)

5.0 oils2 (5.0%)

3.0 oie (3.04%)

1y 2y

Term to Maturity

Using Current Yield Curve Data to Forecast Interest RatesBloomberg 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?

(1)3 month rate, 3 months from now?

(2)1 year rate, 1 year from now?

Answer to Previous Examples3 month rate, 3 months from now:

PE Model: 0.21004%

= 0.21004% Approximation: 0.21%

= (0.14 x 2) – 0.07

= 0.21%

1 year rate, 1 year from now:

PE Model: 0.54028%

= 0.54028% Approximation: 0.5400 = (0.37 x 2) – 0.20 = 0.54%

11

1

t

nn

tniss

ilsie

11

1

t

nn

tniss

ilsie

10007.01

0014.01 2

tnie

10020.01

20037.01

tnie

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.

TIPs Example: Work Through Example and Fill in Years 4 and 5Year 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

CouponRate (Fixed 3.5% at Offering)

InterestPaid (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%

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

CouponRate (Fixed 3.5% at Offering)

InterestPaid (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

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 market’s annual

inflation expectation over the maturity period. Important: Use similar maturities when calculating

Breakeven rate.

10-Year Break Even Inflation Rate (10 Year Conventionals -TIPs 10)

5-Year Break Even Inflation Rate (5 Year Conventionals -TIPs 5 year yield)

TIPs Breakeven 5-Year Forecast (i.e., average annual expected 5 year rate) with Actual CPI

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

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-Visualization.aspx

Set the date for January 2, 2009 and observe the breakeven rate. What was this date telling you about

the market’s expectation regarding inflation?

Recall: The breakeven inflation rate is the difference between the two yield curves.

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-r

ates/Pages/Historic-Yield-Data-Visualization.aspx What is the most recent data telling you about the market’s

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?

Bloomberg Sites for TIPs and Breakeven RatesCurrent TIPs Yields http://www.bloomberg.co

m/ April 11, 2012

Breakeven Rates (10-Year)

http://www.bloomberg.com/quote/USGGBE10:IND

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_Index.php#why

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.

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.”

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 Bernanke’s presentation regarding the flattening yield curve in 2006.

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.”