FNCE 3020Financial Marketsand Institutions

Lecture 5; Part 2Forecasting with the Yield Curve

Forecasting interest ratesForecasting 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:

11

1

t

nn

tniss

ilsie

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:

%606.01

05.01

055.01 2

tnie

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:

%303.0107.01

05.01 2

tnie

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/FIHistoricalYield 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

Where, Ln is the liquidity premium for holding a bond of n maturity.

nnttt

nt Ln

ieieieissils

...21

,

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.

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 rate8.0 o LP Yield Curve7.75 7.50 Difference is the liquidity premium7.257.0 o PE Yield Curve6.756.506.256.05.75 o5.5 o5.255.0

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:

11

1 ,

t

nnt

tniss

ilsie

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:

The 1 year rate, 1 year from now with a 25 basis point liquidity premium (ien-t -lp) is “expected” to be:

%5.6065.01

05.01

20575.01

tnie

%0.606.01

05.01

2)0025.00575.0(1

lptnie

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:

The 1 year rate, 1 year from now with a 75 basis point liquidity premium (ien-t -lp) is “expected” to be:

%5.6065.01

05.01

20575.01

tnie

%0.505.01

05.01

2)0075.00575.0(1

lptnie

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:

The 1 year rate, 1 year from now with a 100 basis point liquidity premium (ien-t -lp) is “expected” to be:

%5.6065.01

05.01

20575.01

tnie

%5.445.01

05.01

2)0100.00575.0(1

lptnie

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%

Yield Curve: Liquidity Premiums and Forecasts (Oie) i rate

6.756.50 oie (No Liquidity Premium) = 6.5%6.256.0 oie (.25% LP) = 6.0%5.75 o5.55.25 Observed Yield Curve5.0 o oie (.75% LP) = 5.0%4.754.5 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 Curvei 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 Expansioni rate

o Lenders supplying longer

term funds (pushes down rates)

Borrowers demanding shorter o

term funds (pushes up rates)

(st) Term to Maturity (lt)

Market Segmentations Yield Curve Near the End of Recessioni 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